SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 1039-1059, June 2024. Abstract. Consider a system of two parallel solid cylinders of equal radius made of a homogeneous material. We study the stability of a liquid bridge of circular cylinder shape between both solid cylinders. It is proved that if the circular cylinder liquid is concave, then it is stable. If the circular cylinder liquid is convex, we establish conditions on the radius of the cylinder liquid and the contact angle that ensure that long convex circular cylinders are not stable. Estimates for the length of these convex cylinders are given.
{"title":"Stability of a Capillary Circular Cylinder between Two Parallel Cylinders","authors":"Rafael López","doi":"10.1137/23m1602139","DOIUrl":"https://doi.org/10.1137/23m1602139","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 1039-1059, June 2024. <br/> Abstract. Consider a system of two parallel solid cylinders of equal radius made of a homogeneous material. We study the stability of a liquid bridge of circular cylinder shape between both solid cylinders. It is proved that if the circular cylinder liquid is concave, then it is stable. If the circular cylinder liquid is convex, we establish conditions on the radius of the cylinder liquid and the contact angle that ensure that long convex circular cylinders are not stable. Estimates for the length of these convex cylinders are given.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925364","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}
Tianyu Kong, Diyi Liu, Mitchell Luskin, Alexander B. Watson
SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 1011-1038, June 2024. Abstract. We consider the problem of numerically computing the quantum dynamics of an electron in twisted bilayer graphene. The challenge is that atomic-scale models of the dynamics are aperiodic for generic twist angles because of the incommensurability of the layers. The Bistritzer–MacDonald PDE model, which is periodic with respect to the bilayer’s moiré pattern, has recently been shown to rigorously describe these dynamics in a parameter regime. In this work, we first prove that the dynamics of the tight-binding model of incommensurate twisted bilayer graphene can be approximated by computations on finite domains. The main ingredient of this proof is a speed of propagation estimate proved using Combes–Thomas estimates. We then provide extensive numerical computations, which clarify the range of validity of the Bistritzer–MacDonald model.
{"title":"Modeling of Electronic Dynamics in Twisted Bilayer Graphene","authors":"Tianyu Kong, Diyi Liu, Mitchell Luskin, Alexander B. Watson","doi":"10.1137/23m1595941","DOIUrl":"https://doi.org/10.1137/23m1595941","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 1011-1038, June 2024. <br/> Abstract. We consider the problem of numerically computing the quantum dynamics of an electron in twisted bilayer graphene. The challenge is that atomic-scale models of the dynamics are aperiodic for generic twist angles because of the incommensurability of the layers. The Bistritzer–MacDonald PDE model, which is periodic with respect to the bilayer’s moiré pattern, has recently been shown to rigorously describe these dynamics in a parameter regime. In this work, we first prove that the dynamics of the tight-binding model of incommensurate twisted bilayer graphene can be approximated by computations on finite domains. The main ingredient of this proof is a speed of propagation estimate proved using Combes–Thomas estimates. We then provide extensive numerical computations, which clarify the range of validity of the Bistritzer–MacDonald model.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925365","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 3, Page 988-1010, June 2024. Abstract. Spatial memory is key in animal movement modeling, but it has been challenging to explicitly model learning to describe memory acquisition. In this paper, we study novel cognitive consumer-resource models with different consumer learning mechanisms and investigate their dynamics. These models consist of two PDEs in composition with one ODE such that the spectrum of the corresponding linearized operator at a constant steady state is unclear. We describe the spectra of the linearized operators and analyze the eigenvalue problems to determine the stability of the constant steady states. We then perform bifurcation analysis by taking the perceptual diffusion rate as the bifurcation parameter. It is found that steady-state and Hopf bifurcations can both occur in these systems, and the bifurcation points are given so that the stability region can be determined. Moreover, rich spatial and spatiotemporal patterns can be generated in such systems via different types of bifurcation. Our effort establishes a new approach to tackling a hybrid model of PDE-ODE composition and provides a deeper understanding of cognitive movement-driven consumer-resource dynamics.
{"title":"Local Perception and Learning Mechanisms in Resource-Consumer Dynamics","authors":"Qingyan Shi, Yongli Song, Hao Wang","doi":"10.1137/23m1598593","DOIUrl":"https://doi.org/10.1137/23m1598593","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 988-1010, June 2024. <br/> Abstract. Spatial memory is key in animal movement modeling, but it has been challenging to explicitly model learning to describe memory acquisition. In this paper, we study novel cognitive consumer-resource models with different consumer learning mechanisms and investigate their dynamics. These models consist of two PDEs in composition with one ODE such that the spectrum of the corresponding linearized operator at a constant steady state is unclear. We describe the spectra of the linearized operators and analyze the eigenvalue problems to determine the stability of the constant steady states. We then perform bifurcation analysis by taking the perceptual diffusion rate as the bifurcation parameter. It is found that steady-state and Hopf bifurcations can both occur in these systems, and the bifurcation points are given so that the stability region can be determined. Moreover, rich spatial and spatiotemporal patterns can be generated in such systems via different types of bifurcation. Our effort establishes a new approach to tackling a hybrid model of PDE-ODE composition and provides a deeper understanding of cognitive movement-driven consumer-resource dynamics.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925136","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 3, Page 940-960, June 2024. Abstract. We propose and analyze a new methodology based on linear-quadratic regulation (LQR) for stabilizing falling liquid films via blowing and suction at the base. LQR methods enable rapidly responding feedback control by precomputing a gain matrix, but they are only suitable for systems of linear ordinary differential equations (ODEs). By contrast, the Navier–Stokes equations that describe the dynamics of a thin liquid film flowing down an inclined plane are too complex to stabilize with standard control-theoretical techniques. To bridge this gap, we use reduced-order models—the Benney equation and a weighted-residual integral boundary layer model—obtained via asymptotic analysis to derive a multilevel control framework. This framework consists of an LQR feedback control designed for a linearized and discretized system of ODEs approximating the reduced-order system, which is then applied to the full Navier–Stokes system. The control scheme is tested via direct numerical simulation (DNS) and compared to analytical predictions of linear stability thresholds and minimum required actuator numbers. Comparing the strategy between the two reduced-order models, we show that in both cases we can successfully stabilize towards a uniform flat film across their respective ranges of valid parameters, with the more accurate weighted-residual model outperforming the Benney-derived controls. The weighted-residual controls are also found to work successfully far beyond their anticipated range of applicability. The proposed methodology increases the feasibility of transferring robust control techniques towards real-world systems and is also generalizable to other forms of actuation.
{"title":"Linear Quadratic Regulation Control for Falling Liquid Films","authors":"Oscar A. Holroyd, Radu Cimpeanu, Susana N. Gomes","doi":"10.1137/23m1548475","DOIUrl":"https://doi.org/10.1137/23m1548475","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 940-960, June 2024. <br/>Abstract. We propose and analyze a new methodology based on linear-quadratic regulation (LQR) for stabilizing falling liquid films via blowing and suction at the base. LQR methods enable rapidly responding feedback control by precomputing a gain matrix, but they are only suitable for systems of linear ordinary differential equations (ODEs). By contrast, the Navier–Stokes equations that describe the dynamics of a thin liquid film flowing down an inclined plane are too complex to stabilize with standard control-theoretical techniques. To bridge this gap, we use reduced-order models—the Benney equation and a weighted-residual integral boundary layer model—obtained via asymptotic analysis to derive a multilevel control framework. This framework consists of an LQR feedback control designed for a linearized and discretized system of ODEs approximating the reduced-order system, which is then applied to the full Navier–Stokes system. The control scheme is tested via direct numerical simulation (DNS) and compared to analytical predictions of linear stability thresholds and minimum required actuator numbers. Comparing the strategy between the two reduced-order models, we show that in both cases we can successfully stabilize towards a uniform flat film across their respective ranges of valid parameters, with the more accurate weighted-residual model outperforming the Benney-derived controls. The weighted-residual controls are also found to work successfully far beyond their anticipated range of applicability. The proposed methodology increases the feasibility of transferring robust control techniques towards real-world systems and is also generalizable to other forms of actuation.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140942552","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 3, Page 961-987, June 2024. Abstract. The quantitative modeling and design of modern short-pulse fiber lasers cannot be performed with averaged models because of large variations in the pulse parameters within each round trip. Instead, lumped models obtained by concatenating models for the various components of the laser are required. Since the optical pulses in lumped models are periodic, their linear stability is investigated using the monodromy operator, which is the linearization of the roundtrip operator about the pulse. A gradient-based optimization method is developed to discover periodic pulses. The computation of the gradient of the objective function involves numerical computation of the action of both the roundtrip operator and the adjoint of the monodromy operator. A novel Fourier split-step method is introduced to compute solutions of the linearization of the nonlinear, nonlocal, stiff equation that models optical propagation in the fiber amplifier. This method is derived by linearizing the two solution operators in a split-step method for the nonlinear equation. The spectrum of the monodromy operator consists of the essential spectrum, for which there is an analytical formula, and the eigenvalues. There is a multiplicity two eigenvalue at [math], which is due to phase and translation invariance. The remaining eigenvalues are determined from a matrix discretization of the monodromy operator. Simulation results verify the accuracy of the numerical methods; show examples of periodically stationary pulses, their spectra, and their eigenfunctions; and discuss their stability.
{"title":"Floquet Stability of Periodically Stationary Pulses in a Short-Pulse Fiber Laser","authors":"Vrushaly Shinglot, John Zweck","doi":"10.1137/23m1598106","DOIUrl":"https://doi.org/10.1137/23m1598106","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 961-987, June 2024. <br/> Abstract. The quantitative modeling and design of modern short-pulse fiber lasers cannot be performed with averaged models because of large variations in the pulse parameters within each round trip. Instead, lumped models obtained by concatenating models for the various components of the laser are required. Since the optical pulses in lumped models are periodic, their linear stability is investigated using the monodromy operator, which is the linearization of the roundtrip operator about the pulse. A gradient-based optimization method is developed to discover periodic pulses. The computation of the gradient of the objective function involves numerical computation of the action of both the roundtrip operator and the adjoint of the monodromy operator. A novel Fourier split-step method is introduced to compute solutions of the linearization of the nonlinear, nonlocal, stiff equation that models optical propagation in the fiber amplifier. This method is derived by linearizing the two solution operators in a split-step method for the nonlinear equation. The spectrum of the monodromy operator consists of the essential spectrum, for which there is an analytical formula, and the eigenvalues. There is a multiplicity two eigenvalue at [math], which is due to phase and translation invariance. The remaining eigenvalues are determined from a matrix discretization of the monodromy operator. Simulation results verify the accuracy of the numerical methods; show examples of periodically stationary pulses, their spectra, and their eigenfunctions; and discuss their stability.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140940043","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 3, Page 915-939, June 2024. Abstract. Foraging is crucial for animals to survive. Many species forage in groups, as individuals communicate to share information about the location of available resources. For example, eusocial foragers, such as honey bees and many ants, recruit members from their central hive or nest to a known foraging site. However, the optimal level of communication and recruitment depends on the overall group size, the distribution of available resources, and the extent of interference between multiple individuals attempting to forage from a site. In this paper, we develop a discrete-time Markov chain model of eusocial foragers, who communicate information with a certain probability. We compare the stochastic model and its corresponding infinite population limit. We find that foraging efficiency tapers off when recruitment probability is too high, a phenomenon that does not occur in the infinite population model, even though it occurs for any finite population size. The marginal inefficiency at high recruitment probability increases as the population increases, similar to a boundary layer. In particular, we prove there is a significant gap between the foraging efficiency of finite and infinite population models in the extreme case of complete communication. We also analyze this phenomenon by approximating the stationary distribution of foragers over sites in terms of mean escape times from multiple quasi-steady states. We conclude that, for any finite group of foragers, an individual who has found a resource should only sometimes recruit others to the same resource. We discuss the relationship between our analysis and multiagent multiarm bandit problems.
{"title":"Finite Population Size Effects on Optimal Communication for Social Foragers","authors":"Hyunjoong Kim, Yoichiro Mori, Joshua B. Plotkin","doi":"10.1137/23m1590007","DOIUrl":"https://doi.org/10.1137/23m1590007","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 915-939, June 2024. <br/> Abstract. Foraging is crucial for animals to survive. Many species forage in groups, as individuals communicate to share information about the location of available resources. For example, eusocial foragers, such as honey bees and many ants, recruit members from their central hive or nest to a known foraging site. However, the optimal level of communication and recruitment depends on the overall group size, the distribution of available resources, and the extent of interference between multiple individuals attempting to forage from a site. In this paper, we develop a discrete-time Markov chain model of eusocial foragers, who communicate information with a certain probability. We compare the stochastic model and its corresponding infinite population limit. We find that foraging efficiency tapers off when recruitment probability is too high, a phenomenon that does not occur in the infinite population model, even though it occurs for any finite population size. The marginal inefficiency at high recruitment probability increases as the population increases, similar to a boundary layer. In particular, we prove there is a significant gap between the foraging efficiency of finite and infinite population models in the extreme case of complete communication. We also analyze this phenomenon by approximating the stationary distribution of foragers over sites in terms of mean escape times from multiple quasi-steady states. We conclude that, for any finite group of foragers, an individual who has found a resource should only sometimes recruit others to the same resource. We discuss the relationship between our analysis and multiagent multiarm bandit problems.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140940084","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}
Javier A. Almonacid, Sebastián A. Domínguez-Rivera, Ryan N. Konno, Nilima Nigam, Stephanie A. Ross, Cassidy Tam, James M. Wakeling
SIAM Journal on Applied Mathematics, Ahead of Print. Abstract. Skeletal muscles are living tissues that can undergo large deformations in short periods of time and that can be activated to produce force. In this paper we use the principles of continuum mechanics to propose a dynamic, fully nonlinear, and three-dimensional model to describe the deformation of these tissues. We model muscles as a fiber-reinforced composite and transversely isotropic material. We introduce a flexible computational framework to approximate the deformations of skeletal muscle to provide new insights into the underlying mechanics of these tissues. The model parameters and mechanical properties are obtained through experimental data and can be specified locally. A semi-implicit in-time, conforming, finite element in space scheme is used to approximate the solutions to the governing nonlinear dynamic model. We provide a series of numerical experiments demonstrating the application of this framework to relevant problems in biomechanics and also discuss questions around model validation.
{"title":"A Three-Dimensional Model of Skeletal Muscle Tissues","authors":"Javier A. Almonacid, Sebastián A. Domínguez-Rivera, Ryan N. Konno, Nilima Nigam, Stephanie A. Ross, Cassidy Tam, James M. Wakeling","doi":"10.1137/22m1506985","DOIUrl":"https://doi.org/10.1137/22m1506985","url":null,"abstract":"SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. Skeletal muscles are living tissues that can undergo large deformations in short periods of time and that can be activated to produce force. In this paper we use the principles of continuum mechanics to propose a dynamic, fully nonlinear, and three-dimensional model to describe the deformation of these tissues. We model muscles as a fiber-reinforced composite and transversely isotropic material. We introduce a flexible computational framework to approximate the deformations of skeletal muscle to provide new insights into the underlying mechanics of these tissues. The model parameters and mechanical properties are obtained through experimental data and can be specified locally. A semi-implicit in-time, conforming, finite element in space scheme is used to approximate the solutions to the governing nonlinear dynamic model. We provide a series of numerical experiments demonstrating the application of this framework to relevant problems in biomechanics and also discuss questions around model validation.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140882290","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 3, Page 856-889, June 2024. Abstract. The Gray–Scott model is a set of reaction-diffusion equations that describes chemical systems far from equilibrium. Interest in this model stems from its ability to generate spatio-temporal structures, including pulses, spots, stripes, and self-replicating patterns. We consider an extension of this model in which the spread of the different chemicals is assumed to be nonlocal and can thus be represented by an integral operator. In particular, we focus on the case of strictly positive, symmetric, [math] convolution kernels that have a finite second moment. Modeling the equations on a finite interval, we prove the existence of small-time weak solutions in the case of nonlocal Dirichlet and Neumann boundary constraints. We then use this result to develop a finite element numerical scheme that helps us explore the effects of nonlocal diffusion on the formation of pulse solutions.
{"title":"Analysis and Simulation of a Nonlocal Gray–Scott Model","authors":"Loic Cappanera, Gabriela Jaramillo, Cory Ward","doi":"10.1137/22m1542441","DOIUrl":"https://doi.org/10.1137/22m1542441","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 856-889, June 2024. <br/>Abstract. The Gray–Scott model is a set of reaction-diffusion equations that describes chemical systems far from equilibrium. Interest in this model stems from its ability to generate spatio-temporal structures, including pulses, spots, stripes, and self-replicating patterns. We consider an extension of this model in which the spread of the different chemicals is assumed to be nonlocal and can thus be represented by an integral operator. In particular, we focus on the case of strictly positive, symmetric, [math] convolution kernels that have a finite second moment. Modeling the equations on a finite interval, we prove the existence of small-time weak solutions in the case of nonlocal Dirichlet and Neumann boundary constraints. We then use this result to develop a finite element numerical scheme that helps us explore the effects of nonlocal diffusion on the formation of pulse solutions.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140882515","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 3, Page 890-914, June 2024. Abstract. We consider an [math]-periodic ([math]) tubular structure, modeled as a magnetic Laplacian on a metric graph, which is periodic along a single axis. We show that the corresponding Hamiltonian admits norm-resolvent convergence to an ODE on [math] which is fourth order at a discrete set of values of the magnetic potential (critical points) and second order generically. In a vicinity of critical points we establish a mixed-order asymptotics. The rate of convergence is also estimated. This represents a physically viable model of a phase transition as the strength of the (constant) magnetic field increases.
{"title":"Phase Transition in a Periodic Tubular Structure","authors":"Alexander V. Kiselev, Kirill Ryadovkin","doi":"10.1137/23m157274x","DOIUrl":"https://doi.org/10.1137/23m157274x","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 890-914, June 2024. <br/> Abstract. We consider an [math]-periodic ([math]) tubular structure, modeled as a magnetic Laplacian on a metric graph, which is periodic along a single axis. We show that the corresponding Hamiltonian admits norm-resolvent convergence to an ODE on [math] which is fourth order at a discrete set of values of the magnetic potential (critical points) and second order generically. In a vicinity of critical points we establish a mixed-order asymptotics. The rate of convergence is also estimated. This represents a physically viable model of a phase transition as the strength of the (constant) magnetic field increases.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140882314","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}
L. Baldassari, M. V. de Hoop, E. Francini, S. Vessella
SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 831-855, June 2024. Abstract. Through coupled physics, we study an early-warning inverse source problem for the constant-coefficient elasto-gravitational equations. It consists of a mixed hyperbolic-elliptic system of partial differential equations describing elastic wave displacement and gravity perturbations produced by a source in a homogeneous bounded medium. Within the Cowling approximation, we prove uniqueness and Lipschitz stability for the inverse problem of recovering the moment tensor and the location of the source from early-time measurements of the changes of the gravitational field. The setup studied in this paper is motivated by gravity-based earthquake early warning systems, which are gaining much attention recently.
{"title":"Early-Warning Inverse Source Problem for the Elasto-Gravitational Equations","authors":"L. Baldassari, M. V. de Hoop, E. Francini, S. Vessella","doi":"10.1137/23m1564651","DOIUrl":"https://doi.org/10.1137/23m1564651","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 831-855, June 2024. <br/> Abstract. Through coupled physics, we study an early-warning inverse source problem for the constant-coefficient elasto-gravitational equations. It consists of a mixed hyperbolic-elliptic system of partial differential equations describing elastic wave displacement and gravity perturbations produced by a source in a homogeneous bounded medium. Within the Cowling approximation, we prove uniqueness and Lipschitz stability for the inverse problem of recovering the moment tensor and the location of the source from early-time measurements of the changes of the gravitational field. The setup studied in this paper is motivated by gravity-based earthquake early warning systems, which are gaining much attention recently.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140833290","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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