SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 139-164, February 2024. 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.
{"title":"A Hierarchy of Kinetic Discrete-Velocity Models for Traffic Flow Derived from a Nonlocal Prigogine–Herman Model","authors":"R. Borsche, A. Klar","doi":"10.1137/23m1583065","DOIUrl":"https://doi.org/10.1137/23m1583065","url":null,"abstract":"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.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139584175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Isaac Klapper, Daniel B. Szyld, Xinli Yu, Karsten Zengler, Tianyu Zhang, Cristal Zúñiga
SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 97-113, February 2024. 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.
{"title":"A Domain Decomposition Method for Solution of a PDE-Constrained Generalized Nash Equilibrium Model of Biofilm Community Metabolism","authors":"Isaac Klapper, Daniel B. Szyld, Xinli Yu, Karsten Zengler, Tianyu Zhang, Cristal Zúñiga","doi":"10.1137/22m1511023","DOIUrl":"https://doi.org/10.1137/22m1511023","url":null,"abstract":"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.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139555071","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 75-96, February 2024. 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.
{"title":"Layer Stripping Approach to Reconstruct Shape Variations in Waveguides Using Locally Resonant Frequencies","authors":"Angéle Niclas, Laurent Seppecher","doi":"10.1137/23m1546336","DOIUrl":"https://doi.org/10.1137/23m1546336","url":null,"abstract":"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.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139517709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 60-74, February 2024. 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.
{"title":"Nonlinear Monotone Energy Stability of Plane Shear Flows: Joseph or Orr Critical Thresholds?","authors":"Giuseppe Mulone","doi":"10.1137/22m1535826","DOIUrl":"https://doi.org/10.1137/22m1535826","url":null,"abstract":"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.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139499964","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 39-59, February 2024. 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.
{"title":"Multiplicity of Neutrally Stable Periodic Orbits with Coexistence in the Chemostat Subject to Periodic Removal Rate","authors":"Thomas Guilmeau, Alain Rapaport","doi":"10.1137/23m1552450","DOIUrl":"https://doi.org/10.1137/23m1552450","url":null,"abstract":"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.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139482962","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Michael Fischer, Laura Kanzler, Christian Schmeiser
SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 1-18, February 2024. 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.
{"title":"One-Dimensional Short-Range Nearest-Neighbor Interaction and Its Nonlinear Diffusion Limit","authors":"Michael Fischer, Laura Kanzler, Christian Schmeiser","doi":"10.1137/23m155520x","DOIUrl":"https://doi.org/10.1137/23m155520x","url":null,"abstract":"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.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139459585","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Luiz Maltez-Faria, Carlos Pérez-Arancibia, Catalin Turc
SIAM Journal on Applied Mathematics, Volume 84, Issue 1, Page 19-38, February 2024. 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.
{"title":"Combined Field-Only Boundary Integral Equations for PEC Electromagnetic Scattering Problem in Spherical Geometries","authors":"Luiz Maltez-Faria, Carlos Pérez-Arancibia, Catalin Turc","doi":"10.1137/23m1561865","DOIUrl":"https://doi.org/10.1137/23m1561865","url":null,"abstract":"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.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139459580","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2522-2544, December 2023. Abstract. This paper concerns the qualitative analysis on a reaction-diffusion SIS (susceptible-infected-susceptible) epidemic model governed by the saturated incidence infection mechanism in advective environments. A variational expression of the basic reproduction number [math] was derived and the global dynamics of the system in terms of [math] was established: the disease-free equilibrium is unique and linearly stable if [math] and at least an endemic equilibrium exists if [math]. More precisely, we explore qualitative properties of the basic reproduction number and investigate the spatial distribution of the individuals with respect to the dispersal and advection. We find that the concentration phenomenon occurs when the advection is large and the infectious disease will be eradicated for the small dispersal of infected individual. Our theoretical results may shed some new insight into the infectious disease prediction and control strategy.
{"title":"Analysis on a Spatial SIS Epidemic Model with Saturated Incidence Function in Advective Environments: I. Conserved Total Population","authors":"Xiaodan Chen, Renhao Cui","doi":"10.1137/22m1534699","DOIUrl":"https://doi.org/10.1137/22m1534699","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2522-2544, December 2023. <br/> Abstract. This paper concerns the qualitative analysis on a reaction-diffusion SIS (susceptible-infected-susceptible) epidemic model governed by the saturated incidence infection mechanism in advective environments. A variational expression of the basic reproduction number [math] was derived and the global dynamics of the system in terms of [math] was established: the disease-free equilibrium is unique and linearly stable if [math] and at least an endemic equilibrium exists if [math]. More precisely, we explore qualitative properties of the basic reproduction number and investigate the spatial distribution of the individuals with respect to the dispersal and advection. We find that the concentration phenomenon occurs when the advection is large and the infectious disease will be eradicated for the small dispersal of infected individual. Our theoretical results may shed some new insight into the infectious disease prediction and control strategy.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138555402","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2499-2521, December 2023. Abstract. We present an effective model of “space-coiled metacrystals” composed of a periodic array of sound rigid blocks into which long slots have been coiled up. The periodic cell of the block contains a coiled slot whose straight parts are at wavelength scale, which enables the appearance of Bragg resonances. These resonances, which prevent high transmission, compete with the Fabry–Pérot resonances of the entire slot, which foster perfect transmission. This results in complex scattering properties driven by the characteristics of the turning regions that act as atoms in a one-dimensional coiled crystal. Using appropriate scaling and combining two-scale homogenization with matched asymptotic techniques, the modeling of such metacrystals is proposed. The resulting model is validated through a comparison with full-wave numerics in both harmonic and transient regimes.
{"title":"Modeling Acoustic Space-Coiled Metacrystals","authors":"Joar Zhou Hagström, Kim Pham, Agnés Maurel","doi":"10.1137/22m1527131","DOIUrl":"https://doi.org/10.1137/22m1527131","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2499-2521, December 2023. <br/> Abstract. We present an effective model of “space-coiled metacrystals” composed of a periodic array of sound rigid blocks into which long slots have been coiled up. The periodic cell of the block contains a coiled slot whose straight parts are at wavelength scale, which enables the appearance of Bragg resonances. These resonances, which prevent high transmission, compete with the Fabry–Pérot resonances of the entire slot, which foster perfect transmission. This results in complex scattering properties driven by the characteristics of the turning regions that act as atoms in a one-dimensional coiled crystal. Using appropriate scaling and combining two-scale homogenization with matched asymptotic techniques, the modeling of such metacrystals is proposed. The resulting model is validated through a comparison with full-wave numerics in both harmonic and transient regimes.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138545315","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Piyush R. Borole, James M. Rosado, MeiRose Neal, Gillian Queisser
SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2418-2442, December 2023. Abstract. In this paper, a coupled electro-calcium model was developed and implemented to computationally explore the effects of neuronal synapse loss, in particular in the context of Alzheimer’s disease. Established parameters affected by Alzheimer’s disease, such as synapse loss, calcium leaks at deteriorating synaptic contacts, and downregulation of the calcium buffer calbindin, are subject to this study. Reconstructed neurons are used to define the computational domain for a system of PDEs and ODEs, discretized by finite differences and solved with a semi-implicit second-order time integrator. The results show neuronal resilience during synapse loss. When incorporating calcium leaks at affected synapses, neurons lose their ability to produce synapse-to-nucleus calcium signals, necessary for learning, plasticity, and neuronal survival. Downregulation of calbindin concentrations partially recovers the signaling pathway to the cell nucleus. These results could define future research pathways toward stabilizing the calcium signaling pathways during Alzheimer’s disease. The coupled electro-calcium model was implemented and solved using MATLAB https://github.com/NeuroBox3D/CalcSim.
{"title":"Neuronal Resilience and Calcium Signaling Pathways in the Context of Synapse Loss and Calcium Leaks: A Computational MODELING Study and Implications for Alzheimer’s Disease","authors":"Piyush R. Borole, James M. Rosado, MeiRose Neal, Gillian Queisser","doi":"10.1137/23m1557842","DOIUrl":"https://doi.org/10.1137/23m1557842","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2418-2442, December 2023. <br/> Abstract. In this paper, a coupled electro-calcium model was developed and implemented to computationally explore the effects of neuronal synapse loss, in particular in the context of Alzheimer’s disease. Established parameters affected by Alzheimer’s disease, such as synapse loss, calcium leaks at deteriorating synaptic contacts, and downregulation of the calcium buffer calbindin, are subject to this study. Reconstructed neurons are used to define the computational domain for a system of PDEs and ODEs, discretized by finite differences and solved with a semi-implicit second-order time integrator. The results show neuronal resilience during synapse loss. When incorporating calcium leaks at affected synapses, neurons lose their ability to produce synapse-to-nucleus calcium signals, necessary for learning, plasticity, and neuronal survival. Downregulation of calbindin concentrations partially recovers the signaling pathway to the cell nucleus. These results could define future research pathways toward stabilizing the calcium signaling pathways during Alzheimer’s disease. The coupled electro-calcium model was implemented and solved using MATLAB https://github.com/NeuroBox3D/CalcSim.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138528033","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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