Society for Industrial and Applied Mathematics: SIAM Journal on Applied Mathematics: Table of Contents
Table of Contents for SIAM Journal on Applied Mathematics. List of articles from both the latest and ahead of print issues.
https://epubs.siam.org/loi/smjmap?ai=s3&mi=3drblq&af=R
Society for Industrial and Applied Mathematics: SIAM Journal on Applied Mathematics: Table of Contents
Society for Industrial and Applied Mathematics
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SIAM Journal on Applied Mathematics
SIAM Journal on Applied Mathematics
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https://epubs.siam.org/loi/smjmap?ai=s3&mi=3drblq&af=R
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Computation of Riesz [math]-Capacity [math] of General Sets in [math] Using Stable Random Walks
https://epubs.siam.org/doi/abs/10.1137/23M1568077?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, <a href="https://epubs.siam.org/toc/smjmap/84/2">Volume 84, Issue 2</a>, Page 317-337, April 2024. <br/> Abstract. A method for computing the Riesz [math]-capacity, [math], of a general set [math] is given. The method is based on simulations of isotropic [math]-stable motion paths in [math]-dimensions. The familiar walk-on-spheres method, often utilized for simulating Brownian motion, is modified to a novel walk-in-and-out-of-balls method adapted for modeling the stable path process on the exterior of regions “probed” by this type of generalized random walk. It accounts for the propensity of this class of random walk to jump through boundaries because of the path discontinuity. This method allows for the computationally efficient simulation of hitting locations of stable paths launched from the exterior of probed sets. Reliable methods of computing capacity from these locations are given, along with non-standard confidence intervals. Illustrative calculations are performed for representative types of sets [math], where both [math] and [math] are varied.
SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 317-337, April 2024. <br/> Abstract. A method for computing the Riesz [math]-capacity, [math], of a general set [math] is given. The method is based on simulations of isotropic [math]-stable motion paths in [math]-dimensions. The familiar walk-on-spheres method, often utilized for simulating Brownian motion, is modified to a novel walk-in-and-out-of-balls method adapted for modeling the stable path process on the exterior of regions “probed” by this type of generalized random walk. It accounts for the propensity of this class of random walk to jump through boundaries because of the path discontinuity. This method allows for the computationally efficient simulation of hitting locations of stable paths launched from the exterior of probed sets. Reliable methods of computing capacity from these locations are given, along with non-standard confidence intervals. Illustrative calculations are performed for representative types of sets [math], where both [math] and [math] are varied.
Computation of Riesz [math]-Capacity [math] of General Sets in [math] Using Stable Random Walks
10.1137/23M1568077
SIAM Journal on Applied Mathematics
2024-03-01T08:00:00Z
John P. Nolan
Debra J. Audus
Jack F. Douglas
Computation of Riesz [math]-Capacity [math] of General Sets in [math] Using Stable Random Walks
84
2
317
337
2024-04-30T07:00:00Z
2024-04-30T07:00:00Z
10.1137/23M1568077
https://epubs.siam.org/doi/abs/10.1137/23M1568077?ai=s3&mi=3drblq&af=R
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Spatiotemporal Patterns in a Lengyel–Epstein Model Near a Turing–Hopf Singular Point
https://epubs.siam.org/doi/abs/10.1137/23M1552668?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, <a href="https://epubs.siam.org/toc/smjmap/84/2">Volume 84, Issue 2</a>, Page 338-361, April 2024. <br/> Abstract. In this paper, a study is carried out on the spatiotemporal dynamics of a Lengyel–Epstein model describing the chlorite-iodine-malonic-acid (CIMA) reaction with time delay and the Neumann boundary condition in a two-dimensional region. The existences for Turing, Hopf, Turing–Turing, Turing–Hopf, and Bogdanov–Takens bifurcations are derived by analyzing the dispersion relation between eigenvalues and wave numbers. In particular, to study the dynamics around a Turing–Hopf bifurcation singularity, the amplitude equations near a codimension-two bifurcation point are derived by employing the weakly nonlinear analysis method. Different spatiotemporal patterns for the system in parameter space are classified and various patterns identified, including spatially homogeneous periodic solutions, mixed mode, coexistence mode, bistable phenomenon, square, hexagon, black eye, two-phase oscillating staggered hexagon lattice, and other complex spatiotemporal patterns. The theoretical predictions are verified by numerical simulations showing an excellent agreement with many reported experiment results not only in chemistry but also in physics and biology. Results presented in this article reveal the mechanism of generating the spatiotemporal patterns of the CIMA reaction.
SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 338-361, April 2024. <br/> Abstract. In this paper, a study is carried out on the spatiotemporal dynamics of a Lengyel–Epstein model describing the chlorite-iodine-malonic-acid (CIMA) reaction with time delay and the Neumann boundary condition in a two-dimensional region. The existences for Turing, Hopf, Turing–Turing, Turing–Hopf, and Bogdanov–Takens bifurcations are derived by analyzing the dispersion relation between eigenvalues and wave numbers. In particular, to study the dynamics around a Turing–Hopf bifurcation singularity, the amplitude equations near a codimension-two bifurcation point are derived by employing the weakly nonlinear analysis method. Different spatiotemporal patterns for the system in parameter space are classified and various patterns identified, including spatially homogeneous periodic solutions, mixed mode, coexistence mode, bistable phenomenon, square, hexagon, black eye, two-phase oscillating staggered hexagon lattice, and other complex spatiotemporal patterns. The theoretical predictions are verified by numerical simulations showing an excellent agreement with many reported experiment results not only in chemistry but also in physics and biology. Results presented in this article reveal the mechanism of generating the spatiotemporal patterns of the CIMA reaction.
Spatiotemporal Patterns in a Lengyel–Epstein Model Near a Turing–Hopf Singular Point
10.1137/23M1552668
SIAM Journal on Applied Mathematics
2024-03-01T08:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Shuangrui Zhao
Pei Yu
Hongbin Wang
Spatiotemporal Patterns in a Lengyel–Epstein Model Near a Turing–Hopf Singular Point
84
2
338
361
2024-04-30T07:00:00Z
2024-04-30T07:00:00Z
10.1137/23M1552668
https://epubs.siam.org/doi/abs/10.1137/23M1552668?ai=s3&mi=3drblq&af=R
© 2024 Society for Industrial and Applied Mathematics
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Coarsening of Thin Films with Weak Condensation
https://epubs.siam.org/doi/abs/10.1137/23M1559336?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, <a href="https://epubs.siam.org/toc/smjmap/84/2">Volume 84, Issue 2</a>, Page 362-386, April 2024. <br/> Abstract. A lubrication model can be used to describe the dynamics of a weakly volatile viscous fluid layer on a hydrophobic substrate. Thin layers of the fluid are unstable to perturbations and break up into slowly evolving interacting droplets. A reduced-order dynamical system is derived from the lubrication model based on the nearest-neighbor droplet interactions in the weak condensation limit. Dynamics for periodic arrays of identical drops and pairwise droplet interactions are investigated, providing insights into the coarsening dynamics of a large droplet system. Weak condensation is shown to be a singular perturbation, fundamentally changing the long-time coarsening dynamics for the droplets and the overall mass of the fluid in two additional regimes of long-time dynamics.
SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 362-386, April 2024. <br/> Abstract. A lubrication model can be used to describe the dynamics of a weakly volatile viscous fluid layer on a hydrophobic substrate. Thin layers of the fluid are unstable to perturbations and break up into slowly evolving interacting droplets. A reduced-order dynamical system is derived from the lubrication model based on the nearest-neighbor droplet interactions in the weak condensation limit. Dynamics for periodic arrays of identical drops and pairwise droplet interactions are investigated, providing insights into the coarsening dynamics of a large droplet system. Weak condensation is shown to be a singular perturbation, fundamentally changing the long-time coarsening dynamics for the droplets and the overall mass of the fluid in two additional regimes of long-time dynamics.
Coarsening of Thin Films with Weak Condensation
10.1137/23M1559336
SIAM Journal on Applied Mathematics
2024-03-06T08:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Hangjie Ji
Thomas P. Witelski
Coarsening of Thin Films with Weak Condensation
84
2
362
386
2024-04-30T07:00:00Z
2024-04-30T07:00:00Z
10.1137/23M1559336
https://epubs.siam.org/doi/abs/10.1137/23M1559336?ai=s3&mi=3drblq&af=R
© 2024 Society for Industrial and Applied Mathematics
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An Optimal Control Problem for the Wigner Equation
https://epubs.siam.org/doi/abs/10.1137/22M1515033?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, <a href="https://epubs.siam.org/toc/smjmap/84/2">Volume 84, Issue 2</a>, Page 387-411, April 2024. <br/> Abstract. The Wigner quasi-density function allows a phase-space formulation of statistical quantum mechanics that is of fundamental importance in theoretical investigation and in applications. This work contributes to these tasks with the formulation and analysis of an optimal control problem for the Wigner equation, which describes the time evolution of the quasi-density function. For this purpose, two possible control mechanisms are considered, and, correspondingly, a detailed analysis in weighted Sobolev spaces for the controlled nonhomogeneous Wigner equation is presented. Further theoretical results are reported concerning existence of optimal controls and differentiability of the control-to-state map and of the ensemble cost functional, which allows the derivation of the optimality system that characterizes the optimal controls sought.
SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 387-411, April 2024. <br/> Abstract. The Wigner quasi-density function allows a phase-space formulation of statistical quantum mechanics that is of fundamental importance in theoretical investigation and in applications. This work contributes to these tasks with the formulation and analysis of an optimal control problem for the Wigner equation, which describes the time evolution of the quasi-density function. For this purpose, two possible control mechanisms are considered, and, correspondingly, a detailed analysis in weighted Sobolev spaces for the controlled nonhomogeneous Wigner equation is presented. Further theoretical results are reported concerning existence of optimal controls and differentiability of the control-to-state map and of the ensemble cost functional, which allows the derivation of the optimality system that characterizes the optimal controls sought.
An Optimal Control Problem for the Wigner Equation
10.1137/22M1515033
SIAM Journal on Applied Mathematics
2024-03-08T08:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Omar Morandi
Nella Rotundo
Alfio Borzì
Luigi Barletti
An Optimal Control Problem for the Wigner Equation
84
2
387
411
2024-04-30T07:00:00Z
2024-04-30T07:00:00Z
10.1137/22M1515033
https://epubs.siam.org/doi/abs/10.1137/22M1515033?ai=s3&mi=3drblq&af=R
© 2024 Society for Industrial and Applied Mathematics
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Tangential Cone Condition for the Full Waveform Forward Operator in the Viscoelastic Regime: The Nonlocal Case
https://epubs.siam.org/doi/abs/10.1137/23M1551845?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, <a href="https://epubs.siam.org/toc/smjmap/84/2">Volume 84, Issue 2</a>, Page 412-432, April 2024. <br/> Abstract. We discuss mapping properties of the parameter-to-state map of full waveform inversion and generalize the results of [M. Eller and A. Rieder, Inverse Problems, 37 (2021), 085011] from the acoustic to the viscoelastic wave equation. In particular, we establish injectivity of the Fréchet derivative of the parameter-to-state map for a semidiscrete seismic inverse problem in the viscoelastic regime. Here the finite-dimensional parameter space is restricted to functions having global support in the propagation medium (the nonlocal case) and that are locally linearly independent. As a consequence, we deduce local conditional well-posedness of this nonlinear inverse problem. Furthermore, we show that the tangential cone condition holds, which is an essential prerequisite in the convergence analysis of a variety of inversion algorithms for nonlinear ill-posed problems.
SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 412-432, April 2024. <br/> Abstract. We discuss mapping properties of the parameter-to-state map of full waveform inversion and generalize the results of [M. Eller and A. Rieder, Inverse Problems, 37 (2021), 085011] from the acoustic to the viscoelastic wave equation. In particular, we establish injectivity of the Fréchet derivative of the parameter-to-state map for a semidiscrete seismic inverse problem in the viscoelastic regime. Here the finite-dimensional parameter space is restricted to functions having global support in the propagation medium (the nonlocal case) and that are locally linearly independent. As a consequence, we deduce local conditional well-posedness of this nonlinear inverse problem. Furthermore, we show that the tangential cone condition holds, which is an essential prerequisite in the convergence analysis of a variety of inversion algorithms for nonlinear ill-posed problems.
Tangential Cone Condition for the Full Waveform Forward Operator in the Viscoelastic Regime: The Nonlocal Case
10.1137/23M1551845
SIAM Journal on Applied Mathematics
2024-03-12T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Matthias Eller
Roland Griesmaier
Andreas Rieder
Tangential Cone Condition for the Full Waveform Forward Operator in the Viscoelastic Regime: The Nonlocal Case
84
2
412
432
2024-04-30T07:00:00Z
2024-04-30T07:00:00Z
10.1137/23M1551845
https://epubs.siam.org/doi/abs/10.1137/23M1551845?ai=s3&mi=3drblq&af=R
© 2024 Society for Industrial and Applied Mathematics
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Finite Amplitude Analysis of Poiseuille Flow in Fluid Overlying Porous Domain
https://epubs.siam.org/doi/abs/10.1137/23M1575809?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, <a href="https://epubs.siam.org/toc/smjmap/84/2">Volume 84, Issue 2</a>, Page 433-463, April 2024. <br/> Abstract. A weakly nonlinear stability analysis of isothermal Poiseuille flow in a fluid overlying porous domain is proposed and investigated in this article. The nonlinear interactions are studied by imposing finite amplitude disturbances to the classical model deliberated in Chang, Chen, and Straughan [J. Fluid Mech., 564 (2006), pp. 287–303]. The order parameter theory is used to ascertain the cubic Landau equation, and the regimes of instability for the bifurcations are determined henceforth. The well-established controlling parameters viz. the depth ratio [math] depth of fluid domain/depth of porous domain), the Beavers–Joseph constant [math], and the Darcy number [math] are inquired upon for the bifurcation phenomena. The imposed finite amplitude disturbances are viewed for bifurcations along the neutral stability curves and away from the critical point as a function of the wave number [math] and the Reynolds number [math]. The even-fluid-layer (porous) mode along the neutral stability curves correlates to the subcritical (supercritical) bifurcation phenomena. On perceiving the bifurcations as a function of [math] and [math] by moving away from the bifurcation/critical point, subcritical bifurcation is observed for increasing [math] and decreasing [math]. In contrast to only fluid flow through a channel, it is found that the inclusion of porous domain aids in the early appearance of subcritical bifurcation when [math]. A considerable difference between the computed skin friction coefficient for the base and the distorted state is observed for small (large) values of [math]. In addition, an intrinsic relation among the mode of instability, bifurcation phenomena, and secondary flow pattern is also observed.
SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 433-463, April 2024. <br/> Abstract. A weakly nonlinear stability analysis of isothermal Poiseuille flow in a fluid overlying porous domain is proposed and investigated in this article. The nonlinear interactions are studied by imposing finite amplitude disturbances to the classical model deliberated in Chang, Chen, and Straughan [J. Fluid Mech., 564 (2006), pp. 287–303]. The order parameter theory is used to ascertain the cubic Landau equation, and the regimes of instability for the bifurcations are determined henceforth. The well-established controlling parameters viz. the depth ratio [math] depth of fluid domain/depth of porous domain), the Beavers–Joseph constant [math], and the Darcy number [math] are inquired upon for the bifurcation phenomena. The imposed finite amplitude disturbances are viewed for bifurcations along the neutral stability curves and away from the critical point as a function of the wave number [math] and the Reynolds number [math]. The even-fluid-layer (porous) mode along the neutral stability curves correlates to the subcritical (supercritical) bifurcation phenomena. On perceiving the bifurcations as a function of [math] and [math] by moving away from the bifurcation/critical point, subcritical bifurcation is observed for increasing [math] and decreasing [math]. In contrast to only fluid flow through a channel, it is found that the inclusion of porous domain aids in the early appearance of subcritical bifurcation when [math]. A considerable difference between the computed skin friction coefficient for the base and the distorted state is observed for small (large) values of [math]. In addition, an intrinsic relation among the mode of instability, bifurcation phenomena, and secondary flow pattern is also observed.
Finite Amplitude Analysis of Poiseuille Flow in Fluid Overlying Porous Domain
10.1137/23M1575809
SIAM Journal on Applied Mathematics
2024-03-12T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
A. Aleria
A. Khan
P. Bera
Finite Amplitude Analysis of Poiseuille Flow in Fluid Overlying Porous Domain
84
2
433
463
2024-04-30T07:00:00Z
2024-04-30T07:00:00Z
10.1137/23M1575809
https://epubs.siam.org/doi/abs/10.1137/23M1575809?ai=s3&mi=3drblq&af=R
© 2024 Society for Industrial and Applied Mathematics
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A Generalization of the Wiener–Hopf Method for an Equation in Two Variables with Three Unknown Functions
https://epubs.siam.org/doi/abs/10.1137/23M1562445?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, <a href="https://epubs.siam.org/toc/smjmap/84/2">Volume 84, Issue 2</a>, Page 464-476, April 2024. <br/> Abstract. This manuscript presents an analytic solution to a generalization of the Wiener–Hopf equation in two variables and with three unknown functions. This equation arises in many applications, for example, when solving the discrete Helmholtz equation associated with scattering on a domain with perpendicular boundary. The traditional Wiener–Hopf method is suitable for problems involving boundary data on co-linear semi-infinite intervals, not for boundaries at an angle. This significant extension will enable the analytical solution to a new class of problems with more boundary configurations. Progress is made by defining an underlining manifold that links the two variables. This allows one to meromorphically continue the unknown functions on this manifold and formulate a jump condition. As a result the problem is fully solvable in terms of Cauchy-type integrals, which is surprising since this is not always possible for this type of functional equation.
SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 464-476, April 2024. <br/> Abstract. This manuscript presents an analytic solution to a generalization of the Wiener–Hopf equation in two variables and with three unknown functions. This equation arises in many applications, for example, when solving the discrete Helmholtz equation associated with scattering on a domain with perpendicular boundary. The traditional Wiener–Hopf method is suitable for problems involving boundary data on co-linear semi-infinite intervals, not for boundaries at an angle. This significant extension will enable the analytical solution to a new class of problems with more boundary configurations. Progress is made by defining an underlining manifold that links the two variables. This allows one to meromorphically continue the unknown functions on this manifold and formulate a jump condition. As a result the problem is fully solvable in terms of Cauchy-type integrals, which is surprising since this is not always possible for this type of functional equation.
A Generalization of the Wiener–Hopf Method for an Equation in Two Variables with Three Unknown Functions
10.1137/23M1562445
SIAM Journal on Applied Mathematics
2024-03-19T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Anastasia V. Kisil
A Generalization of the Wiener–Hopf Method for an Equation in Two Variables with Three Unknown Functions
84
2
464
476
2024-04-30T07:00:00Z
2024-04-30T07:00:00Z
10.1137/23M1562445
https://epubs.siam.org/doi/abs/10.1137/23M1562445?ai=s3&mi=3drblq&af=R
© 2024 Society for Industrial and Applied Mathematics
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Steady Wind-Generated Gravity-Capillary Waves on Viscous Liquid Film Flows
https://epubs.siam.org/doi/abs/10.1137/23M1586318?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, <a href="https://epubs.siam.org/toc/smjmap/84/2">Volume 84, Issue 2</a>, Page 477-496, April 2024. <br/> Abstract. Steady gravity-capillary periodic waves on the surface of a thin viscous liquid film supported by an air stream on an inclined wall are investigated. Based on lubrication approximation and thin air-foil theory, this problem is reduced to an integro-differential equation. The small-amplitude analysis is carried out to obtain two analytical solutions up to the second order. Numerical computation shows there exist two distinct primary bifurcation branches starting from infinitesimal waves, which approach solitary wave configuration in the long-wave limit when the values of physical parameters are above certain thresholds. New families of solutions manifest themselves either as secondary bifurcation occurring on primary branches or as isolated solution branches. The limiting configurations of the primary solution branches with the increase of two parameters are studied in two different cases, where one and two limiting configurations are obtained, respectively. For the latter case, the approximation of the configurations is given.
SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 477-496, April 2024. <br/> Abstract. Steady gravity-capillary periodic waves on the surface of a thin viscous liquid film supported by an air stream on an inclined wall are investigated. Based on lubrication approximation and thin air-foil theory, this problem is reduced to an integro-differential equation. The small-amplitude analysis is carried out to obtain two analytical solutions up to the second order. Numerical computation shows there exist two distinct primary bifurcation branches starting from infinitesimal waves, which approach solitary wave configuration in the long-wave limit when the values of physical parameters are above certain thresholds. New families of solutions manifest themselves either as secondary bifurcation occurring on primary branches or as isolated solution branches. The limiting configurations of the primary solution branches with the increase of two parameters are studied in two different cases, where one and two limiting configurations are obtained, respectively. For the latter case, the approximation of the configurations is given.
Steady Wind-Generated Gravity-Capillary Waves on Viscous Liquid Film Flows
10.1137/23M1586318
SIAM Journal on Applied Mathematics
2024-03-21T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Y. Meng
D. T. Papageorgiou
J.-M. Vanden-Broeck
Steady Wind-Generated Gravity-Capillary Waves on Viscous Liquid Film Flows
84
2
477
496
2024-04-30T07:00:00Z
2024-04-30T07:00:00Z
10.1137/23M1586318
https://epubs.siam.org/doi/abs/10.1137/23M1586318?ai=s3&mi=3drblq&af=R
© 2024 Society for Industrial and Applied Mathematics
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Conservation Laws with Nonlocal Velocity: The Singular Limit Problem
https://epubs.siam.org/doi/abs/10.1137/22M1530471?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, <a href="https://epubs.siam.org/toc/smjmap/84/2">Volume 84, Issue 2</a>, Page 497-522, April 2024. <br/> Abstract. We consider conservation laws with nonlocal velocity and show, for nonlocal weights of exponential type, that the unique solutions converge in a weak or strong sense (dependent on the regularity of the velocity) to the entropy solution of the local conservation law when the nonlocal weight approaches a Dirac distribution. To this end, we first establish a uniform total variation bound on the nonlocal velocity, which can be used to pass to the limit in the weak solution. For the required entropy admissibility, we use a tailored entropy-flux pair and take advantage of a well-known result that a single strictly convex entropy-flux pair is sufficient for uniqueness, given some additional constraints on the velocity. For general weights, we show that the monotonicity of the initial datum is preserved over time, which enables us to prove convergence to the local entropy solution for rather general kernels if the initial datum is monotone. This case covers the archetypes of local conservation laws: shock waves and rarefactions. These results suggest that a “nonlocal in the velocity” approximation might be better suited to approximating local conservation laws than a nonlocal in the solution approximation, in which such monotonicity only holds for specific velocities.
SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 497-522, April 2024. <br/> Abstract. We consider conservation laws with nonlocal velocity and show, for nonlocal weights of exponential type, that the unique solutions converge in a weak or strong sense (dependent on the regularity of the velocity) to the entropy solution of the local conservation law when the nonlocal weight approaches a Dirac distribution. To this end, we first establish a uniform total variation bound on the nonlocal velocity, which can be used to pass to the limit in the weak solution. For the required entropy admissibility, we use a tailored entropy-flux pair and take advantage of a well-known result that a single strictly convex entropy-flux pair is sufficient for uniqueness, given some additional constraints on the velocity. For general weights, we show that the monotonicity of the initial datum is preserved over time, which enables us to prove convergence to the local entropy solution for rather general kernels if the initial datum is monotone. This case covers the archetypes of local conservation laws: shock waves and rarefactions. These results suggest that a “nonlocal in the velocity” approximation might be better suited to approximating local conservation laws than a nonlocal in the solution approximation, in which such monotonicity only holds for specific velocities.
Conservation Laws with Nonlocal Velocity: The Singular Limit Problem
10.1137/22M1530471
SIAM Journal on Applied Mathematics
2024-03-21T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Jan Friedrich
Simone Göttlich
Alexander Keimer
Lukas Pflug
Conservation Laws with Nonlocal Velocity: The Singular Limit Problem
84
2
497
522
2024-04-30T07:00:00Z
2024-04-30T07:00:00Z
10.1137/22M1530471
https://epubs.siam.org/doi/abs/10.1137/22M1530471?ai=s3&mi=3drblq&af=R
© 2024 Society for Industrial and Applied Mathematics
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Singularities of Capillary-Gravity Waves on Dielectric Fluid Under Normal Electric Fields
https://epubs.siam.org/doi/abs/10.1137/23M1575743?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, <a href="https://epubs.siam.org/toc/smjmap/84/2">Volume 84, Issue 2</a>, Page 523-542, April 2024. <br/> Abstract. As summarized by Papageorgiou [Annu. Rev. Fluid Mech., 51 (2019), pp. 155–187], a strong normal electric field can cause instability of the interface in a hydrodynamic system. In the present work, singularities arising in electrocapillary-gravity waves on a dielectric fluid of finite depth due to an electric field imposed in the direction perpendicular to the undisturbed free surface are investigated. In shallow water, for a small-amplitude periodic disturbance in the linearly unstable regime, the outcome of the system evolution is that the gas-liquid interface touches the solid bottom boundary, causing a rupture. A quasi-linear hyperbolic model is derived for the long-wave limit and used to study the formation of the touch-down singularity. The theoretical predictions are compared with the fully nonlinear computations by a time-dependent conformal mapping for the electrified Euler equations, showing good agreement. On the other hand, a nonlinear dispersive model system is derived for the deep-water scenario, which predicts the blowup singularity (i.e., the wave amplitude tends to infinity in a finite time). However, when the fluid thickness is significantly large, one can numerically show the self-intersection nonphysical wave structure or 2/3 power cusp singularity in the full Euler equations.
SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 523-542, April 2024. <br/> Abstract. As summarized by Papageorgiou [Annu. Rev. Fluid Mech., 51 (2019), pp. 155–187], a strong normal electric field can cause instability of the interface in a hydrodynamic system. In the present work, singularities arising in electrocapillary-gravity waves on a dielectric fluid of finite depth due to an electric field imposed in the direction perpendicular to the undisturbed free surface are investigated. In shallow water, for a small-amplitude periodic disturbance in the linearly unstable regime, the outcome of the system evolution is that the gas-liquid interface touches the solid bottom boundary, causing a rupture. A quasi-linear hyperbolic model is derived for the long-wave limit and used to study the formation of the touch-down singularity. The theoretical predictions are compared with the fully nonlinear computations by a time-dependent conformal mapping for the electrified Euler equations, showing good agreement. On the other hand, a nonlinear dispersive model system is derived for the deep-water scenario, which predicts the blowup singularity (i.e., the wave amplitude tends to infinity in a finite time). However, when the fluid thickness is significantly large, one can numerically show the self-intersection nonphysical wave structure or 2/3 power cusp singularity in the full Euler equations.
Singularities of Capillary-Gravity Waves on Dielectric Fluid Under Normal Electric Fields
10.1137/23M1575743
SIAM Journal on Applied Mathematics
2024-03-26T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Tao Gao
Zhan Wang
Demetrios Papageorgiou
Singularities of Capillary-Gravity Waves on Dielectric Fluid Under Normal Electric Fields
84
2
523
542
2024-04-30T07:00:00Z
2024-04-30T07:00:00Z
10.1137/23M1575743
https://epubs.siam.org/doi/abs/10.1137/23M1575743?ai=s3&mi=3drblq&af=R
© 2024 Society for Industrial and Applied Mathematics
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Two-Dimensional Sloshing: Domains with Interior “High Spots”
https://epubs.siam.org/doi/abs/10.1137/22M1541332?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, <a href="https://epubs.siam.org/toc/smjmap/84/2">Volume 84, Issue 2</a>, Page 543-555, April 2024. <br/> Abstract. Considering the two-dimensional sloshing problem, our main focus is to construct domains with interior high spots; that is, points, where the free surface elevation for the fundamental eigenmode attains its critical values. The so-called semi-inverse procedure is applied for this purpose. The existence of high spots is proved rigorously for some domains. Many of the constructed domains have multiple interior high spots and all of them are bulbous at least on one side.
SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 543-555, April 2024. <br/> Abstract. Considering the two-dimensional sloshing problem, our main focus is to construct domains with interior high spots; that is, points, where the free surface elevation for the fundamental eigenmode attains its critical values. The so-called semi-inverse procedure is applied for this purpose. The existence of high spots is proved rigorously for some domains. Many of the constructed domains have multiple interior high spots and all of them are bulbous at least on one side.
Two-Dimensional Sloshing: Domains with Interior “High Spots”
10.1137/22M1541332
SIAM Journal on Applied Mathematics
2024-03-26T07:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Nikolay Kuznetsov
Oleg Motygin
Two-Dimensional Sloshing: Domains with Interior “High Spots”
84
2
543
555
2024-04-30T07:00:00Z
2024-04-30T07:00:00Z
10.1137/22M1541332
https://epubs.siam.org/doi/abs/10.1137/22M1541332?ai=s3&mi=3drblq&af=R
© 2024 Society for Industrial and Applied Mathematics
-
One-Dimensional Short-Range Nearest-Neighbor Interaction and Its Nonlinear Diffusion Limit
https://epubs.siam.org/doi/abs/10.1137/23M155520X?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, <a href="https://epubs.siam.org/toc/smjmap/84/1">Volume 84, Issue 1</a>, Page 1-18, February 2024. <br/> Abstract. Repulsion between individuals within a finite radius is encountered in numerous applications, including cell exclusion, i.e., avoidance of overlapping cells, bird flocks, or microscopic pedestrian models. We define such individual-based particle dynamics in one spatial dimension with minimal assumptions of the repulsion force [math] as well as their external velocity [math] and prove their characteristic properties. Moreover, we are able to perform a rigorous limit from the microscopic to the macroscopic scale, where we could recover the finite interaction radius as a density threshold. Specific choices for the repulsion force [math] lead to well-known nonlinear diffusion equations on the macroscopic scale, as, e.g., the porous medium equation. At both scaling levels, numerical simulations are presented and compared to underline the analytical results.
SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 1-18, February 2024. <br/> Abstract. Repulsion between individuals within a finite radius is encountered in numerous applications, including cell exclusion, i.e., avoidance of overlapping cells, bird flocks, or microscopic pedestrian models. We define such individual-based particle dynamics in one spatial dimension with minimal assumptions of the repulsion force [math] as well as their external velocity [math] and prove their characteristic properties. Moreover, we are able to perform a rigorous limit from the microscopic to the macroscopic scale, where we could recover the finite interaction radius as a density threshold. Specific choices for the repulsion force [math] lead to well-known nonlinear diffusion equations on the macroscopic scale, as, e.g., the porous medium equation. At both scaling levels, numerical simulations are presented and compared to underline the analytical results.
One-Dimensional Short-Range Nearest-Neighbor Interaction and Its Nonlinear Diffusion Limit
10.1137/23M155520X
SIAM Journal on Applied Mathematics
2024-01-12T08:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Michael Fischer
Laura Kanzler
Christian Schmeiser
One-Dimensional Short-Range Nearest-Neighbor Interaction and Its Nonlinear Diffusion Limit
84
1
1
18
2024-02-29T08:00:00Z
2024-02-29T08:00:00Z
10.1137/23M155520X
https://epubs.siam.org/doi/abs/10.1137/23M155520X?ai=s3&mi=3drblq&af=R
© 2024 Society for Industrial and Applied Mathematics
-
Combined Field-Only Boundary Integral Equations for PEC Electromagnetic Scattering Problem in Spherical Geometries
https://epubs.siam.org/doi/abs/10.1137/23M1561865?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, <a href="https://epubs.siam.org/toc/smjmap/84/1">Volume 84, Issue 1</a>, Page 19-38, February 2024. <br/> Abstract. We analyze the well-posedness of certain field-only boundary integral equations (BIEs) for frequency domain electromagnetic scattering from perfectly conducting spheres. Starting from the observations that (1) the three components of the scattered electric field [math] and (2) scalar quantity [math] are radiative solutions of the Helmholtz equation, we see that novel boundary integral equation formulations of electromagnetic scattering from perfectly conducting obstacles can be derived using Green’s identities applied to the aforementioned quantities and the boundary conditions on the surface of the scatterer. The unknowns of these formulations are the normal derivatives of the three components of the scattered electric field and the normal component of the scattered electric field on the surface of the scatterer, and thus these formulations are referred to as field-only BIEs. In this paper we use the combined field methodology of Burton and Miller within the field-only BIE approach, and we derive new boundary integral formulations that feature only Helmholtz boundary integral operators, which we subsequently show to be well posed for all positive frequencies in the case of spherical scatterers. Relying on the spectral properties of Helmholtz boundary integral operators in spherical geometries, we show that the combined field-only boundary integral operators are diagonalizable in the case of spherical geometries and their eigenvalues are nonzero for all frequencies. Furthermore, we show that for spherical geometries one of the field-only integral formulations considered in this paper exhibits eigenvalues clustering at one—a property similar to second-kind integral equations.
SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 19-38, February 2024. <br/> Abstract. We analyze the well-posedness of certain field-only boundary integral equations (BIEs) for frequency domain electromagnetic scattering from perfectly conducting spheres. Starting from the observations that (1) the three components of the scattered electric field [math] and (2) scalar quantity [math] are radiative solutions of the Helmholtz equation, we see that novel boundary integral equation formulations of electromagnetic scattering from perfectly conducting obstacles can be derived using Green’s identities applied to the aforementioned quantities and the boundary conditions on the surface of the scatterer. The unknowns of these formulations are the normal derivatives of the three components of the scattered electric field and the normal component of the scattered electric field on the surface of the scatterer, and thus these formulations are referred to as field-only BIEs. In this paper we use the combined field methodology of Burton and Miller within the field-only BIE approach, and we derive new boundary integral formulations that feature only Helmholtz boundary integral operators, which we subsequently show to be well posed for all positive frequencies in the case of spherical scatterers. Relying on the spectral properties of Helmholtz boundary integral operators in spherical geometries, we show that the combined field-only boundary integral operators are diagonalizable in the case of spherical geometries and their eigenvalues are nonzero for all frequencies. Furthermore, we show that for spherical geometries one of the field-only integral formulations considered in this paper exhibits eigenvalues clustering at one—a property similar to second-kind integral equations.
Combined Field-Only Boundary Integral Equations for PEC Electromagnetic Scattering Problem in Spherical Geometries
10.1137/23M1561865
SIAM Journal on Applied Mathematics
2024-01-12T08:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Luiz Maltez-Faria
Carlos Pérez-Arancibia
Catalin Turc
Combined Field-Only Boundary Integral Equations for PEC Electromagnetic Scattering Problem in Spherical Geometries
84
1
19
38
2024-02-29T08:00:00Z
2024-02-29T08:00:00Z
10.1137/23M1561865
https://epubs.siam.org/doi/abs/10.1137/23M1561865?ai=s3&mi=3drblq&af=R
© 2024 Society for Industrial and Applied Mathematics
-
Multiplicity of Neutrally Stable Periodic Orbits with Coexistence in the Chemostat Subject to Periodic Removal Rate
https://epubs.siam.org/doi/abs/10.1137/23M1552450?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, <a href="https://epubs.siam.org/toc/smjmap/84/1">Volume 84, Issue 1</a>, Page 39-59, February 2024. <br/> Abstract. We identify a taxonomic property on the growth functions in the multispecies chemostat model which ensures the coexistence of a subset of species under periodic removal rate. We show that proportions of some powers of the species densities are periodic functions, leading to an infinity of distinct neutrally stable periodic orbits depending on the initial condition. This condition on the species for neutral stability possesses the feature to be independent of the shape of the periodic signal for a given mean value. We also give conditions allowing the coexistence of two distinct subsets of species. Although these conditions are nongeneric, we show in simulations that when these conditions are only approximately satisfied, the behavior of the solutions is close to that of the nongeneric case over a long time interval, justifying the interest of our study.
SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 39-59, February 2024. <br/> Abstract. We identify a taxonomic property on the growth functions in the multispecies chemostat model which ensures the coexistence of a subset of species under periodic removal rate. We show that proportions of some powers of the species densities are periodic functions, leading to an infinity of distinct neutrally stable periodic orbits depending on the initial condition. This condition on the species for neutral stability possesses the feature to be independent of the shape of the periodic signal for a given mean value. We also give conditions allowing the coexistence of two distinct subsets of species. Although these conditions are nongeneric, we show in simulations that when these conditions are only approximately satisfied, the behavior of the solutions is close to that of the nongeneric case over a long time interval, justifying the interest of our study.
Multiplicity of Neutrally Stable Periodic Orbits with Coexistence in the Chemostat Subject to Periodic Removal Rate
10.1137/23M1552450
SIAM Journal on Applied Mathematics
2024-01-16T08:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Thomas Guilmeau
Alain Rapaport
Multiplicity of Neutrally Stable Periodic Orbits with Coexistence in the Chemostat Subject to Periodic Removal Rate
84
1
39
59
2024-02-29T08:00:00Z
2024-02-29T08:00:00Z
10.1137/23M1552450
https://epubs.siam.org/doi/abs/10.1137/23M1552450?ai=s3&mi=3drblq&af=R
© 2024 Society for Industrial and Applied Mathematics
-
Nonlinear Monotone Energy Stability of Plane Shear Flows: Joseph or Orr Critical Thresholds?
https://epubs.siam.org/doi/abs/10.1137/22M1535826?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, <a href="https://epubs.siam.org/toc/smjmap/84/1">Volume 84, Issue 1</a>, Page 60-74, February 2024. <br/> Abstract. Critical Reynolds numbers for the monotone exponential energy stability of Couette and Poiseuille plane flows were obtained by Orr in 1907 [Proc. Roy. Irish Acad. A, 27 (1907), pp. 9–68, 69–138] in a famous paper, and by Joseph in 1966 [J. Fluid Mech., 33 (1966), pp. 617–621], Joseph and Carmi in 1969 [Quart. Appl. Math., 26 (1969), pp. 575–579], and Busse in 1972 [Arch. Ration. Mech. Anal., 47 (1972), pp. 28–35]. All these authors obtained their results applying variational methods to compute the maximum of a functional ratio derived from the Reynolds–Orr energy identity. Orr and Joseph obtained different results; for instance, in the Couette case Orr computed the critical Reynolds value of 44.3 (on spanwise perturbations) and Joseph 20.65 (on streamwise perturbations). Recently in [P. Falsaperla, G. Mulone, and C. Perrone, Eur. J. Mech. B Fluids, 93 (2022), pp. 93–100], the authors conjectured that the search of the maximum should be restricted to a subspace of the space of kinematically admissible perturbations. With this conjecture, the critical nonlinear energy Reynolds number was found among spanwise perturbations (a Squire theorem for nonlinear systems). With a direct proof and an appropriate and original decomposition of the dissipation terms in the Reynolds–Orr identity we show the validity of this conjecture in the space of three-dimensional perturbations.
SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 60-74, February 2024. <br/> Abstract. Critical Reynolds numbers for the monotone exponential energy stability of Couette and Poiseuille plane flows were obtained by Orr in 1907 [Proc. Roy. Irish Acad. A, 27 (1907), pp. 9–68, 69–138] in a famous paper, and by Joseph in 1966 [J. Fluid Mech., 33 (1966), pp. 617–621], Joseph and Carmi in 1969 [Quart. Appl. Math., 26 (1969), pp. 575–579], and Busse in 1972 [Arch. Ration. Mech. Anal., 47 (1972), pp. 28–35]. All these authors obtained their results applying variational methods to compute the maximum of a functional ratio derived from the Reynolds–Orr energy identity. Orr and Joseph obtained different results; for instance, in the Couette case Orr computed the critical Reynolds value of 44.3 (on spanwise perturbations) and Joseph 20.65 (on streamwise perturbations). Recently in [P. Falsaperla, G. Mulone, and C. Perrone, Eur. J. Mech. B Fluids, 93 (2022), pp. 93–100], the authors conjectured that the search of the maximum should be restricted to a subspace of the space of kinematically admissible perturbations. With this conjecture, the critical nonlinear energy Reynolds number was found among spanwise perturbations (a Squire theorem for nonlinear systems). With a direct proof and an appropriate and original decomposition of the dissipation terms in the Reynolds–Orr identity we show the validity of this conjecture in the space of three-dimensional perturbations.
Nonlinear Monotone Energy Stability of Plane Shear Flows: Joseph or Orr Critical Thresholds?
10.1137/22M1535826
SIAM Journal on Applied Mathematics
2024-01-18T08:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Giuseppe Mulone
Nonlinear Monotone Energy Stability of Plane Shear Flows: Joseph or Orr Critical Thresholds?
84
1
60
74
2024-02-29T08:00:00Z
2024-02-29T08:00:00Z
10.1137/22M1535826
https://epubs.siam.org/doi/abs/10.1137/22M1535826?ai=s3&mi=3drblq&af=R
© 2024 Society for Industrial and Applied Mathematics
-
Layer Stripping Approach to Reconstruct Shape Variations in Waveguides Using Locally Resonant Frequencies
https://epubs.siam.org/doi/abs/10.1137/23M1546336?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, <a href="https://epubs.siam.org/toc/smjmap/84/1">Volume 84, Issue 1</a>, Page 75-96, February 2024. <br/> Abstract. This article presents a new method to reconstruct slowly varying width defects in two-dimensional waveguides using one-side section measurements at locally resonant frequencies. At these frequencies, locally resonant modes propagate in the waveguide up to a “cut-off” position. In this particular point, the local width of the waveguide can be recovered. Given multifrequency data measured on a section of the waveguide, we perform an efficient layer stripping approach to recover, section by section, the shape variations. It provides an L infinity-stable method to reconstruct the width of a slowly monotonous varying waveguide. We validate this method on numerical data and discuss its limits.
SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 75-96, February 2024. <br/> Abstract. This article presents a new method to reconstruct slowly varying width defects in two-dimensional waveguides using one-side section measurements at locally resonant frequencies. At these frequencies, locally resonant modes propagate in the waveguide up to a “cut-off” position. In this particular point, the local width of the waveguide can be recovered. Given multifrequency data measured on a section of the waveguide, we perform an efficient layer stripping approach to recover, section by section, the shape variations. It provides an L infinity-stable method to reconstruct the width of a slowly monotonous varying waveguide. We validate this method on numerical data and discuss its limits.
Layer Stripping Approach to Reconstruct Shape Variations in Waveguides Using Locally Resonant Frequencies
10.1137/23M1546336
SIAM Journal on Applied Mathematics
2024-01-22T08:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Angéle Niclas
Laurent Seppecher
Layer Stripping Approach to Reconstruct Shape Variations in Waveguides Using Locally Resonant Frequencies
84
1
75
96
2024-02-29T08:00:00Z
2024-02-29T08:00:00Z
10.1137/23M1546336
https://epubs.siam.org/doi/abs/10.1137/23M1546336?ai=s3&mi=3drblq&af=R
© 2024 Society for Industrial and Applied Mathematics
-
A Domain Decomposition Method for Solution of a PDE-Constrained Generalized Nash Equilibrium Model of Biofilm Community Metabolism
https://epubs.siam.org/doi/abs/10.1137/22M1511023?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, <a href="https://epubs.siam.org/toc/smjmap/84/1">Volume 84, Issue 1</a>, Page 97-113, February 2024. <br/> Abstract. Microbes are able to deploy different strategies in response to, and depending upon, local environmental conditions. In the setting of a microbial community, this property induces a Nash equilibrium problem because access to environmental resources is bounded. If microbes are also distributed in space, then those resources are subject to transport limitations (encoded in a PDE) and so microbial strategies at one location influence resources and, hence, microbial strategies, at another. Here we formulate the resulting PDE-coupled generalized Nash equilibrium problem for a multispecies biofilm community, and propose a domain-decomposition-based method for its solution. An example consisting of a model with two microbial species biofilm with 33 externally transported chemical concentrations is presented.
SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 97-113, February 2024. <br/> Abstract. Microbes are able to deploy different strategies in response to, and depending upon, local environmental conditions. In the setting of a microbial community, this property induces a Nash equilibrium problem because access to environmental resources is bounded. If microbes are also distributed in space, then those resources are subject to transport limitations (encoded in a PDE) and so microbial strategies at one location influence resources and, hence, microbial strategies, at another. Here we formulate the resulting PDE-coupled generalized Nash equilibrium problem for a multispecies biofilm community, and propose a domain-decomposition-based method for its solution. An example consisting of a model with two microbial species biofilm with 33 externally transported chemical concentrations is presented.
A Domain Decomposition Method for Solution of a PDE-Constrained Generalized Nash Equilibrium Model of Biofilm Community Metabolism
10.1137/22M1511023
SIAM Journal on Applied Mathematics
2024-01-24T08:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Isaac Klapper
Daniel B. Szyld
Xinli Yu
Karsten Zengler
Tianyu Zhang
Cristal Zúñiga
A Domain Decomposition Method for Solution of a PDE-Constrained Generalized Nash Equilibrium Model of Biofilm Community Metabolism
84
1
97
113
2024-02-29T08:00:00Z
2024-02-29T08:00:00Z
10.1137/22M1511023
https://epubs.siam.org/doi/abs/10.1137/22M1511023?ai=s3&mi=3drblq&af=R
© 2024 Society for Industrial and Applied Mathematics
-
Tipping Points in Seed Dispersal Mutualism Driven by Environmental Stochasticity
https://epubs.siam.org/doi/abs/10.1137/22M1531579?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, <a href="https://epubs.siam.org/toc/smjmap/84/1">Volume 84, Issue 1</a>, Page 114-138, February 2024. <br/> Abstract. The mechanism of seed dispersal mutualism is fundamental to understanding vegetation diversity and its conservation. In this study, we propose a stochastic model that extends the classical framework of seed dispersal mutualism to explore the effects of environmental stochasticity on mutualistic interactions between seed dispersers and plants. We first provide a comprehensive picture of the long-term dynamics of seed dispersal mutualism in deterministic and stochastic environments. We then analyze the relationship between stochasticity and the probability and time that seed dispersal mutualism tips between stable states. Additionally, we evaluate the extinction risk of seed dispersal mutualism for different population values and accordingly assign extinction warning levels to these values. The analysis reveals that the impact of environmental stochasticity on tipping phenomena is scenario-dependent but follows some interpretable trends. The probability (resp., time) of tipping towards the extinction state typically increases (resp., decreases) monotonically with noise intensity, while the probability of tipping towards the coexistence state typically peaks at intermediate noise intensity. Noise in animal populations contributes to tipping toward the coexistence state, whereas noise in plant populations slows down the tipping toward the coexistence state. Noise-induced changes in warning levels of initial population values are most pronounced near the boundaries of the basin of attraction, but sufficiently loud noise (especially for plant populations) may alter the risk far from these boundaries. These findings provide a theoretical explanation for the effect of environmental stochasticity on multistability transitions in seed dispersal mutualism and can be utilized to study the interplay between other population systems and environmental stochasticity.
SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 114-138, February 2024. <br/> Abstract. The mechanism of seed dispersal mutualism is fundamental to understanding vegetation diversity and its conservation. In this study, we propose a stochastic model that extends the classical framework of seed dispersal mutualism to explore the effects of environmental stochasticity on mutualistic interactions between seed dispersers and plants. We first provide a comprehensive picture of the long-term dynamics of seed dispersal mutualism in deterministic and stochastic environments. We then analyze the relationship between stochasticity and the probability and time that seed dispersal mutualism tips between stable states. Additionally, we evaluate the extinction risk of seed dispersal mutualism for different population values and accordingly assign extinction warning levels to these values. The analysis reveals that the impact of environmental stochasticity on tipping phenomena is scenario-dependent but follows some interpretable trends. The probability (resp., time) of tipping towards the extinction state typically increases (resp., decreases) monotonically with noise intensity, while the probability of tipping towards the coexistence state typically peaks at intermediate noise intensity. Noise in animal populations contributes to tipping toward the coexistence state, whereas noise in plant populations slows down the tipping toward the coexistence state. Noise-induced changes in warning levels of initial population values are most pronounced near the boundaries of the basin of attraction, but sufficiently loud noise (especially for plant populations) may alter the risk far from these boundaries. These findings provide a theoretical explanation for the effect of environmental stochasticity on multistability transitions in seed dispersal mutualism and can be utilized to study the interplay between other population systems and environmental stochasticity.
Tipping Points in Seed Dispersal Mutualism Driven by Environmental Stochasticity
10.1137/22M1531579
SIAM Journal on Applied Mathematics
2024-01-30T08:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Tao Feng
Zhipeng Qiu
Hao Wang
Tipping Points in Seed Dispersal Mutualism Driven by Environmental Stochasticity
84
1
114
138
2024-02-29T08:00:00Z
2024-02-29T08:00:00Z
10.1137/22M1531579
https://epubs.siam.org/doi/abs/10.1137/22M1531579?ai=s3&mi=3drblq&af=R
© 2024 Society for Industrial and Applied Mathematics
-
A Hierarchy of Kinetic Discrete-Velocity Models for Traffic Flow Derived from a Nonlocal Prigogine–Herman Model
https://epubs.siam.org/doi/abs/10.1137/23M1583065?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, <a href="https://epubs.siam.org/toc/smjmap/84/1">Volume 84, Issue 1</a>, Page 139-164, February 2024. <br/> Abstract. Starting from a nonlocal version of the Prigogine–Herman traffic model, we derive a natural hierarchy of kinetic discrete-velocity models for traffic flow consisting of systems of quasi-linear hyperbolic equations with relaxation terms. The hyperbolic main part of these models turns out to have several favorable features. In particular, we determine Riemann invariants and prove richness and total linear degeneracy of the hyperbolic systems. Moreover, a physically reasonable invariant domain is obtained for all equations of the hierarchy. Additionally, we investigate the full relaxation system with respect to stability and persistence of periodic (stop-and-go-type) solutions and derive a condition for the appearance of such solutions. Finally, numerical results for various situations are presented, illustrating the analytical findings.
SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 139-164, February 2024. <br/> Abstract. Starting from a nonlocal version of the Prigogine–Herman traffic model, we derive a natural hierarchy of kinetic discrete-velocity models for traffic flow consisting of systems of quasi-linear hyperbolic equations with relaxation terms. The hyperbolic main part of these models turns out to have several favorable features. In particular, we determine Riemann invariants and prove richness and total linear degeneracy of the hyperbolic systems. Moreover, a physically reasonable invariant domain is obtained for all equations of the hierarchy. Additionally, we investigate the full relaxation system with respect to stability and persistence of periodic (stop-and-go-type) solutions and derive a condition for the appearance of such solutions. Finally, numerical results for various situations are presented, illustrating the analytical findings.
A Hierarchy of Kinetic Discrete-Velocity Models for Traffic Flow Derived from a Nonlocal Prigogine–Herman Model
10.1137/23M1583065
SIAM Journal on Applied Mathematics
2024-01-30T08:00:00Z
© 2024 Society for Industrial and Applied Mathematics
R. Borsche
A. Klar
A Hierarchy of Kinetic Discrete-Velocity Models for Traffic Flow Derived from a Nonlocal Prigogine–Herman Model
84
1
139
164
2024-02-29T08:00:00Z
2024-02-29T08:00:00Z
10.1137/23M1583065
https://epubs.siam.org/doi/abs/10.1137/23M1583065?ai=s3&mi=3drblq&af=R
© 2024 Society for Industrial and Applied Mathematics
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An Inversion Scheme for Elastic Diffraction Tomography Based on Mode Separation
https://epubs.siam.org/doi/abs/10.1137/22M1538909?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, <a href="https://epubs.siam.org/toc/smjmap/84/1">Volume 84, Issue 1</a>, Page 165-188, February 2024. <br/> Abstract. We consider the problem of elastic diffraction tomography, which consists in reconstructing elastic properties (i.e., mass density and elastic Lamé parameters) of a weakly scattering medium from full-field data of scattered waves outside the medium. Elastic diffraction tomography refers to the elastic inverse scattering problem after linearization using a first-order Born approximation. In this paper, we prove the Fourier diffraction theorem, which relates the two-dimensional Fourier transform of scattered waves with the Fourier transform of the scatterer in the three-dimensional spatial Fourier domain. Elastic wave mode separation is performed, which decomposes a wave into five modes. A new two-step inversion process is developed, providing information on the modes first and second on the elastic parameters. Finally, we discuss reconstructions with plane wave excitation experiments for different tomographic setups and with different plane wave excitation frequencies, respectively.
SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 165-188, February 2024. <br/> Abstract. We consider the problem of elastic diffraction tomography, which consists in reconstructing elastic properties (i.e., mass density and elastic Lamé parameters) of a weakly scattering medium from full-field data of scattered waves outside the medium. Elastic diffraction tomography refers to the elastic inverse scattering problem after linearization using a first-order Born approximation. In this paper, we prove the Fourier diffraction theorem, which relates the two-dimensional Fourier transform of scattered waves with the Fourier transform of the scatterer in the three-dimensional spatial Fourier domain. Elastic wave mode separation is performed, which decomposes a wave into five modes. A new two-step inversion process is developed, providing information on the modes first and second on the elastic parameters. Finally, we discuss reconstructions with plane wave excitation experiments for different tomographic setups and with different plane wave excitation frequencies, respectively.
An Inversion Scheme for Elastic Diffraction Tomography Based on Mode Separation
10.1137/22M1538909
SIAM Journal on Applied Mathematics
2024-02-01T08:00:00Z
© 2024 Bochra Mejri
Bochra Mejri
Otmar Scherzer
An Inversion Scheme for Elastic Diffraction Tomography Based on Mode Separation
84
1
165
188
2024-02-29T08:00:00Z
2024-02-29T08:00:00Z
10.1137/22M1538909
https://epubs.siam.org/doi/abs/10.1137/22M1538909?ai=s3&mi=3drblq&af=R
© 2024 Bochra Mejri
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Jacobi Processes with Jumps as Neuronal Models: A First Passage Time Analysis
https://epubs.siam.org/doi/abs/10.1137/22M1516877?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, <a href="https://epubs.siam.org/toc/smjmap/84/1">Volume 84, Issue 1</a>, Page 189-214, February 2024. <br/> Abstract. To overcome some limits of classical neuronal models, we propose a Markovian generalization of the classical model based on Jacobi processes by introducing downwards jumps to describe the activity of a single neuron. The statistical analysis of interspike intervals is performed by studying the first passage times of the proposed Markovian Jacobi process with jumps through a constant boundary. In particular, we characterize its Laplace transform, which is expressed in terms of some generalization of hypergeometric functions that we introduce, and deduce a closed-form expression for its expectation. Our approach, which is original in the context of first-passage-time problems, relies on intertwining relations between the semigroups of the classical Jacobi process and its generalization, which have been recently established in [P. Cheridito et al., J. Ec. Polytech. - Math., 8 (2021), pp. 331–378]. A numerical investigation of the firing rate of the considered neuron is performed for some choices of the involved parameters and of the jump distributions.
SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 189-214, February 2024. <br/> Abstract. To overcome some limits of classical neuronal models, we propose a Markovian generalization of the classical model based on Jacobi processes by introducing downwards jumps to describe the activity of a single neuron. The statistical analysis of interspike intervals is performed by studying the first passage times of the proposed Markovian Jacobi process with jumps through a constant boundary. In particular, we characterize its Laplace transform, which is expressed in terms of some generalization of hypergeometric functions that we introduce, and deduce a closed-form expression for its expectation. Our approach, which is original in the context of first-passage-time problems, relies on intertwining relations between the semigroups of the classical Jacobi process and its generalization, which have been recently established in [P. Cheridito et al., J. Ec. Polytech. - Math., 8 (2021), pp. 331–378]. A numerical investigation of the firing rate of the considered neuron is performed for some choices of the involved parameters and of the jump distributions.
Jacobi Processes with Jumps as Neuronal Models: A First Passage Time Analysis
10.1137/22M1516877
SIAM Journal on Applied Mathematics
2024-02-02T08:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Giuseppe D’Onofrio
Pierre Patie
Laura Sacerdote
Jacobi Processes with Jumps as Neuronal Models: A First Passage Time Analysis
84
1
189
214
2024-02-29T08:00:00Z
2024-02-29T08:00:00Z
10.1137/22M1516877
https://epubs.siam.org/doi/abs/10.1137/22M1516877?ai=s3&mi=3drblq&af=R
© 2024 Society for Industrial and Applied Mathematics
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Linear Regularized 13-Moment Equations with Onsager Boundary Conditions for General Gas Molecules
https://epubs.siam.org/doi/abs/10.1137/23M1556472?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, <a href="https://epubs.siam.org/toc/smjmap/84/1">Volume 84, Issue 1</a>, Page 215-245, February 2024. <br/> Abstract. We develop the steady-state regularized 13-moment equations in the linear regime for rarefied gas dynamics with general collision models. For small Knudsen numbers, the model is accurate up to the super-Burnett order, and the resulting system of moment equations is shown to have a symmetric structure. We also propose Onsager boundary conditions for the moment equations that guarantee the stability of the equations. The validity of our model is verified by benchmark examples for the one-dimensional channel flows.
SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 215-245, February 2024. <br/> Abstract. We develop the steady-state regularized 13-moment equations in the linear regime for rarefied gas dynamics with general collision models. For small Knudsen numbers, the model is accurate up to the super-Burnett order, and the resulting system of moment equations is shown to have a symmetric structure. We also propose Onsager boundary conditions for the moment equations that guarantee the stability of the equations. The validity of our model is verified by benchmark examples for the one-dimensional channel flows.
Linear Regularized 13-Moment Equations with Onsager Boundary Conditions for General Gas Molecules
10.1137/23M1556472
SIAM Journal on Applied Mathematics
2024-02-02T08:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Zhenning Cai
Manuel Torrilhon
Siyao Yang
Linear Regularized 13-Moment Equations with Onsager Boundary Conditions for General Gas Molecules
84
1
215
245
2024-02-29T08:00:00Z
2024-02-29T08:00:00Z
10.1137/23M1556472
https://epubs.siam.org/doi/abs/10.1137/23M1556472?ai=s3&mi=3drblq&af=R
© 2024 Society for Industrial and Applied Mathematics
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The Scattering Phase: Seen at Last
https://epubs.siam.org/doi/abs/10.1137/23M1547147?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, <a href="https://epubs.siam.org/toc/smjmap/84/1">Volume 84, Issue 1</a>, Page 246-261, February 2024. <br/> Abstract. The scattering phase, defined as [math] where [math] is the (unitary) scattering matrix, is the analogue of the counting function for eigenvalues when dealing with exterior domains and is closely related to Kreĭn’s spectral shift function. We revisit classical results on asymptotics of the scattering phase and point out that it is never monotone in the case of strong trapping of waves. Perhaps more importantly, we provide the first numerical calculations of scattering phases for nonradial scatterers. They show that the asymptotic Weyl law is accurate even at low frequencies and reveal effects of trapping such as lack of monotonicity. This is achieved by using the recent high level multiphysics finite element software FreeFEM.
SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 246-261, February 2024. <br/> Abstract. The scattering phase, defined as [math] where [math] is the (unitary) scattering matrix, is the analogue of the counting function for eigenvalues when dealing with exterior domains and is closely related to Kreĭn’s spectral shift function. We revisit classical results on asymptotics of the scattering phase and point out that it is never monotone in the case of strong trapping of waves. Perhaps more importantly, we provide the first numerical calculations of scattering phases for nonradial scatterers. They show that the asymptotic Weyl law is accurate even at low frequencies and reveal effects of trapping such as lack of monotonicity. This is achieved by using the recent high level multiphysics finite element software FreeFEM.
The Scattering Phase: Seen at Last
10.1137/23M1547147
SIAM Journal on Applied Mathematics
2024-02-12T08:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Jeffrey Galkowski
Pierre Marchand
Jian Wang
Maciej Zworski
The Scattering Phase: Seen at Last
84
1
246
261
2024-02-29T08:00:00Z
2024-02-29T08:00:00Z
10.1137/23M1547147
https://epubs.siam.org/doi/abs/10.1137/23M1547147?ai=s3&mi=3drblq&af=R
© 2024 Society for Industrial and Applied Mathematics
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A Mathematical Theory of Microscale Hydrodynamic Cloaking and Shielding by Electro-Osmosis
https://epubs.siam.org/doi/abs/10.1137/23M1554837?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, <a href="https://epubs.siam.org/toc/smjmap/84/1">Volume 84, Issue 1</a>, Page 262-284, February 2024. <br/> Abstract. In this paper, we develop a general mathematical framework for perfect and approximate hydrodynamic cloaking and shielding of electro-osmotic flow, which is governed by a coupled PDE system via the field-effect electro-osmosis. We first establish the representation formula of the solution of the coupled system using the layer potential techniques. Based on the Fourier series, the perfect hydrodynamic cloaking and shielding conditions are derived for the control region with the cross-sectional shape being an annulus or a confocal ellipses. Then we further propose an optimization scheme for the design of approximate cloaks and shields within general geometries. The well-posedness of the optimization problem is proved. In particular, the conditions that can ensure the occurrence of approximate cloaks and shields for general geometries are also established. Our theoretical findings are validated and supplemented by a variety of numerical results. The results in this paper also provide a mathematical foundation for more complex hydrodynamic cloaking and shielding.
SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 262-284, February 2024. <br/> Abstract. In this paper, we develop a general mathematical framework for perfect and approximate hydrodynamic cloaking and shielding of electro-osmotic flow, which is governed by a coupled PDE system via the field-effect electro-osmosis. We first establish the representation formula of the solution of the coupled system using the layer potential techniques. Based on the Fourier series, the perfect hydrodynamic cloaking and shielding conditions are derived for the control region with the cross-sectional shape being an annulus or a confocal ellipses. Then we further propose an optimization scheme for the design of approximate cloaks and shields within general geometries. The well-posedness of the optimization problem is proved. In particular, the conditions that can ensure the occurrence of approximate cloaks and shields for general geometries are also established. Our theoretical findings are validated and supplemented by a variety of numerical results. The results in this paper also provide a mathematical foundation for more complex hydrodynamic cloaking and shielding.
A Mathematical Theory of Microscale Hydrodynamic Cloaking and Shielding by Electro-Osmosis
10.1137/23M1554837
SIAM Journal on Applied Mathematics
2024-02-12T08:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Hongyu Liu
Zhi-Qiang Miao
Guang-Hui Zheng
A Mathematical Theory of Microscale Hydrodynamic Cloaking and Shielding by Electro-Osmosis
84
1
262
284
2024-02-29T08:00:00Z
2024-02-29T08:00:00Z
10.1137/23M1554837
https://epubs.siam.org/doi/abs/10.1137/23M1554837?ai=s3&mi=3drblq&af=R
© 2024 Society for Industrial and Applied Mathematics
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Heat Generation Using Lorentzian Nanoparticles. The Full Maxwell System
https://epubs.siam.org/doi/abs/10.1137/23M1547597?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, <a href="https://epubs.siam.org/toc/smjmap/84/1">Volume 84, Issue 1</a>, Page 285-315, February 2024. <br/> Abstract. We analyze and quantify the amount of heat generated by a nanoparticle, injected in a background medium, while excited by incident electromagnetic waves. These nanoparticles are dispersive with electric permittivity following the Lorentz model. The purpose is to determine the quantity of heat generated extremely close to the nanoparticle (at a distance proportional to the radius of the nanoparticle). This study extends our previous results, derived in the 2D TM and TE regimes, to the full Maxwell system. We show that by exciting the medium with incident frequencies close to the plasmonic or Dielectric resonant frequencies, we can generate any desired amount of heat close to the injected nanoparticle while the amount of heat decreases away from it. These results offer a wide range of potential applications in the areas of photo-thermal therapy, drug delivery, and material science, to cite a few. To do so, we employ time-domain integral equations and asymptotic analysis techniques to study the corresponding mathematical model for heat generation. This model is given by the heat equation where the body source term comes from the modulus of the electric field generated by the used incident electromagnetic field. Therefore, we first analyze the dominant term of this electric field by studying the full Maxwell scattering problem in the presence of plasmonic or all-dielectric nanoparticles. As a second step, we analyze the propagation of this dominant electric field in the estimation of the heat potential. For both the electromagnetic and parabolic models, the presence of the nanoparticles is translated into the appearance of large scales in the contrasts for the heat-conductivity (for the parabolic model) and the permittivity (for the full Maxwell system) between the nanoparticle and its surroundings.
SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 285-315, February 2024. <br/> Abstract. We analyze and quantify the amount of heat generated by a nanoparticle, injected in a background medium, while excited by incident electromagnetic waves. These nanoparticles are dispersive with electric permittivity following the Lorentz model. The purpose is to determine the quantity of heat generated extremely close to the nanoparticle (at a distance proportional to the radius of the nanoparticle). This study extends our previous results, derived in the 2D TM and TE regimes, to the full Maxwell system. We show that by exciting the medium with incident frequencies close to the plasmonic or Dielectric resonant frequencies, we can generate any desired amount of heat close to the injected nanoparticle while the amount of heat decreases away from it. These results offer a wide range of potential applications in the areas of photo-thermal therapy, drug delivery, and material science, to cite a few. To do so, we employ time-domain integral equations and asymptotic analysis techniques to study the corresponding mathematical model for heat generation. This model is given by the heat equation where the body source term comes from the modulus of the electric field generated by the used incident electromagnetic field. Therefore, we first analyze the dominant term of this electric field by studying the full Maxwell scattering problem in the presence of plasmonic or all-dielectric nanoparticles. As a second step, we analyze the propagation of this dominant electric field in the estimation of the heat potential. For both the electromagnetic and parabolic models, the presence of the nanoparticles is translated into the appearance of large scales in the contrasts for the heat-conductivity (for the parabolic model) and the permittivity (for the full Maxwell system) between the nanoparticle and its surroundings.
Heat Generation Using Lorentzian Nanoparticles. The Full Maxwell System
10.1137/23M1547597
SIAM Journal on Applied Mathematics
2024-02-20T08:00:00Z
© 2024 Society for Industrial and Applied Mathematics
Arpan Mukherjee
Mourad Sini
Heat Generation Using Lorentzian Nanoparticles. The Full Maxwell System
84
1
285
315
2024-02-29T08:00:00Z
2024-02-29T08:00:00Z
10.1137/23M1547597
https://epubs.siam.org/doi/abs/10.1137/23M1547597?ai=s3&mi=3drblq&af=R
© 2024 Society for Industrial and Applied Mathematics
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Circadian Regulation of Electrolyte and Water Transport in the Rat Kidney
https://epubs.siam.org/doi/abs/10.1137/22M1480732?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. Circadian oscillations have been reported in major renal functions such as renal blood flow, glomerular filtration rate, and urinary excretion. These oscillations can be explained, in part, by the rhythmic variations in renal transporter expressions. However, given that a multitude of renal transporters are regulated by the circadian clock, and that the functions of some of these transporters are coupled, the underlying mechanisms that link variations in transporter expression to the observed changes in kidney function have yet to be fully elucidated. To better understand the impact of the circadian clock on renal solute and water transport, we have developed a computational model of the epithelial transport of the rat kidney that represents the observed rhythmic variations in glomerular filtration rate (GFR) and in the activities of Na[math]/H[math] exchanger 3, sodium-gLucose cotransporter 1, epithelial Na[math] channels, pendrin, and renal outer-medullary K[math] channels. The model predicts the rhythmic oscillations in GFR and key renal transporter activities give rise to a significant shift in transport loads among different nephron segments. Together, these oscillations yield 3-4-fold daily fluctuations in urine output and urinary electrolyte excretion rates.
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. Circadian oscillations have been reported in major renal functions such as renal blood flow, glomerular filtration rate, and urinary excretion. These oscillations can be explained, in part, by the rhythmic variations in renal transporter expressions. However, given that a multitude of renal transporters are regulated by the circadian clock, and that the functions of some of these transporters are coupled, the underlying mechanisms that link variations in transporter expression to the observed changes in kidney function have yet to be fully elucidated. To better understand the impact of the circadian clock on renal solute and water transport, we have developed a computational model of the epithelial transport of the rat kidney that represents the observed rhythmic variations in glomerular filtration rate (GFR) and in the activities of Na[math]/H[math] exchanger 3, sodium-gLucose cotransporter 1, epithelial Na[math] channels, pendrin, and renal outer-medullary K[math] channels. The model predicts the rhythmic oscillations in GFR and key renal transporter activities give rise to a significant shift in transport loads among different nephron segments. Together, these oscillations yield 3-4-fold daily fluctuations in urine output and urinary electrolyte excretion rates.
Circadian Regulation of Electrolyte and Water Transport in the Rat Kidney
10.1137/22M1480732
SIAM Journal on Applied Mathematics
2022-12-14T08:00:00Z
© 2022 Society for Industrial and Applied Mathematics
Melissa M. Stadt
Stephanie Abo
Anita T. Layton
Circadian Regulation of Electrolyte and Water Transport in the Rat Kidney
S1
S16
10.1137/22M1480732
https://epubs.siam.org/doi/abs/10.1137/22M1480732?ai=s3&mi=3drblq&af=R
© 2022 Society for Industrial and Applied Mathematics
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A Local Continuum Model of Cell-Cell Adhesion
https://epubs.siam.org/doi/abs/10.1137/22M1506079?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. Cell-cell adhesion is one the most fundamental mechanisms regulating collective cell migration during tissue development, homeostasis, and repair, allowing cell populations to self-organize and eventually form and maintain complex tissue shapes. Cells interact with each other via the formation of protrusions or filopodia and they adhere to other cells through binding of cell surface proteins. The resulting adhesive forces are then related to cell size and shape and, often, continuum models represent them by nonlocal attractive interactions. In this paper, we present a new continuum model of cell-cell adhesion which can be derived from a general nonlocal model in the limit of short-range interactions. This new model is local, resembling a system of thin-film type equations, with the various model parameters playing the role of surface tensions between different cell populations. Numerical simulations in one and two dimensions reveal that the local model maintains the diversity of cell sorting patterns observed both in experiments and in previously used nonlocal models. In addition, it also has the advantage of having explicit stationary solutions, which provides a direct link between the model parameters and the differential adhesion hypothesis.
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. Cell-cell adhesion is one the most fundamental mechanisms regulating collective cell migration during tissue development, homeostasis, and repair, allowing cell populations to self-organize and eventually form and maintain complex tissue shapes. Cells interact with each other via the formation of protrusions or filopodia and they adhere to other cells through binding of cell surface proteins. The resulting adhesive forces are then related to cell size and shape and, often, continuum models represent them by nonlocal attractive interactions. In this paper, we present a new continuum model of cell-cell adhesion which can be derived from a general nonlocal model in the limit of short-range interactions. This new model is local, resembling a system of thin-film type equations, with the various model parameters playing the role of surface tensions between different cell populations. Numerical simulations in one and two dimensions reveal that the local model maintains the diversity of cell sorting patterns observed both in experiments and in previously used nonlocal models. In addition, it also has the advantage of having explicit stationary solutions, which provides a direct link between the model parameters and the differential adhesion hypothesis.
A Local Continuum Model of Cell-Cell Adhesion
10.1137/22M1506079
SIAM Journal on Applied Mathematics
2023-04-27T07:00:00Z
© 2023 Society for Industrial and Applied Mathematics
C. Falcó
R. E. Baker
J. A. Carrillo
A Local Continuum Model of Cell-Cell Adhesion
S17
S42
10.1137/22M1506079
https://epubs.siam.org/doi/abs/10.1137/22M1506079?ai=s3&mi=3drblq&af=R
© 2023 Society for Industrial and Applied Mathematics
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Dynamical Behavior of a Colony Migration System: Do Colony Size and Quorum Threshold Affect Collective Decision?
https://epubs.siam.org/doi/abs/10.1137/22M1478690?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. Social insects are ecologically and evolutionarily the most successful organisms on earth and can achieve robust collective behaviors through local interactions among group members. Colony migration has been considered as a leading example of collective decision making in social insects. In this paper, a piecewise colony migration system with recruitment switching is proposed to explore underlying mechanisms and synergistic effects of colony size and quorum on the outcomes of collective decision. The dynamical behavior of the nonsmooth system is studied, and sufficient conditions for the existence and stability of equilibrium are provided. The theoretical results suggest that large colonies are more likely to emigrate to a new site. More interesting findings include but are not limited to that (a) the system may exhibit oscillation when the colony size is below a critical level and (b) the system may also exhibit a bistable state, i.e., the colony migrates to a new site or the old nest depending on the initial size of recruiters. Bifurcation analysis shows that the variations of colony size and quorum threshold greatly impact the dynamics. The results suggest that it is important to distinguish between two populations of recruiters in modeling. This work may provide important insights on how simple and local interactions achieve the collective migrating activity in social insects.
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. Social insects are ecologically and evolutionarily the most successful organisms on earth and can achieve robust collective behaviors through local interactions among group members. Colony migration has been considered as a leading example of collective decision making in social insects. In this paper, a piecewise colony migration system with recruitment switching is proposed to explore underlying mechanisms and synergistic effects of colony size and quorum on the outcomes of collective decision. The dynamical behavior of the nonsmooth system is studied, and sufficient conditions for the existence and stability of equilibrium are provided. The theoretical results suggest that large colonies are more likely to emigrate to a new site. More interesting findings include but are not limited to that (a) the system may exhibit oscillation when the colony size is below a critical level and (b) the system may also exhibit a bistable state, i.e., the colony migrates to a new site or the old nest depending on the initial size of recruiters. Bifurcation analysis shows that the variations of colony size and quorum threshold greatly impact the dynamics. The results suggest that it is important to distinguish between two populations of recruiters in modeling. This work may provide important insights on how simple and local interactions achieve the collective migrating activity in social insects.
Dynamical Behavior of a Colony Migration System: Do Colony Size and Quorum Threshold Affect Collective Decision?
10.1137/22M1478690
SIAM Journal on Applied Mathematics
2023-04-27T07:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Lisha Wang
Zhipeng Qiu
Takao Sasaki
Yun Kang
Dynamical Behavior of a Colony Migration System: Do Colony Size and Quorum Threshold Affect Collective Decision?
S43
S64
10.1137/22M1478690
https://epubs.siam.org/doi/abs/10.1137/22M1478690?ai=s3&mi=3drblq&af=R
© 2023 Society for Industrial and Applied Mathematics
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A Gaussian Process Model for Insulin Secretion Reconstruction with Uncertainty Quantification: Applications in Cystic Fibrosis
https://epubs.siam.org/doi/abs/10.1137/22M1506225?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. Investigation of biological systems often requires reconstruction of an unobservable continuous process from discrete time-series data sampled from a related process or processes. When the reconstructed process cannot be validated with experimental data, it is particularly important to quantify the uncertainty on the inferred process, and new methodologies are needed to support both the inference and uncertainty quantification. This work derives a novel statistical model that combines an established differential model of intra- and extravascular C-peptide dynamics with a Gaussian process model of insulin secretion rate (ISR) in order to provide clinical measures of beta-cell function with quantified uncertainty. These measures are computed from the ISR that is inferred from measured C-peptide data. The model is first validated using synthetic data, and then applied to oral glucose tolerance test (OGTT) data from youth participants with and without cystic fibrosis (CF). Because CF is characterized by scarring and fibrosis of the pancreas, impairment of beta-cell function, rather than reduced insulin sensitivity, is implicated in the early etiology of CF-related diabetes (CFRD). ISR-derived measures of beta-cell function show worsening beta-cell function from healthy control to CF to CFRD groups consistent with previous reports on dysglycemia in CF. However, the model additionally allows uncertainty in the data to be propagated to ISR and ISR-derived measures of beta-cell function. These results provide insight into uncertainty in ISR-derived measures of beta cell function, characterize interindividual variability in CFRD etiology, and provide novel metrics to quantify the pathogenesis of CFRD.
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. Investigation of biological systems often requires reconstruction of an unobservable continuous process from discrete time-series data sampled from a related process or processes. When the reconstructed process cannot be validated with experimental data, it is particularly important to quantify the uncertainty on the inferred process, and new methodologies are needed to support both the inference and uncertainty quantification. This work derives a novel statistical model that combines an established differential model of intra- and extravascular C-peptide dynamics with a Gaussian process model of insulin secretion rate (ISR) in order to provide clinical measures of beta-cell function with quantified uncertainty. These measures are computed from the ISR that is inferred from measured C-peptide data. The model is first validated using synthetic data, and then applied to oral glucose tolerance test (OGTT) data from youth participants with and without cystic fibrosis (CF). Because CF is characterized by scarring and fibrosis of the pancreas, impairment of beta-cell function, rather than reduced insulin sensitivity, is implicated in the early etiology of CF-related diabetes (CFRD). ISR-derived measures of beta-cell function show worsening beta-cell function from healthy control to CF to CFRD groups consistent with previous reports on dysglycemia in CF. However, the model additionally allows uncertainty in the data to be propagated to ISR and ISR-derived measures of beta-cell function. These results provide insight into uncertainty in ISR-derived measures of beta cell function, characterize interindividual variability in CFRD etiology, and provide novel metrics to quantify the pathogenesis of CFRD.
A Gaussian Process Model for Insulin Secretion Reconstruction with Uncertainty Quantification: Applications in Cystic Fibrosis
10.1137/22M1506225
SIAM Journal on Applied Mathematics
2023-04-28T08:09:30Z
© 2023 Society for Industrial and Applied Mathematics
Justin Garrish
Christine Chan
Douglas Nychka
Cecilia Diniz Behn
A Gaussian Process Model for Insulin Secretion Reconstruction with Uncertainty Quantification: Applications in Cystic Fibrosis
S65
S81
10.1137/22M1506225
https://epubs.siam.org/doi/abs/10.1137/22M1506225?ai=s3&mi=3drblq&af=R
© 2023 Society for Industrial and Applied Mathematics
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Analyzing and Mimicking the Optimized Flight Physics of Soaring Birds: A Differential Geometric Control and Extremum Seeking System Approach with Real Time Implementation
https://epubs.siam.org/doi/abs/10.1137/22M1505566?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. The mystery of soaring birds, such as albatrosses and eagles, has intrigued biologists, physicists, aeronautical/control engineers, and applied mathematicians for centuries. These fascinating avian organisms are able to fly for long durations while expending little to no energy, utilizing wind to gain lift. This flight technique/maneuver is called dynamic soaring (DS). For biologists and physicists, the DS phenomenon is nothing but a wonder of the very elegant ability of these birds to interact with nature and use its physical ether in an optimal way for better survival and energy efficiency. For the engineering community, the DS phenomenon is a source of inspiration and an unequivocal opportunity for biomimicking. Mathematical characterization of the DS phenomenon in the literature has been limited to optimal control configurations that utilized developments in numerical optimization algorithms along with control methods to identify the optimal DS trajectory taken (or to be taken) by the bird/mimicking system. Unfortunately, all of these methods are highly complex and non-real-time. Hence, the mathematical characterization of the DS problem, we believe, appears to be at odds with the phenomenon/birds-behavior. In this paper, we provide a novel two-layered mathematical approach to characterize, model, mimic, and control DS in a simple real-time implementation, which we believe more effectively decodes the biological behavior of soaring birds. First, we present a differential geometric control formulation and analysis of the DS problem, which allow us to introduce a control system that is simple yet controllable. Second, we establish a link between the DS philosophy and a class of dynamical control systems known as extremum seeking systems. This linkage provides the control input that makes DS a real-time reality. We believe our framework accurately describes the biological behavior of soaring birds and opens the door for geometric control theory and extremum seeking systems to be utilized in biological systems and natural phenomena. Simulation results are provided along with comparisons to powerful optimal control solvers, illustrating the advantages of the introduced method.
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. The mystery of soaring birds, such as albatrosses and eagles, has intrigued biologists, physicists, aeronautical/control engineers, and applied mathematicians for centuries. These fascinating avian organisms are able to fly for long durations while expending little to no energy, utilizing wind to gain lift. This flight technique/maneuver is called dynamic soaring (DS). For biologists and physicists, the DS phenomenon is nothing but a wonder of the very elegant ability of these birds to interact with nature and use its physical ether in an optimal way for better survival and energy efficiency. For the engineering community, the DS phenomenon is a source of inspiration and an unequivocal opportunity for biomimicking. Mathematical characterization of the DS phenomenon in the literature has been limited to optimal control configurations that utilized developments in numerical optimization algorithms along with control methods to identify the optimal DS trajectory taken (or to be taken) by the bird/mimicking system. Unfortunately, all of these methods are highly complex and non-real-time. Hence, the mathematical characterization of the DS problem, we believe, appears to be at odds with the phenomenon/birds-behavior. In this paper, we provide a novel two-layered mathematical approach to characterize, model, mimic, and control DS in a simple real-time implementation, which we believe more effectively decodes the biological behavior of soaring birds. First, we present a differential geometric control formulation and analysis of the DS problem, which allow us to introduce a control system that is simple yet controllable. Second, we establish a link between the DS philosophy and a class of dynamical control systems known as extremum seeking systems. This linkage provides the control input that makes DS a real-time reality. We believe our framework accurately describes the biological behavior of soaring birds and opens the door for geometric control theory and extremum seeking systems to be utilized in biological systems and natural phenomena. Simulation results are provided along with comparisons to powerful optimal control solvers, illustrating the advantages of the introduced method.
Analyzing and Mimicking the Optimized Flight Physics of Soaring Birds: A Differential Geometric Control and Extremum Seeking System Approach with Real Time Implementation
10.1137/22M1505566
SIAM Journal on Applied Mathematics
2023-06-26T07:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Sameh A. Eisa
Sameer Pokhrel
Analyzing and Mimicking the Optimized Flight Physics of Soaring Birds: A Differential Geometric Control and Extremum Seeking System Approach with Real Time Implementation
S82
S104
10.1137/22M1505566
https://epubs.siam.org/doi/abs/10.1137/22M1505566?ai=s3&mi=3drblq&af=R
© 2023 Society for Industrial and Applied Mathematics
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Algebraic Study of Receptor-Ligand Systems: A Dose-Response Analysis
https://epubs.siam.org/doi/abs/10.1137/22M1506262?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. The study of a receptor-ligand system generally relies on the analysis of its dose-response (or concentration-effect) curve, which quantifies the relation between ligand concentration and the biological effect (or cellular response) induced when binding its specific cell surface receptor. Mathematical models of receptor-ligand systems have been developed to compute a dose-response curve under the assumption that the biological effect is proportional to the number of ligand-bound receptors. Given a dose-response curve, two quantities (or metrics) have been defined to characterize the properties of the ligand-receptor system under consideration: amplitude and potency (or half-maximal effective concentration, and denoted by EC[math]). Both the amplitude and the EC[math] are key quantities commonly used in pharmaco-dynamic modeling, yet a comprehensive mathematical investigation of the behavior of these two metrics is still outstanding; for a large (and important) family of receptors, called cytokine receptors, we still do not know how amplitude and EC[math] depend on receptor copy numbers. Here we make use of algebraic approaches (Gröbner basis) to study these metrics for a large class of receptor-ligand models, with a focus on cytokine receptors. In particular, we introduce a method, making use of two motivating examples based on the interleukin-7 (IL-7) receptor, to compute analytic expressions for the amplitude and the EC[math]. We then extend the method to a wider class of receptor-ligand systems, sequential receptor-ligand systems with extrinsic kinase, and provide some examples. The algebraic methods developed in this paper not only reduce computational costs and numerical errors, but allow us to explicitly identify key molecular parameters and rates which determine the behavior of the dose-response curve. Thus, the proposed methods provide a novel and useful approach to perform model validation, assay design and parameter exploration of receptor-ligand systems.
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. The study of a receptor-ligand system generally relies on the analysis of its dose-response (or concentration-effect) curve, which quantifies the relation between ligand concentration and the biological effect (or cellular response) induced when binding its specific cell surface receptor. Mathematical models of receptor-ligand systems have been developed to compute a dose-response curve under the assumption that the biological effect is proportional to the number of ligand-bound receptors. Given a dose-response curve, two quantities (or metrics) have been defined to characterize the properties of the ligand-receptor system under consideration: amplitude and potency (or half-maximal effective concentration, and denoted by EC[math]). Both the amplitude and the EC[math] are key quantities commonly used in pharmaco-dynamic modeling, yet a comprehensive mathematical investigation of the behavior of these two metrics is still outstanding; for a large (and important) family of receptors, called cytokine receptors, we still do not know how amplitude and EC[math] depend on receptor copy numbers. Here we make use of algebraic approaches (Gröbner basis) to study these metrics for a large class of receptor-ligand models, with a focus on cytokine receptors. In particular, we introduce a method, making use of two motivating examples based on the interleukin-7 (IL-7) receptor, to compute analytic expressions for the amplitude and the EC[math]. We then extend the method to a wider class of receptor-ligand systems, sequential receptor-ligand systems with extrinsic kinase, and provide some examples. The algebraic methods developed in this paper not only reduce computational costs and numerical errors, but allow us to explicitly identify key molecular parameters and rates which determine the behavior of the dose-response curve. Thus, the proposed methods provide a novel and useful approach to perform model validation, assay design and parameter exploration of receptor-ligand systems.
Algebraic Study of Receptor-Ligand Systems: A Dose-Response Analysis
10.1137/22M1506262
SIAM Journal on Applied Mathematics
2023-07-12T07:00:00Z
© 2023 SIAM. Published by SIAM under the terms of the Creative Commons 4.0 license
Léa Sta
Michael F. Adamer
Carmen Molina-París
Algebraic Study of Receptor-Ligand Systems: A Dose-Response Analysis
S105
S150
10.1137/22M1506262
https://epubs.siam.org/doi/abs/10.1137/22M1506262?ai=s3&mi=3drblq&af=R
© 2023 SIAM. Published by SIAM under the terms of the Creative Commons 4.0 license
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Mechanisms for Producing Oscillatory Plane Waves in Discrete and Continuum Models
https://epubs.siam.org/doi/abs/10.1137/22M1506523?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. Plane waves have commonly been observed in recordings of human brains. These waves take the form of spatial phase gradients in the oscillatory potentials picked up by implanted electrodes. We first show that long but finite chains of nearest-neighbor coupled phase oscillators can produce an almost constant phase gradient when the edge effects interact with small heterogeneities in the local frequency. Next, we introduce a continuum model with nonlocal coupling and use singular perturbation methods to show similar interactions between the boundaries and small frequency differences. Finally, we show that networks of Wilson–Cowan equations can generate plane waves with the same mechanism.
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. Plane waves have commonly been observed in recordings of human brains. These waves take the form of spatial phase gradients in the oscillatory potentials picked up by implanted electrodes. We first show that long but finite chains of nearest-neighbor coupled phase oscillators can produce an almost constant phase gradient when the edge effects interact with small heterogeneities in the local frequency. Next, we introduce a continuum model with nonlocal coupling and use singular perturbation methods to show similar interactions between the boundaries and small frequency differences. Finally, we show that networks of Wilson–Cowan equations can generate plane waves with the same mechanism.
Mechanisms for Producing Oscillatory Plane Waves in Discrete and Continuum Models
10.1137/22M1506523
SIAM Journal on Applied Mathematics
2023-07-13T07:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Andrea J. Welsh
Bard Ermentrout
Mechanisms for Producing Oscillatory Plane Waves in Discrete and Continuum Models
S151
S171
10.1137/22M1506523
https://epubs.siam.org/doi/abs/10.1137/22M1506523?ai=s3&mi=3drblq&af=R
© 2023 Society for Industrial and Applied Mathematics
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The Role of Clearance in Neurodegenerative Diseases
https://epubs.siam.org/doi/abs/10.1137/22M1487801?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. Alzheimer’s disease, the most common form of dementia, is a systemic neurological disorder associated with the formation of toxic, pathological aggregates of proteins within the brain that lead to severe cognitive decline, and eventually, death. In normal physiological conditions, the brain rids itself of toxic proteins using various clearance mechanisms. The efficacy of brain clearance can be adversely affected by the presence of toxic proteins and is also known to decline with age. Motivated by recent findings, such as the connection between brain cerebrospinal fluid clearance and sleep, we propose a mathematical model coupling the progression of toxic proteins over the brain’s structural network and protein clearance. The model is used to study the interplay between clearance in the brain, toxic seeding, brain network connectivity, aging, and progression in neurodegenerative diseases such as Alzheimer’s disease. Our findings provide a theoretical framework for the growing body of medical research showing that clearance plays an important role in the etiology, progression, and treatment of Alzheimer’s disease.
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. Alzheimer’s disease, the most common form of dementia, is a systemic neurological disorder associated with the formation of toxic, pathological aggregates of proteins within the brain that lead to severe cognitive decline, and eventually, death. In normal physiological conditions, the brain rids itself of toxic proteins using various clearance mechanisms. The efficacy of brain clearance can be adversely affected by the presence of toxic proteins and is also known to decline with age. Motivated by recent findings, such as the connection between brain cerebrospinal fluid clearance and sleep, we propose a mathematical model coupling the progression of toxic proteins over the brain’s structural network and protein clearance. The model is used to study the interplay between clearance in the brain, toxic seeding, brain network connectivity, aging, and progression in neurodegenerative diseases such as Alzheimer’s disease. Our findings provide a theoretical framework for the growing body of medical research showing that clearance plays an important role in the etiology, progression, and treatment of Alzheimer’s disease.
The Role of Clearance in Neurodegenerative Diseases
10.1137/22M1487801
SIAM Journal on Applied Mathematics
2023-07-17T07:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Georgia S. Brennan
Travis B. Thompson
Hadrien Oliveri
Marie E. Rognes
Alain Goriely
The Role of Clearance in Neurodegenerative Diseases
S172
S198
10.1137/22M1487801
https://epubs.siam.org/doi/abs/10.1137/22M1487801?ai=s3&mi=3drblq&af=R
© 2023 Society for Industrial and Applied Mathematics
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Optimal Epidemic Control by Social Distancing and Vaccination of an Infection Structured by Time Since Infection: The COVID-19 Case Study
https://epubs.siam.org/doi/abs/10.1137/22M1499406?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. Motivated by the issue of COVID-19 mitigation, in this work we tackle the general problem of optimally controlling an epidemic outbreak of a communicable disease structured by age since exposure, with the aid of two types of control instruments, namely social distancing and vaccination by a vaccine at least partly effective in protecting from infection. By our analyses we could prove the existence of (at least) one optimal control pair. We derived first-order necessary conditions for optimality and proved some useful properties of such optimal solutions. Our general model can be specialized to include a number of subcases relevant for epidemics like COVID-19, such as, e.g., the arrival of vaccines in a second stage of the epidemic, and vaccine rationing, making social distancing the only optimizable instrument. A worked example provides a number of further insights on the relationships between key control and epidemic parameters.
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. Motivated by the issue of COVID-19 mitigation, in this work we tackle the general problem of optimally controlling an epidemic outbreak of a communicable disease structured by age since exposure, with the aid of two types of control instruments, namely social distancing and vaccination by a vaccine at least partly effective in protecting from infection. By our analyses we could prove the existence of (at least) one optimal control pair. We derived first-order necessary conditions for optimality and proved some useful properties of such optimal solutions. Our general model can be specialized to include a number of subcases relevant for epidemics like COVID-19, such as, e.g., the arrival of vaccines in a second stage of the epidemic, and vaccine rationing, making social distancing the only optimizable instrument. A worked example provides a number of further insights on the relationships between key control and epidemic parameters.
Optimal Epidemic Control by Social Distancing and Vaccination of an Infection Structured by Time Since Infection: The COVID-19 Case Study
10.1137/22M1499406
SIAM Journal on Applied Mathematics
2023-07-19T07:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Alberto d’Onofrio
Mimmo Iannelli
Piero Manfredi
Gabriela Marinoschi
Optimal Epidemic Control by Social Distancing and Vaccination of an Infection Structured by Time Since Infection: The COVID-19 Case Study
S199
S224
10.1137/22M1499406
https://epubs.siam.org/doi/abs/10.1137/22M1499406?ai=s3&mi=3drblq&af=R
© 2023 Society for Industrial and Applied Mathematics
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Spatial Dynamics with Heterogeneity
https://epubs.siam.org/doi/abs/10.1137/22M1509850?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. Spatial systems with heterogeneities are ubiquitous in nature, from precipitation, temperature, and soil gradients controlling vegetation growth to morphogen gradients controlling gene expression in embryos. Such systems, generally described by nonlinear dynamical systems, often display complex parameter dependence and exhibit bifurcations. The dynamics of heterogeneous spatially extended systems passing through bifurcations are still relatively poorly understood, yet recent theoretical studies and experimental data highlight the resulting complex behaviors and their relevance to real-world applications. We explore the consequences of spatial heterogeneities passing through bifurcations via two examples strongly motivated by applications. These model systems illustrate that studying heterogeneity-induced behaviors in spatial systems is crucial for a better understanding of ecological transitions and functional organization in brain development.
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. Spatial systems with heterogeneities are ubiquitous in nature, from precipitation, temperature, and soil gradients controlling vegetation growth to morphogen gradients controlling gene expression in embryos. Such systems, generally described by nonlinear dynamical systems, often display complex parameter dependence and exhibit bifurcations. The dynamics of heterogeneous spatially extended systems passing through bifurcations are still relatively poorly understood, yet recent theoretical studies and experimental data highlight the resulting complex behaviors and their relevance to real-world applications. We explore the consequences of spatial heterogeneities passing through bifurcations via two examples strongly motivated by applications. These model systems illustrate that studying heterogeneity-induced behaviors in spatial systems is crucial for a better understanding of ecological transitions and functional organization in brain development.
Spatial Dynamics with Heterogeneity
10.1137/22M1509850
SIAM Journal on Applied Mathematics
2023-07-19T07:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Denis D. Patterson
A. Carla Staver
Simon A. Levin
Jonathan D. Touboul
Spatial Dynamics with Heterogeneity
S225
S248
10.1137/22M1509850
https://epubs.siam.org/doi/abs/10.1137/22M1509850?ai=s3&mi=3drblq&af=R
© 2023 Society for Industrial and Applied Mathematics
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Critical Patch Size of a Two-Population Reaction Diffusion Model Describing Brain Tumor Growth
https://epubs.siam.org/doi/abs/10.1137/22M1509631?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. The critical patch (KISS) size is the minimum habitat size needed for a population to survive in a region. Habitats larger than the critical patch size allow a population to persist, while smaller habitats lead to extinction. We perform a rigorous derivation of the critical patch size associated with a 2-population glioblastoma multiforme (GBM) model that divides the tumor cells into proliferating and quiescent/necrotic populations. We determine that the critical patch size of our model is consistent with that of the Fisher–Kolmogorov–Petrovsky–Piskunov equation, one of the first reaction-diffusion models proposed for GBM, and does not depend on parameters pertaining to the quiescent/necrotic population. The critical patch size may indicate that GBM tumors have a minimum size depending on the location in the brain. We also derive a theoretical relationship between the size of a GBM tumor at steady-state and its maximum cell density, which has potential applications for patient-specific parameter estimation based on magnetic resonance imaging data. Finally, we identify a positively invariant region for our model, which guarantees that solutions remain positive and bounded from above for all time.
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. The critical patch (KISS) size is the minimum habitat size needed for a population to survive in a region. Habitats larger than the critical patch size allow a population to persist, while smaller habitats lead to extinction. We perform a rigorous derivation of the critical patch size associated with a 2-population glioblastoma multiforme (GBM) model that divides the tumor cells into proliferating and quiescent/necrotic populations. We determine that the critical patch size of our model is consistent with that of the Fisher–Kolmogorov–Petrovsky–Piskunov equation, one of the first reaction-diffusion models proposed for GBM, and does not depend on parameters pertaining to the quiescent/necrotic population. The critical patch size may indicate that GBM tumors have a minimum size depending on the location in the brain. We also derive a theoretical relationship between the size of a GBM tumor at steady-state and its maximum cell density, which has potential applications for patient-specific parameter estimation based on magnetic resonance imaging data. Finally, we identify a positively invariant region for our model, which guarantees that solutions remain positive and bounded from above for all time.
Critical Patch Size of a Two-Population Reaction Diffusion Model Describing Brain Tumor Growth
10.1137/22M1509631
SIAM Journal on Applied Mathematics
2023-07-19T07:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Duane C. Harris
Changhan He
Mark C. Preul
Eric J. Kostelich
Yang Kuang
Critical Patch Size of a Two-Population Reaction Diffusion Model Describing Brain Tumor Growth
S249
S268
10.1137/22M1509631
https://epubs.siam.org/doi/abs/10.1137/22M1509631?ai=s3&mi=3drblq&af=R
© 2023 Society for Industrial and Applied Mathematics
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Extreme Diffusion with Point-Sink Killing Fields: Application to Fast Calcium Signaling at Synapses
https://epubs.siam.org/doi/abs/10.1137/22M1476319?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. The extreme narrow escape theory describes the statistical properties of the fastest among many identical stochastic particles to escape from a narrow window. We study here the escape time of the fastest particle when a killing term is added inside a one-dimensional interval. Killing represents a degradation that leads to removal of the moving particles with a given probability. Using the time dependent flux for the solution of the diffusion equation, we compute asymptotically the mean time for the fastest to escape alive. We use the present theory to study the role of several killing distributions on the mean extreme escape time for the fastest and compare the results with Brownian simulations. Finally, we discuss some applications to calcium dynamics in neuronal cells.
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. The extreme narrow escape theory describes the statistical properties of the fastest among many identical stochastic particles to escape from a narrow window. We study here the escape time of the fastest particle when a killing term is added inside a one-dimensional interval. Killing represents a degradation that leads to removal of the moving particles with a given probability. Using the time dependent flux for the solution of the diffusion equation, we compute asymptotically the mean time for the fastest to escape alive. We use the present theory to study the role of several killing distributions on the mean extreme escape time for the fastest and compare the results with Brownian simulations. Finally, we discuss some applications to calcium dynamics in neuronal cells.
Extreme Diffusion with Point-Sink Killing Fields: Application to Fast Calcium Signaling at Synapses
10.1137/22M1476319
SIAM Journal on Applied Mathematics
2023-07-21T07:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Suney Toste
David Holcman
Extreme Diffusion with Point-Sink Killing Fields: Application to Fast Calcium Signaling at Synapses
S269
S296
10.1137/22M1476319
https://epubs.siam.org/doi/abs/10.1137/22M1476319?ai=s3&mi=3drblq&af=R
© 2023 Society for Industrial and Applied Mathematics
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Nonparametric Inference for the Reproductive Rate in Generalized Compartmental Models
https://epubs.siam.org/doi/abs/10.1137/22M1505499?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. We develop a tractable nonparametric model for the time-varying reproductive rate of infectious diseases that combines the structure of a deterministic compartmental model and a stochastic model for incidence data. We use Bayesian inference to estimate, with uncertainty, the reproductive rate of the Coronavirus 2019 outbreak in the U.S. states of California, Florida, Michigan, New Mexico, New York, and Texas from January 2020 to March 2022. Employing the inferred reproductive rates, we estimate the posterior distribution of the time-varying reproduction numbers for each state. Compering the time-varying reproduction numbers across the states, we identify some epidemic waves, potentially driven from changes in human behavior and virus mutations.
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. We develop a tractable nonparametric model for the time-varying reproductive rate of infectious diseases that combines the structure of a deterministic compartmental model and a stochastic model for incidence data. We use Bayesian inference to estimate, with uncertainty, the reproductive rate of the Coronavirus 2019 outbreak in the U.S. states of California, Florida, Michigan, New Mexico, New York, and Texas from January 2020 to March 2022. Employing the inferred reproductive rates, we estimate the posterior distribution of the time-varying reproduction numbers for each state. Compering the time-varying reproduction numbers across the states, we identify some epidemic waves, potentially driven from changes in human behavior and virus mutations.
Nonparametric Inference for the Reproductive Rate in Generalized Compartmental Models
10.1137/22M1505499
SIAM Journal on Applied Mathematics
2023-07-25T07:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Imelda Trejo
Yen Ting Lin
Amanda Patrick
Nicolas Hengartner
Nonparametric Inference for the Reproductive Rate in Generalized Compartmental Models
S297
S315
10.1137/22M1505499
https://epubs.siam.org/doi/abs/10.1137/22M1505499?ai=s3&mi=3drblq&af=R
© 2023 Society for Industrial and Applied Mathematics
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Path Integration and the Structural Sensitivity Problem in Partially Specified Biological Models
https://epubs.siam.org/doi/abs/10.1137/22M1499029?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. Biological systems are known to be inherently uncertain and complex, and it is often difficult to justify rigorously functional forms used in a mathematical model. Generally, one chooses some simple function having qualitatively correct behavior without concern for the precise choice of function; the assumption has been that qualitatively similar functions will produce qualitatively similar behavior from the model. However, it has been shown that, in some cases, the qualitative predictions from a model are sensitive to the particular functional form used; this property is known as structural sensitivity. A promising tool for quantification of structural sensitivity is the use of partially specified models, in which some number of functions in equations are not defined explicitly. However, in this approach we cannot rely on the traditional parameter-based framework, where all functional forms are well defined but contain parameters to be determined. The main difficulties are that, mathematically, we need to deal with an infinite-dimensional function space and that a well-defined measure on that space is needed. We propose a novel framework to reveal the structural sensitivity and quantify uncertainty in partially specified biological models based on ordinary differential equations backed up by empirical data. Our method uses path integration, previously introduced in theoretical physics. As an insightful example, we explore structural sensitivity of a well-known tritrophic food chain model in which the functional response of the predator is uncertain, using available experimental data on protozoan predation on bacteria. For the mentioned model, we compare the novel framework with the classical methods of parameter-based sensitivity analysis and demonstrate distinct outcomes for the two approaches. Finally, we discuss a further extension of the proposed framework.
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. Biological systems are known to be inherently uncertain and complex, and it is often difficult to justify rigorously functional forms used in a mathematical model. Generally, one chooses some simple function having qualitatively correct behavior without concern for the precise choice of function; the assumption has been that qualitatively similar functions will produce qualitatively similar behavior from the model. However, it has been shown that, in some cases, the qualitative predictions from a model are sensitive to the particular functional form used; this property is known as structural sensitivity. A promising tool for quantification of structural sensitivity is the use of partially specified models, in which some number of functions in equations are not defined explicitly. However, in this approach we cannot rely on the traditional parameter-based framework, where all functional forms are well defined but contain parameters to be determined. The main difficulties are that, mathematically, we need to deal with an infinite-dimensional function space and that a well-defined measure on that space is needed. We propose a novel framework to reveal the structural sensitivity and quantify uncertainty in partially specified biological models based on ordinary differential equations backed up by empirical data. Our method uses path integration, previously introduced in theoretical physics. As an insightful example, we explore structural sensitivity of a well-known tritrophic food chain model in which the functional response of the predator is uncertain, using available experimental data on protozoan predation on bacteria. For the mentioned model, we compare the novel framework with the classical methods of parameter-based sensitivity analysis and demonstrate distinct outcomes for the two approaches. Finally, we discuss a further extension of the proposed framework.
Path Integration and the Structural Sensitivity Problem in Partially Specified Biological Models
10.1137/22M1499029
SIAM Journal on Applied Mathematics
2023-07-27T07:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Lourdes Juan
Jackson Kulik
Katharine R. Long
Andrew Y. Morozov
Jacob Slocum
Path Integration and the Structural Sensitivity Problem in Partially Specified Biological Models
S316
S335
10.1137/22M1499029
https://epubs.siam.org/doi/abs/10.1137/22M1499029?ai=s3&mi=3drblq&af=R
© 2023 Society for Industrial and Applied Mathematics
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Discrete Inverse Method for Extracting Disease Transmission Rates from Accessible Infection Data
https://epubs.siam.org/doi/abs/10.1137/22M1498796?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. Accurate estimation of the transmissibility of an infectious disease is critical to understanding disease transmission dynamics and designing effective control strategies. However, it has always been difficult to estimate the transmission rates due to the unobservability and multiple contributing factors. In this paper, we develop a data-driven inverse method based on discretizations of compartmental differential equation models for estimating time-varying transmission rates of infectious diseases. By developing iteration algorithms for three typical classes of infectious diseases, namely, a disease with seasonal cycles, a disease with nonseasonal cycles, and a disease with no obvious periodicity, we demonstrate that the discrete inverse method is a valuable tool for extracting information from available pandemic or epidemic incidence data. We also obtain insights for some epidemiological phenomena and issues of concern based on each application. Our method is highly intuitive and generates rapid implementation even with multiple years of data instances. In particular, it can be used in conjunction with other data-driven technologies, such as machine learning, to forecast future disease dynamics based on future weather conditions, policy decisions, or human mobility trends, providing guidance to public health authorities.
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. Accurate estimation of the transmissibility of an infectious disease is critical to understanding disease transmission dynamics and designing effective control strategies. However, it has always been difficult to estimate the transmission rates due to the unobservability and multiple contributing factors. In this paper, we develop a data-driven inverse method based on discretizations of compartmental differential equation models for estimating time-varying transmission rates of infectious diseases. By developing iteration algorithms for three typical classes of infectious diseases, namely, a disease with seasonal cycles, a disease with nonseasonal cycles, and a disease with no obvious periodicity, we demonstrate that the discrete inverse method is a valuable tool for extracting information from available pandemic or epidemic incidence data. We also obtain insights for some epidemiological phenomena and issues of concern based on each application. Our method is highly intuitive and generates rapid implementation even with multiple years of data instances. In particular, it can be used in conjunction with other data-driven technologies, such as machine learning, to forecast future disease dynamics based on future weather conditions, policy decisions, or human mobility trends, providing guidance to public health authorities.
Discrete Inverse Method for Extracting Disease Transmission Rates from Accessible Infection Data
10.1137/22M1498796
SIAM Journal on Applied Mathematics
2023-08-17T07:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Xiunan Wang
Hao Wang
Discrete Inverse Method for Extracting Disease Transmission Rates from Accessible Infection Data
S336
S361
10.1137/22M1498796
https://epubs.siam.org/doi/abs/10.1137/22M1498796?ai=s3&mi=3drblq&af=R
© 2023 Society for Industrial and Applied Mathematics
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Modelling Oxygenic Photogranules: Microbial Ecology and Process Performance
https://epubs.siam.org/doi/abs/10.1137/22M1483013?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. This work addresses the modelling of oxygenic photogranules (OPGs), by introducing a mathematical model which describes both the genesis and growth of photogranules and the related treatment process. The photogranule has been modelled as a free boundary domain with radial symmetry, which evolves over time as a result of microbial growth, attachment, and detachment processes. Hyperbolic and parabolic PDEs have been considered to model at mesoscale the transport and growth of sessile biomass and the diffusion and conversion of soluble substrates. The macroscale behavior of the system has been modelled through first order impulsive ordinary differential equations (IDEs), which reproduce a sequencing batch reactor (SBR) configuration. Phototrophic biomass has been considered for the first time in granular biofilms, and cyanobacteria and microalgae have been accounted separately, to model their metabolic differences. To describe the key role of cyanobacteria in the photogranulation process, the attachment velocity of all suspended microbial species has been modelled as a function of the cyanobacteria concentration in suspended form. The model takes into account the main biological processes involved in OPG-based systems: metabolic activity of cyanobacteria, microalgae, heterotrophic and nitrifying bacteria, microbial decay, extracellular polymeric substances (EPS) secretion, symbiotic and competitive interactions between different species, light-dark cycle, light attenuation across the granule, and photoinhibition phenomena. The model has been integrated numerically, and the results show its consistency in describing the photogranule evolution and ecology, and highlight the advantages of the OPG technology, analyzing the effects of the influent wastewater composition and light conditions on the process.
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. This work addresses the modelling of oxygenic photogranules (OPGs), by introducing a mathematical model which describes both the genesis and growth of photogranules and the related treatment process. The photogranule has been modelled as a free boundary domain with radial symmetry, which evolves over time as a result of microbial growth, attachment, and detachment processes. Hyperbolic and parabolic PDEs have been considered to model at mesoscale the transport and growth of sessile biomass and the diffusion and conversion of soluble substrates. The macroscale behavior of the system has been modelled through first order impulsive ordinary differential equations (IDEs), which reproduce a sequencing batch reactor (SBR) configuration. Phototrophic biomass has been considered for the first time in granular biofilms, and cyanobacteria and microalgae have been accounted separately, to model their metabolic differences. To describe the key role of cyanobacteria in the photogranulation process, the attachment velocity of all suspended microbial species has been modelled as a function of the cyanobacteria concentration in suspended form. The model takes into account the main biological processes involved in OPG-based systems: metabolic activity of cyanobacteria, microalgae, heterotrophic and nitrifying bacteria, microbial decay, extracellular polymeric substances (EPS) secretion, symbiotic and competitive interactions between different species, light-dark cycle, light attenuation across the granule, and photoinhibition phenomena. The model has been integrated numerically, and the results show its consistency in describing the photogranule evolution and ecology, and highlight the advantages of the OPG technology, analyzing the effects of the influent wastewater composition and light conditions on the process.
Modelling Oxygenic Photogranules: Microbial Ecology and Process Performance
10.1137/22M1483013
SIAM Journal on Applied Mathematics
2023-09-19T07:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Alberto Tenore
Maria Rosaria Mattei
Luigi Frunzo
Modelling Oxygenic Photogranules: Microbial Ecology and Process Performance
S362
S391
10.1137/22M1483013
https://epubs.siam.org/doi/abs/10.1137/22M1483013?ai=s3&mi=3drblq&af=R
© 2023 Society for Industrial and Applied Mathematics
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Applications of Mathematical Programming to Genetic Biocontrol
https://epubs.siam.org/doi/abs/10.1137/22M1509862?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. We review existing approaches to optimizing the deployment of genetic biocontrol technologies—tools used to prevent vector-borne diseases such as malaria and dengue—and formulate a mathematical program that enables the incorporation of crucial ecological and logistical details. The model is comprised of equality constraints grounded in discretized dynamic population equations, inequality constraints representative of operational limitations including resource restrictions, and an objective function that jointly minimizes the count of competent mosquito vectors and the number of transgenic organisms released to mitigate them over a specified time period. We explore how nonlinear programming (NLP) and mixed integer nonlinear programming (MINLP) can advance the state of the art in designing the operational implementation of three distinct transgenic public health interventions, two of which are presently in active use around the world.
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. We review existing approaches to optimizing the deployment of genetic biocontrol technologies—tools used to prevent vector-borne diseases such as malaria and dengue—and formulate a mathematical program that enables the incorporation of crucial ecological and logistical details. The model is comprised of equality constraints grounded in discretized dynamic population equations, inequality constraints representative of operational limitations including resource restrictions, and an objective function that jointly minimizes the count of competent mosquito vectors and the number of transgenic organisms released to mitigate them over a specified time period. We explore how nonlinear programming (NLP) and mixed integer nonlinear programming (MINLP) can advance the state of the art in designing the operational implementation of three distinct transgenic public health interventions, two of which are presently in active use around the world.
Applications of Mathematical Programming to Genetic Biocontrol
10.1137/22M1509862
SIAM Journal on Applied Mathematics
2023-09-20T07:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Váleri N. Vásquez
John M. Marshall
Applications of Mathematical Programming to Genetic Biocontrol
S392
S411
10.1137/22M1509862
https://epubs.siam.org/doi/abs/10.1137/22M1509862?ai=s3&mi=3drblq&af=R
© 2023 Society for Industrial and Applied Mathematics
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Resource-Driven Pattern Formation in Consumer-Resource Systems with Asymmetric Dispersal on a Plane
https://epubs.siam.org/doi/abs/10.1137/22M1506006?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. This paper considers resource-driven pattern formation in consumer-resource systems. Here, a planar pattern consists of many big patches, and a big patch can be regarded as combination of many patches on the plane. The consumer moves between patches asymmetrically, while the asymmetry is driven by the resource abundance. Based on experimental models with linearly-linked patches, we propose a planarly-linked-patch model with asymmetric dispersal. Using dynamical systems theory, we show global stability of equilibria in the model, and demonstrate how the resource-driven dispersal forms patterns. It is shown that appropriate asymmetry in dispersal would make the consumer persist in the system, even in sink patches. The asymmetry could also make the consumer’s total population abundance larger than that without dispersal. However, inappropriate asymmetry would make the consumer go into extinction, even in source patches. Dispersal rates are also shown to play a role in the persistence and abundance increase. Our results are consistent with experimental observations and provide new insights. Numerical simulations by the model reproduce various vegetation patterns in the real world. This work has potential applications in spatial pattern formation in biological research.
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. This paper considers resource-driven pattern formation in consumer-resource systems. Here, a planar pattern consists of many big patches, and a big patch can be regarded as combination of many patches on the plane. The consumer moves between patches asymmetrically, while the asymmetry is driven by the resource abundance. Based on experimental models with linearly-linked patches, we propose a planarly-linked-patch model with asymmetric dispersal. Using dynamical systems theory, we show global stability of equilibria in the model, and demonstrate how the resource-driven dispersal forms patterns. It is shown that appropriate asymmetry in dispersal would make the consumer persist in the system, even in sink patches. The asymmetry could also make the consumer’s total population abundance larger than that without dispersal. However, inappropriate asymmetry would make the consumer go into extinction, even in source patches. Dispersal rates are also shown to play a role in the persistence and abundance increase. Our results are consistent with experimental observations and provide new insights. Numerical simulations by the model reproduce various vegetation patterns in the real world. This work has potential applications in spatial pattern formation in biological research.
Resource-Driven Pattern Formation in Consumer-Resource Systems with Asymmetric Dispersal on a Plane
10.1137/22M1506006
SIAM Journal on Applied Mathematics
2023-10-19T07:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Weiting Song
Shikun Wang
Yuanshi Wang
Donald DeAngelis
Resource-Driven Pattern Formation in Consumer-Resource Systems with Asymmetric Dispersal on a Plane
S412
S428
10.1137/22M1506006
https://epubs.siam.org/doi/abs/10.1137/22M1506006?ai=s3&mi=3drblq&af=R
© 2023 Society for Industrial and Applied Mathematics
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A Non-Local Kinetic Model for Cell Migration: A Study of the Interplay Between Contact Guidance and Steric Hindrance
https://epubs.siam.org/doi/abs/10.1137/22M1506389?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. We propose a non-local model for contact guidance and steric hindrance depending on a single external cue, namely the extracellular matrix, that affects in a twofold way the polarization and speed of motion of the cells. We start from a microscopic description of the stochastic processes underlying the cell re-orientation mechanism related to the change of cell speed and direction. Then, we formally derive the corresponding kinetic model that implements exactly the prescribed microscopic dynamics, and, from it, it is possible to deduce the macroscopic limit in the appropriate regime. Moreover, we test our model in several scenarios. In particular, we numerically investigate the minimal microscopic mechanisms that are necessary to reproduce cell dynamics by comparing the outcomes of our model with some experimental results related to breast cancer cell migration. This allows us to validate the proposed modeling approach and to highlight its capability of predicting qualitative cell behaviors in diverse heterogeneous microenvironments.
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. We propose a non-local model for contact guidance and steric hindrance depending on a single external cue, namely the extracellular matrix, that affects in a twofold way the polarization and speed of motion of the cells. We start from a microscopic description of the stochastic processes underlying the cell re-orientation mechanism related to the change of cell speed and direction. Then, we formally derive the corresponding kinetic model that implements exactly the prescribed microscopic dynamics, and, from it, it is possible to deduce the macroscopic limit in the appropriate regime. Moreover, we test our model in several scenarios. In particular, we numerically investigate the minimal microscopic mechanisms that are necessary to reproduce cell dynamics by comparing the outcomes of our model with some experimental results related to breast cancer cell migration. This allows us to validate the proposed modeling approach and to highlight its capability of predicting qualitative cell behaviors in diverse heterogeneous microenvironments.
A Non-Local Kinetic Model for Cell Migration: A Study of the Interplay Between Contact Guidance and Steric Hindrance
10.1137/22M1506389
SIAM Journal on Applied Mathematics
2023-10-24T07:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Martina Conte
Nadia Loy
A Non-Local Kinetic Model for Cell Migration: A Study of the Interplay Between Contact Guidance and Steric Hindrance
S429
S451
10.1137/22M1506389
https://epubs.siam.org/doi/abs/10.1137/22M1506389?ai=s3&mi=3drblq&af=R
© 2023 Society for Industrial and Applied Mathematics
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Wearable Data Assimilation to Estimate the Circadian Phase
https://epubs.siam.org/doi/abs/10.1137/22M1509680?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. The circadian clock is an internal timer that coordinates the daily rhythms of behavior and physiology, including sleep and hormone secretion. Accurately tracking the state of the circadian clock, or circadian phase, holds immense potential for precision medicine. Wearable devices present an opportunity to estimate the circadian phase in the real world, as they can noninvasively monitor various physiological outputs influenced by the circadian clock. However, accurately estimating circadian phase from wearable data remains challenging, primarily due to the lack of methods that integrate minute-by-minute wearable data with prior knowledge of the circadian phase. To address this issue, we propose a framework that integrates multitime scale physiological data and estimates the circadian phase, along with an efficient implementation algorithm based on Bayesian inference and a new state space estimation method called the level set Kalman filter. Our numerical experiments indicate that our approach outperforms previous methods for circadian phase estimation consistently. Furthermore, our method enables us to examine the contribution of noise from different sources to the estimation, which was not feasible with prior methods. We found that internal noise unrelated to external stimuli is a crucial factor in determining estimation results. Last, we developed a user-friendly computational package and applied it to real-world data to demonstrate the potential value of our approach. Our results provide a foundation for systematically understanding the real-world dynamics of the circadian clock.
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. The circadian clock is an internal timer that coordinates the daily rhythms of behavior and physiology, including sleep and hormone secretion. Accurately tracking the state of the circadian clock, or circadian phase, holds immense potential for precision medicine. Wearable devices present an opportunity to estimate the circadian phase in the real world, as they can noninvasively monitor various physiological outputs influenced by the circadian clock. However, accurately estimating circadian phase from wearable data remains challenging, primarily due to the lack of methods that integrate minute-by-minute wearable data with prior knowledge of the circadian phase. To address this issue, we propose a framework that integrates multitime scale physiological data and estimates the circadian phase, along with an efficient implementation algorithm based on Bayesian inference and a new state space estimation method called the level set Kalman filter. Our numerical experiments indicate that our approach outperforms previous methods for circadian phase estimation consistently. Furthermore, our method enables us to examine the contribution of noise from different sources to the estimation, which was not feasible with prior methods. We found that internal noise unrelated to external stimuli is a crucial factor in determining estimation results. Last, we developed a user-friendly computational package and applied it to real-world data to demonstrate the potential value of our approach. Our results provide a foundation for systematically understanding the real-world dynamics of the circadian clock.
Wearable Data Assimilation to Estimate the Circadian Phase
10.1137/22M1509680
SIAM Journal on Applied Mathematics
2023-11-09T08:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Dae Wook Kim
Minki P. Lee
Daniel B. Forger
Wearable Data Assimilation to Estimate the Circadian Phase
S452
S475
10.1137/22M1509680
https://epubs.siam.org/doi/abs/10.1137/22M1509680?ai=s3&mi=3drblq&af=R
© 2023 Society for Industrial and Applied Mathematics
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Fast Solver for Diffusive Transport Times on Dynamic Intracellular Networks
https://epubs.siam.org/doi/abs/10.1137/22M1509308?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. The transport of particles in cells is influenced by the properties of intracellular networks they traverse while searching for localized target regions or reaction partners. Moreover, given the rapid turnover in many intracellular structures, it is crucial to understand how temporal changes in the network structure affect diffusive transport. In this work, we use network theory to characterize complex intracellular biological environments across scales. We develop an efficient computational method to compute the mean first passage times for simulating a particle diffusing along two-dimensional planar networks extracted from fluorescence microscopy imaging. We first benchmark this methodology in the context of synthetic networks, and subsequently apply it to live-cell data from endoplasmic reticulum tubular networks.
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. The transport of particles in cells is influenced by the properties of intracellular networks they traverse while searching for localized target regions or reaction partners. Moreover, given the rapid turnover in many intracellular structures, it is crucial to understand how temporal changes in the network structure affect diffusive transport. In this work, we use network theory to characterize complex intracellular biological environments across scales. We develop an efficient computational method to compute the mean first passage times for simulating a particle diffusing along two-dimensional planar networks extracted from fluorescence microscopy imaging. We first benchmark this methodology in the context of synthetic networks, and subsequently apply it to live-cell data from endoplasmic reticulum tubular networks.
Fast Solver for Diffusive Transport Times on Dynamic Intracellular Networks
10.1137/22M1509308
SIAM Journal on Applied Mathematics
2023-11-14T08:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Lachlan Elam
Mónica C. Quiñones-Frías
Ying Zhang
Avital A. Rodal
Thomas G. Fai
Fast Solver for Diffusive Transport Times on Dynamic Intracellular Networks
S476
S492
10.1137/22M1509308
https://epubs.siam.org/doi/abs/10.1137/22M1509308?ai=s3&mi=3drblq&af=R
© 2023 Society for Industrial and Applied Mathematics
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Detecting and Resetting Tipping Points to Create More HIV Post-Treatment Controllers with Bifurcation and Sensitivity Analysis
https://epubs.siam.org/doi/abs/10.1137/22M1485255?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. The existence of HIV post-treatment controllers (PTCs) offers hope for an HIV functional cure, and understanding the critical mechanisms determining PTC represents a key step toward this goal. Here, we have studied these mechanisms by analyzing an established mathematical model for HIV viral dynamics. In mathematical models, critical mechanisms are represented by parameters that affect the tipping points to induce qualitatively different dynamics, and in cases with multiple stability, the initial conditions of the system also play a role in determining the fate of the solution. As such, for the tipping points in parameter space, we developed and implemented a sensitivity analysis of the threshold conditions of the associated bifurcations to identify the critical mechanisms for this model. Our results suggest that the infected cell death rate and the saturation parameter for cytotoxic T lymphocyte proliferation significantly affect post-treatment control. For the case with multiple stability, in state space of initial conditions, we first investigated the saddle-type equilibrium point to identify its stable manifold, which delimits trapping regions associated to the high and low viral set points. The identified stable manifold serves as a guide for the loads of immune cells and HIV virus at the time of therapy termination to achieve post-treatment control.
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. The existence of HIV post-treatment controllers (PTCs) offers hope for an HIV functional cure, and understanding the critical mechanisms determining PTC represents a key step toward this goal. Here, we have studied these mechanisms by analyzing an established mathematical model for HIV viral dynamics. In mathematical models, critical mechanisms are represented by parameters that affect the tipping points to induce qualitatively different dynamics, and in cases with multiple stability, the initial conditions of the system also play a role in determining the fate of the solution. As such, for the tipping points in parameter space, we developed and implemented a sensitivity analysis of the threshold conditions of the associated bifurcations to identify the critical mechanisms for this model. Our results suggest that the infected cell death rate and the saturation parameter for cytotoxic T lymphocyte proliferation significantly affect post-treatment control. For the case with multiple stability, in state space of initial conditions, we first investigated the saddle-type equilibrium point to identify its stable manifold, which delimits trapping regions associated to the high and low viral set points. The identified stable manifold serves as a guide for the loads of immune cells and HIV virus at the time of therapy termination to achieve post-treatment control.
Detecting and Resetting Tipping Points to Create More HIV Post-Treatment Controllers with Bifurcation and Sensitivity Analysis
10.1137/22M1485255
SIAM Journal on Applied Mathematics
2023-11-15T08:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Wenjing Zhang
Leif A. Ellingson
Detecting and Resetting Tipping Points to Create More HIV Post-Treatment Controllers with Bifurcation and Sensitivity Analysis
S493
S514
10.1137/22M1485255
https://epubs.siam.org/doi/abs/10.1137/22M1485255?ai=s3&mi=3drblq&af=R
© 2023 Society for Industrial and Applied Mathematics
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Cell Polarity and Movement with Reaction-Diffusion and Moving Boundary: Rigorous Model Analysis and Robust Simulations
https://epubs.siam.org/doi/abs/10.1137/22M1506766?ai=s3&mi=3drblq&af=R
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. Cell polarity and movement are fundamental to many biological functions. Experimental and theoretical studies have indicated that interactions of certain proteins lead to the cell polarization which plays a key role in controlling the cell movement. We study the cell polarity and movement based on a class of biophysical models that consist of reaction-diffusion equations for different proteins and the dynamics of a moving cell boundary. Such a moving boundary is often simulated by a phase-field model. We first apply the matched asymptotic analysis to give a rigorous derivation of the sharp-interface model of the cell boundary from a phase-field model. We then develop a robust numerical approach that combines the level-set method to track the sharp boundary of a moving cell and accurate discretization techniques for solving the reaction-diffusion equations on the moving cell region. Our extensive numerical simulations predict the cell polarization under various kinds of stimuli and capture both the linear and the circular trajectories of a moving cell for a long period of time. In particular, we have identified some key parameters controlling different cell trajectories that are less accurately predicted by reduced models. Our work has linked different models and also developed tools that can be adapted for the challenging three-dimensional simulations.
SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. Cell polarity and movement are fundamental to many biological functions. Experimental and theoretical studies have indicated that interactions of certain proteins lead to the cell polarization which plays a key role in controlling the cell movement. We study the cell polarity and movement based on a class of biophysical models that consist of reaction-diffusion equations for different proteins and the dynamics of a moving cell boundary. Such a moving boundary is often simulated by a phase-field model. We first apply the matched asymptotic analysis to give a rigorous derivation of the sharp-interface model of the cell boundary from a phase-field model. We then develop a robust numerical approach that combines the level-set method to track the sharp boundary of a moving cell and accurate discretization techniques for solving the reaction-diffusion equations on the moving cell region. Our extensive numerical simulations predict the cell polarization under various kinds of stimuli and capture both the linear and the circular trajectories of a moving cell for a long period of time. In particular, we have identified some key parameters controlling different cell trajectories that are less accurately predicted by reduced models. Our work has linked different models and also developed tools that can be adapted for the challenging three-dimensional simulations.
Cell Polarity and Movement with Reaction-Diffusion and Moving Boundary: Rigorous Model Analysis and Robust Simulations
10.1137/22M1506766
SIAM Journal on Applied Mathematics
2023-11-16T08:00:00Z
© 2023 Society for Industrial and Applied Mathematics
Shuang Liu
Li-Tien Cheng
Bo Li
Cell Polarity and Movement with Reaction-Diffusion and Moving Boundary: Rigorous Model Analysis and Robust Simulations
S515
S537
10.1137/22M1506766
https://epubs.siam.org/doi/abs/10.1137/22M1506766?ai=s3&mi=3drblq&af=R
© 2023 Society for Industrial and Applied Mathematics