Michael Fischer, Laura Kanzler, Christian Schmeiser
{"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":"51 1","pages":""},"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
{"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":"54 1","pages":""},"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}
{"title":"THE DIFFUSIVE ULTRASOUND MODULATED BIOLUMINESCENCE TOMOGRAPHY WITH PARTIAL DATA AND UNCERTAIN OPTICAL PARAMETERS.","authors":"Tianyu Yang, Yang Yang","doi":"10.1137/24m1657791","DOIUrl":"10.1137/24m1657791","url":null,"abstract":"<p><p>The paper studies an imaging problem in the diffusive ultrasound-modulated bioluminescence tomography with partial boundary measurement in an anisotropic medium. Assuming plane-wave modulation, we transform the imaging problem to an inverse problem with internal data, and derive a reconstruction procedure to recover the bioluminescent source. Subsequently, an uncertainty quantification estimate is established to assess the robustness of the reconstruction. To facilitate practical implementation, we discretize the diffusive model using the staggered grid scheme, resulting in a discrete formulation of the UMBLT inverse problem. A discrete reconstruction procedure is then presented along with a discrete uncertainty quantification estimate. Finally, the reconstruction procedure is quantitatively validated through numerical examples to demonstrate the efficacy and reliability of the proposed approach and estimates.</p>","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"84 6","pages":"2393-2416"},"PeriodicalIF":2.1,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12435549/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145076670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"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":"23 1","pages":""},"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}
{"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":"68 1","pages":""},"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
{"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":"3 1","pages":""},"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}
{"title":"Design of Defected Non-hermitian Chains of Resonator Dimers for Spatial and Spatio-temporal Localizations","authors":"Habib Ammari, Erik Orvehed Hiltunen, Thea Kosche","doi":"10.1137/23m1573896","DOIUrl":"https://doi.org/10.1137/23m1573896","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2443-2468, December 2023. <br/> Abstract. The aim of this article is to advance the field of metamaterials by proposing formulas for the design of high-contrast metamaterials with prescribed subwavelength defect mode eigenfrequencies. This is achieved in two settings: (i) design of non-Hermitian static materials and (ii) design of instantly changing non-Hermitian time-dependent materials. The design of static materials is achieved via characterizing equations for the defect mode eigenfrequencies in the setting of a defected dimer material. These characterizing equations are the basis for obtaining formulas for the material parameters of the defect which admit given defect mode eigenfrequencies. Explicit formulas are provided in the setting of one and two given defect mode eigenfrequencies in the setting of a defected chain of dimers. In the time-dependent case, we first analyze the influence of time boundaries on the subwavelength solutions. We find that subwavelength solutions are preserved if and only if the material parameters satisfy a temporal Snell’s law across the time boundary. The same result also identifies the change of the time frequencies uniquely. Combining this result with those on the design of static materials, we obtain an explicit formula for the material design of instantly changing defected dimer materials which admit subwavelength modes with prescribed time-dependent defect mode eigenfrequency. Finally, we use this formula to create materials which admit spatio-temporally localized defect modes.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"71 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138527994","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}
{"title":"Spectral Patterns of Elastic Transmission Eigenfunctions: Boundary Localization, Surface Resonance, and Stress Concentration","authors":"Yan Jiang, Hongyu Liu, Jiachuan Zhang, Kai Zhang","doi":"10.1137/22m1538417","DOIUrl":"https://doi.org/10.1137/22m1538417","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2469-2498, December 2023. <br/> Abstract. We present a comprehensive study of new discoveries on the spectral patterns of elastic transmission eigenfunctions, including boundary localization, surface resonance, and stress concentration. In the case where the domain is radial and the underlying parameters are constant, we give rigorous justifications and derive a thorough understanding of those intriguing geometric and physical patterns. We also present numerical examples to verify that the same results hold in general geometric and parameter setups.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"43 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138527996","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}
{"title":"Homogenization for a Variational Problem with a Slip Interface Condition","authors":"Miao-jung Yvonne Ou, Silvia Jiménez Bolaños","doi":"10.1137/22m1506961","DOIUrl":"https://doi.org/10.1137/22m1506961","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2390-2417, December 2023. <br/> Abstract. Inspired by applications, we study the effect of interface slip on the effective wave propagation in poroelastic materials, which are composites consisting of elastic frames whose pore space is filled with fluid. The current literature on the homogenization for the poroelastic wave equations are all based on the no-slip interface condition posed on the microscale. However, for certain pore fluids, the no-slip condition is known to be physically invalid. In the literature, slip boundary conditions have been considered for porous materials with rigid solid frames. For these rigid porous materials, the wave can only propagate in the pore fluid and hence the equations for the microscale are posed only in the pore space. Consequently, the slip on the interface involves only the fluid velocity and the fluid stress. In contrast, for poroelastic materials, the wave can propagate not only in the pore fluid but also in the solid frame; hence the slip conditions involve the velocities on both sides of the interface, rather than just the fluid side. With this slip condition, a variational boundary value problem governing the small vibrations of a periodic mixture of an elastic solid and a slightly viscous fluid is studied in this paper. The method of two-scale convergence is used to obtain the macroscopic behavior of the solution and to identify the role played by the slip interface condition.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"79 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-11-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138527999","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}
{"title":"Multiscale Modeling and Analysis of Growth of Plant Tissues","authors":"Arezki Boudaoud, Annamaria Kiss, Mariya Ptashnyk","doi":"10.1137/23m1553315","DOIUrl":"https://doi.org/10.1137/23m1553315","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 83, Issue 6, Page 2354-2389, December 2023. <br/> Abstract. How morphogenesis depends on cell properties is an active direction of research. Here, we focus on mechanical models of growing plant tissues, where microscopic (sub)cellular structure is taken into account. In order to establish links between microscopic and macroscopic tissue properties, we perform a multiscale analysis of a model of growing plant tissue with subcellular resolution. We use homogenization to rigorously derive the corresponding macroscopic tissue-scale model. Tissue-scale mechanical properties are computed from microscopic structural and material properties, taking into account deformation by the growth field. We then consider case studies and numerically compare the detailed microscopic model and the tissue-scale model, both implemented using the finite element method. We find that the macroscopic model can be used to efficiently make predictions about several configurations of interest. Our work will help making links between microscopic measurements and macroscopic observations in growing tissues.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"23 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138527987","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}