SIAM Journal on Applied Mathematics最新文献_第3页

An Asymptotic Analysis of Space Charge Layers in a Mathematical Model of a Solid Electrolyte 固体电解质数学模型中空间电荷层的渐近分析

IF 1.9 4区数学

SIAM Journal on Applied Mathematics Pub Date : 2024-07-04 DOI: 10.1137/23m1580954

Laura M. Keane, Iain R. Moyles

{"title":"An Asymptotic Analysis of Space Charge Layers in a Mathematical Model of a Solid Electrolyte","authors":"Laura M. Keane, Iain R. Moyles","doi":"10.1137/23m1580954","DOIUrl":"https://doi.org/10.1137/23m1580954","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1413-1438, August 2024. Abstract. We review a model for a solid electrolyte derived under thermodynamics principles. We nondimensionalize and scale the model to identify small parameters where we identify a scaling that controls the width of the space charge layer in the electrolyte. We present asymptotic analyses and numerical solutions for the one-dimensional zero charge flux equilibrium problem. We introduce an auxiliary variable to remove singularities from the domain in order to facilitate robust numerical simulations. From the asymptotics, we identify three distinct regions: bulk, boundary, and intermediate layers. The boundary and intermediate layers form the space charge layer of the solid electrolyte, which we can further distinguish as strong and weak space charge layers, respectively. The weak space charge layer is characterized by a length, [math], which is equivalent to the Debye length of a standard liquid electrolyte. The strong space charge layer is characterized by a scaled Debye length, which is larger than [math]. We find that both layers exhibit distinct behavior; we see quadratic behavior in the strong space charge layer and exponential behavior in the weak space charge layer. We find that matching between these two asymptotic regimes is not standard, and we implement a pseudomatching approach to facilitate the transition between the quadratic and exponential behaviors. We demonstrate excellent agreement between asymptotics and simulation.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"40 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141549443","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

Diffraction and Interaction of Interfacial Solitons in a Two-Layer Fluid of Great Depth 大深度双层流体中界面孤子的衍射与相互作用

IF 1.9 4区数学

SIAM Journal on Applied Mathematics Pub Date : 2024-07-03 DOI: 10.1137/23m1572349

Lei Hu, Xu-Dan Luo, Zhan Wang

{"title":"Diffraction and Interaction of Interfacial Solitons in a Two-Layer Fluid of Great Depth","authors":"Lei Hu, Xu-Dan Luo, Zhan Wang","doi":"10.1137/23m1572349","DOIUrl":"https://doi.org/10.1137/23m1572349","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1385-1412, August 2024. Abstract. This paper aims to present a novel isotropic bidirectional model for studying weakly dispersive and weakly nonlinear atmospheric internal waves in a three-dimensional system consisting of two superimposed, incompressible, and inviscid fluids. The newly developed equation is the Benjamin–Benney–Luke (BBL) equation, a generalization of the famous two-dimensional Benjamin–Ono (2DBO) equation and the Benney–Luke equation, derived using the nonlocal Ablowitz–Fokas–Musslimani formulation of water waves. The evolution results of the BBL and 2DBO equations, performed by implementing the classic fourth-order Runge–Kutta method, the pseudospectral scheme with the integrating factor method, and the windowing scheme, show that the anisotropic 2DBO equation agrees well with the isotropic BBL model for problems being investigated, namely the focus is the central part of the soliton evolution/interaction zone. By applying the Whitham modulation theory, modulation equations for the 2DBO equation are obtained in this paper for analyzing the soliton dynamics in five different initial-value problems (truncated line soliton, line soliton, bent-stem soliton, bent soliton, and reverse bent soliton). In addition, corresponding numerical results are obtained and shown to agree well with the theoretical predictions. Both theoretical and numerical results reveal the formation conditions of the Mach expansion, as well as the specific relationship between the amplitude of the Mach stem and the initial data.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"68 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141552941","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

Spatiotemporal Dynamic Analysis of Delayed Diffusive Pine Wilt Disease Model with Nonlocal Effect 具有非局部效应的延迟扩散松树枯萎病模型的时空动态分析

IF 1.9 4区数学

SIAM Journal on Applied Mathematics Pub Date : 2024-07-01 DOI: 10.1137/23m1575305

Yanchuang Hou, Yuting Ding

{"title":"Spatiotemporal Dynamic Analysis of Delayed Diffusive Pine Wilt Disease Model with Nonlocal Effect","authors":"Yanchuang Hou, Yuting Ding","doi":"10.1137/23m1575305","DOIUrl":"https://doi.org/10.1137/23m1575305","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1312-1336, August 2024. Abstract. Pine wilt disease is one of the most serious forest diseases and pests in China, which seriously influences the realization of the goal of “carbon peak and carbon neutrality.” In our article, we divide longhorns into susceptible ones and infected ones since pine wilt disease is spread by longhorns. Considering the saturation incidence of pine wilt disease, we establish a delayed reaction-diffusion model with nonlocal effect for susceptible and infected longhorns. First, we consider the well-posedness of solutions and the type of equilibria for the nonspatial system. Next, we discuss the dynamics of the spatial system with nonlocal effect. According to the multiple time scales method, we derive the normal form of Hopf bifurcation for a system associated with nonlocal effect, and the stability and direction of bifurcating periodic solutions are analyzed. Finally, using real data for China to perform data analysis, we select suitable values of parameters. Numerical simulations are presented to illustrate the ecological significance. Combined with the current situation, we provide some theoretical support for the prevention and control of pine wilt disease in China. Especially, we find that the nonlocal term can induce spatially stable inhomogeneous bifurcating periodic solutions.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"23 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141521645","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

Inverse Resonance Problem for Love Seismic Surface Waves 爱地震表面波的反共振问题

IF 1.9 4区数学

SIAM Journal on Applied Mathematics Pub Date : 2024-07-01 DOI: 10.1137/23m155877x

Samuele Sottile

引用次数: 0

Connecting GANs, Mean-Field Games, and Optimal Transport 连接 GAN、均场博弈和最优传输

IF 1.9 4区数学

SIAM Journal on Applied Mathematics Pub Date : 2024-07-01 DOI: 10.1137/22m1499534

Haoyang Cao, Xin Guo, Mathieu Laurière

{"title":"Connecting GANs, Mean-Field Games, and Optimal Transport","authors":"Haoyang Cao, Xin Guo, Mathieu Laurière","doi":"10.1137/22m1499534","DOIUrl":"https://doi.org/10.1137/22m1499534","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1255-1287, August 2024. Abstract. Generative adversarial networks (GANs) have enjoyed tremendous success in image generation and processing and have recently attracted growing interest in financial modeling. This paper analyzes GANs from the perspectives of mean-field games (MFGs) and optimal transport: GANs are interpreted as MFGs under the Pareto optimality criterion or mean-field controls; meanwhile, GANs are to minimize the optimal transport cost indexed by the generator from the known latent distribution to the unknown true distribution of data. In particular, we provide a universal approximation result, which shows that there exists an appropriate neural network architecture for GANs training to capture the mean-field solution. The derivation of this universal approximation result leads to an explicit construction of the deep neural network for the transport mapping. The MFGs perspective of GANs leads to a GAN-based computational method (MFGANs) to solve MFGs: one neural network for the backward Hamilton–Jacobi–Bellman equation and one neural network for the forward Fokker–Planck equation, with the two neural networks trained in an adversarial way. Numerical experiments demonstrate superior performance of this proposed algorithm, especially in higher dimensional cases, when compared with existing neural network approaches.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"52 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141521646","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

Identifying Active Anomalies in a Multilayered Medium by Passive Measurement in EIT 通过电子信息技术中的被动测量识别多层介质中的主动异常

IF 1.9 4区数学

SIAM Journal on Applied Mathematics Pub Date : 2024-07-01 DOI: 10.1137/23m1599458

Youjun Deng, Hongyu Liu, Yajuan Wang

{"title":"Identifying Active Anomalies in a Multilayered Medium by Passive Measurement in EIT","authors":"Youjun Deng, Hongyu Liu, Yajuan Wang","doi":"10.1137/23m1599458","DOIUrl":"https://doi.org/10.1137/23m1599458","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1362-1384, August 2024. Abstract. We propose to study an inverse problem of determining multiple anomalies embedded in a multilayered background medium by the associated electric measurement which arises in Electrical Impedance Tomography (EIT). There are several salient features of our study. First, the anomaly considered in our study is extremely general which is characterized by its location, support, varying size, conductivity parameter, as well as a carry-on source intensity. Second, we make use of the measurement of the electric field generated by the active anomalies. This corresponds to a single passive measurement. Third, the background medium is of a multilayered and piecewise-constant structure and can be used to model a more general scenario from practical applications; say, e.g., the human body. Under the condition that the anomalies are small, but still in multiple scales considering their varying sizes, we derive a sharp formula of the electric field in terms of the polarization tensors, which enables us to establish comprehensive unique identifiability results in determining the characteristic parameters of the active anomalies in different situations.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"347 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508785","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

Whitham Modulation Theory and Two-Phase Instabilities for Generalized Nonlinear Schrödinger Equations with Full Dispersion 全分散广义非线性薛定谔方程的惠瑟姆调制理论和两相不稳定性

IF 1.9 4区数学

SIAM Journal on Applied Mathematics Pub Date : 2024-07-01 DOI: 10.1137/23m1603078

Patrick Sprenger, Mark A. Hoefer, Boaz Ilan

{"title":"Whitham Modulation Theory and Two-Phase Instabilities for Generalized Nonlinear Schrödinger Equations with Full Dispersion","authors":"Patrick Sprenger, Mark A. Hoefer, Boaz Ilan","doi":"10.1137/23m1603078","DOIUrl":"https://doi.org/10.1137/23m1603078","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1337-1361, August 2024. Abstract. The generalized nonlinear Schrödinger equation with full dispersion (FDNLS) is considered in the semiclassical regime. The Whitham modulation equations are obtained for the FDNLS equation with general linear dispersion and a generalized, local nonlinearity. Assuming the existence of a four-parameter family of two-phase solutions, a multiple-scales approach yields a system of four independent, first-order, quasi-linear conservation laws of hydrodynamic type that correspond to the slow evolution of the two wavenumbers, mass, and momentum of modulated periodic traveling waves. The modulation equations are further analyzed in the dispersionless and weakly nonlinear regimes. The ill-posedness of the dispersionless equations corresponds to the classical criterion for modulational instability (MI). For modulations of linear waves, ill-posedness coincides with the generalized MI criterion, recently identified by Amiranashvili and Tobisch [New J. Phys., 21 (2019), 033029]. A new instability index is identified by the transition from real to complex characteristics for the weakly nonlinear modulation equations. This instability is associated with long wavelength modulations of nonlinear two-phase wavetrains and can exist even when the corresponding one-phase wavetrain is stable according to the generalized MI criterion. Another interpretation is that while infinitesimal perturbations of a periodic wave may not grow, small but finite amplitude perturbations may grow, hence this index identifies a nonlinear instability mechanism for one-phase waves. Classifications of instability indices for multiple FDNLS equations with higher-order dispersion, including applications to finite-depth water waves and the discrete NLS equation, are presented and compared with direct numerical simulations.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"37 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141521644","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

A Stabilizing Effect of Advection on Planar Interfaces in Singularly Perturbed Reaction-Diffusion Equations 奇异扰动反应-扩散方程中平面界面上的平流稳定效应

IF 1.9 4区数学

SIAM Journal on Applied Mathematics Pub Date : 2024-06-10 DOI: 10.1137/23m1610872

Paul Carter

引用次数: 0

Exact Power Spectrum in a Minimal Hybrid Model of Stochastic Gene Expression Oscillations 随机基因表达振荡最小混合模型中的精确功率谱

IF 1.9 4区数学

SIAM Journal on Applied Mathematics Pub Date : 2024-06-10 DOI: 10.1137/23m1560914

Chen Jia, Hong Qian, Michael Q. Zhang

{"title":"Exact Power Spectrum in a Minimal Hybrid Model of Stochastic Gene Expression Oscillations","authors":"Chen Jia, Hong Qian, Michael Q. Zhang","doi":"10.1137/23m1560914","DOIUrl":"https://doi.org/10.1137/23m1560914","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 1204-1226, June 2024. Abstract. Stochastic oscillations in individual cells are usually characterized by a nonmonotonic power spectrum with an oscillatory autocorrelation function. Here we develop an analytical approach to stochastic oscillations in a minimal hybrid model of stochastic gene expression including promoter state switching, protein synthesis and degradation, as well as a genetic feedback loop. The oscillations observed in our model are noise-induced since the deterministic theory predicts stable fixed points. The autocorrelated function, power spectrum, and steady-state distribution of protein concentration fluctuations are computed in closed form. Using the exactly solvable model, we illustrate sustained oscillations as a circular motion along a stochastic hysteresis loop induced by gene state switching. A triphasic stochastic bifurcation upon the increasing strength of negative feedback is observed, which reveals how stochastic bursts evolve into stochastic oscillations. In our model, oscillations tend to occur when the protein is relatively stable and when gene switching is relatively slow. Translational bursting is found to enhance the robustness and broaden the region of stochastic oscillations. These results provide deeper insights into R. Thomas’s two conjectures for single-cell gene expression kinetics.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"60 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508787","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

Longitudinal Shear Flow over a Superhydrophobic Grating with Partially Invaded Grooves and Curved Menisci 带有部分内陷凹槽和弯曲半月板的超疏水光栅上的纵向剪切流

IF 1.9 4区数学

SIAM Journal on Applied Mathematics Pub Date : 2024-06-05 DOI: 10.1137/23m1616522

Ehud Yariv

引用次数: 0