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A Three-Dimensional Model of Skeletal Muscle Tissues 骨骼肌组织的三维模型
IF 1.9 4区 数学
SIAM Journal on Applied Mathematics Pub Date : 2024-05-07 DOI: 10.1137/22m1506985
Javier A. Almonacid, Sebastián A. Domínguez-Rivera, Ryan N. Konno, Nilima Nigam, Stephanie A. Ross, Cassidy Tam, James M. Wakeling
{"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":"3 1","pages":""},"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}
引用次数: 0
Analysis and Simulation of a Nonlocal Gray–Scott Model 非局部格雷-斯科特模型的分析与模拟
IF 1.9 4区 数学
SIAM Journal on Applied Mathematics Pub Date : 2024-05-06 DOI: 10.1137/22m1542441
Loic Cappanera, Gabriela Jaramillo, Cory Ward
{"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":"47 1","pages":""},"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}
引用次数: 0
Phase Transition in a Periodic Tubular Structure 周期管状结构中的相变
IF 1.9 4区 数学
SIAM Journal on Applied Mathematics Pub Date : 2024-05-06 DOI: 10.1137/23m157274x
Alexander V. Kiselev, Kirill Ryadovkin
{"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":"20 1","pages":""},"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}
引用次数: 0
Early-Warning Inverse Source Problem for the Elasto-Gravitational Equations 弹性引力方程的预警反源问题
IF 1.9 4区 数学
SIAM Journal on Applied Mathematics Pub Date : 2024-05-03 DOI: 10.1137/23m1564651
L. Baldassari, M. V. de Hoop, E. Francini, S. Vessella
{"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":"36 1","pages":""},"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}
引用次数: 0
On Long Waves and Solitons in Particle Lattices with Forces of Infinite Range 论具有无限范围力的粒子晶格中的长波和孤子
IF 1.9 4区 数学
SIAM Journal on Applied Mathematics Pub Date : 2024-05-03 DOI: 10.1137/23m1607209
Benjamin Ingimarson, Robert L. Pego
{"title":"On Long Waves and Solitons in Particle Lattices with Forces of Infinite Range","authors":"Benjamin Ingimarson, Robert L. Pego","doi":"10.1137/23m1607209","DOIUrl":"https://doi.org/10.1137/23m1607209","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 808-830, June 2024. <br/> Abstract. We study waves on infinite one-dimensional lattices of particles that each interact with all others through power-law forces [math]. The inverse-cube case corresponds to Calogero–Moser systems which are well known to be completely integrable for any finite number of particles. The formal long-wave limit for unidirectional waves in these lattices is the Korteweg–de Vries equation if [math], but with [math] it is a nonlocal dispersive PDE that reduces to the Benjamin–Ono equation for [math]. For the infinite Calogero–Moser lattice, we find explicit formulas that describe solitary and periodic traveling waves.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"36 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140833362","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}
引用次数: 0
Stoichiometry-Dependent Fear Effect in a Food Chain Model 食物链模型中依赖化学计量的恐惧效应
IF 1.9 4区 数学
SIAM Journal on Applied Mathematics Pub Date : 2024-05-02 DOI: 10.1137/23m1581613
Tianxu Wang, Hao Wang
{"title":"Stoichiometry-Dependent Fear Effect in a Food Chain Model","authors":"Tianxu Wang, Hao Wang","doi":"10.1137/23m1581613","DOIUrl":"https://doi.org/10.1137/23m1581613","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 783-807, June 2024. <br/>Abstract. Evidence shows that resource quality can determine the costs and benefits of the fear effect on consumer dynamics. However, mechanistic modeling and analysis are lacking. This paper formulates a tritrophic level food chain model that integrates both stoichiometric food quality and fear effect. We establish the well-posedness of the model and examine the existence and stability of equilibria. Through extensive numerical simulations, we validate our findings and visually explore the interactive effects of fear and food quality. Our results reveal that the fear effect from predators stabilizes the system. Furthermore, we demonstrate that the fear effect amplifies the influence of food quality on consumers. When food quality is favorable, the fear effect enhances consumer production efficiency, whereas, in the case of poor food quality, the fear effect exacerbates the decline in production efficiency caused by low-nutrient food.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"62 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140833330","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}
引用次数: 0
Multistability for Nematic Liquid Crystals in Cuboids with Degenerate Planar Boundary Conditions 具有退化平面边界条件的立方体中向列液晶的多稳定性
IF 1.9 4区 数学
SIAM Journal on Applied Mathematics Pub Date : 2024-04-26 DOI: 10.1137/23m1604606
Baoming Shi, Yucen Han, Apala Majumdar, Lei Zhang
{"title":"Multistability for Nematic Liquid Crystals in Cuboids with Degenerate Planar Boundary Conditions","authors":"Baoming Shi, Yucen Han, Apala Majumdar, Lei Zhang","doi":"10.1137/23m1604606","DOIUrl":"https://doi.org/10.1137/23m1604606","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 756-781, April 2024. <br/> Abstract. We study nematic configurations within three-dimensional (3D) cuboids, with planar degenerate boundary conditions on the cuboid faces, in the Landau–de Gennes framework. There are two geometry-dependent variables: the edge length of the square cross-section, [math], and the parameter [math], which is a measure of the cuboid height. Theoretically, we prove the existence and uniqueness of the global minimizer with a small enough cuboid size. We develop a new numerical scheme for the high-index saddle dynamics to deal with the surface energies. We report on a plethora of (meta)stable states, and their dependence on [math] and [math], and in particular how the 3D states are connected with their two-dimensional counterparts on squares and rectangles. Notably, we find families of almost uniaxial stable states constructed from the topological classification of tangent unit-vector fields and study transition pathways between them. We also provide a phase diagram of competing (meta)stable states as a function of [math] and [math].","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"32 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140805645","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}
引用次数: 0
Multiplicity of Endemic Equilibria for a Diffusive SIS Epidemic Model with Mass-Action 具有大规模行动的扩散性 SIS 流行病模型的地方性均衡的多重性
IF 1.9 4区 数学
SIAM Journal on Applied Mathematics Pub Date : 2024-04-16 DOI: 10.1137/23m1613888
Keoni Castellano, Rachidi B. Salako
{"title":"Multiplicity of Endemic Equilibria for a Diffusive SIS Epidemic Model with Mass-Action","authors":"Keoni Castellano, Rachidi B. Salako","doi":"10.1137/23m1613888","DOIUrl":"https://doi.org/10.1137/23m1613888","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 732-755, April 2024. <br/> Abstract. We study a diffusive Susceptible-Infected-Susceptible (SIS) epidemic model with the mass-action transmission mechanism and show, under appropriate assumptions on the parameters, the existence of multiple endemic equilibria (EE). Our results answer some open questions on previous studies related to disease extinction or persistence when [math] and the multiplicity of EE solutions when [math]. Interestingly, even with such a simple nonlinearity induced by the mass-action, we show that the diffusive epidemic model may have an S-shaped or backward bifurcation curve of EE solutions. This strongly highlights the impacts of environmental heterogeneity on the spread of infectious diseases as the basic reproduction number alone is insufficient as a threshold quantity to predict its extinction. Our results also shed some light on the significance of disease transmission mechanisms.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"176 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140613108","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}
引用次数: 0
Moving Singularities of the Forced Fisher–KPP Equation: An Asymptotic Approach 强迫费希尔-KPP方程的移动奇点：渐近方法
IF 1.9 4区 数学
SIAM Journal on Applied Mathematics Pub Date : 2024-04-15 DOI: 10.1137/23m1552905
Markus Kaczvinszki, Stefan Braun
{"title":"Moving Singularities of the Forced Fisher–KPP Equation: An Asymptotic Approach","authors":"Markus Kaczvinszki, Stefan Braun","doi":"10.1137/23m1552905","DOIUrl":"https://doi.org/10.1137/23m1552905","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 710-731, April 2024. <br/> Abstract. The creation of hairpin or lambda vortices, typical for the early stages of the laminar-turbulent transition process in various boundary layer flows, in some sense may be associated with blow-up solutions of the Fisher–Kolmogorov–Petrovsky–Piskunov equation. In contrast to the usual applications of this nonlinear evolution equation of the reaction-diffusion type, the solution quantity in the present context needs to stay neither bounded nor positive. We focus on the solution behavior beyond a finite-time point blow-up event, which consists of two moving singularities (representing the cores of the vortex legs) propagating in opposite directions, and their initial motion is determined with the method of matched asymptotic expansions. After resolving subtleties concerning the transition between logarithmic and algebraic expansion terms regarding asymptotic layers, we find that the internal singularity structure resembles a combination of second- and first-order poles in the form of a singular traveling wave with a time-dependent speed imprinted through the characteristics of the preceding blow-up event.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"57 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140593502","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}
引用次数: 0
Stability for Inverse Source Problems of the Stochastic Helmholtz Equation with a White Noise 带有白噪声的随机亥姆霍兹方程反源问题的稳定性
IF 1.9 4区 数学
SIAM Journal on Applied Mathematics Pub Date : 2024-04-11 DOI: 10.1137/23m1586331
Peijun Li, Ying Liang
{"title":"Stability for Inverse Source Problems of the Stochastic Helmholtz Equation with a White Noise","authors":"Peijun Li, Ying Liang","doi":"10.1137/23m1586331","DOIUrl":"https://doi.org/10.1137/23m1586331","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 2, Page 687-709, April 2024. <br/> Abstract. This paper is concerned with the stability estimates for inverse source problems of the stochastic Helmholtz equation driven by white noise. The well-posedness is established for the direct source problems, which ensures the existence and uniqueness of solutions. The stability estimates are deduced for the inverse source problems, which aim to determine the strength of the random source. To enhance the stability of the inverse source problems, we incorporate a priori information regarding the regularity and support of the strength. In the case of homogeneous media, a Hölder stability estimate is established, providing a quantitative measure of the stability for reconstructing the source strength. For the more challenging scenario of inhomogeneous media, a logarithmic stability estimate is presented, capturing the intricate interactions between the source and the varying medium properties.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"42 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140593599","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}
引用次数: 0
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