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.
{"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. <br/> 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}
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.
{"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. <br/> 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}
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.
{"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. <br/> 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}
SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1288-1311, August 2024. Abstract. In this paper, we solve an inverse resonance problem for the half-solid with vanishing stresses on the surface: Lamb’s problem. Using a semiclassical approach, we are able to simplify this three-dimensional problem of the elastic wave equation for the half-solid as a Schrödinger equation with Robin boundary conditions on the half-line. We obtain asymptotic values on the number and the location of the resonances with respect to the wave number. Moreover, we prove that the mapping from real compactly supported potentials to the Jost functions in a suitable class of entire functions is one-to-one and onto and we produce an algorithm in order to retrieve the shear modulus from the eigenvalues and resonances.
{"title":"Inverse Resonance Problem for Love Seismic Surface Waves","authors":"Samuele Sottile","doi":"10.1137/23m155877x","DOIUrl":"https://doi.org/10.1137/23m155877x","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1288-1311, August 2024. <br/> Abstract. In this paper, we solve an inverse resonance problem for the half-solid with vanishing stresses on the surface: Lamb’s problem. Using a semiclassical approach, we are able to simplify this three-dimensional problem of the elastic wave equation for the half-solid as a Schrödinger equation with Robin boundary conditions on the half-line. We obtain asymptotic values on the number and the location of the resonances with respect to the wave number. Moreover, we prove that the mapping from real compactly supported potentials to the Jost functions in a suitable class of entire functions is one-to-one and onto and we produce an algorithm in order to retrieve the shear modulus from the eigenvalues and resonances.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"43 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141521643","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 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.
{"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. <br/> 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}
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.
{"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. <br/> 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}
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.
{"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. <br/> 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}
SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 1227-1253, June 2024. Abstract. We consider planar traveling fronts between stable steady states in two-component singularly perturbed reaction-diffusion-advection equations, where a small quantity [math] represents the ratio of diffusion coefficients. The fronts under consideration are large amplitude and contain a sharp interface, induced by traversing a fast heteroclinic orbit in a suitable slow-fast framework. We explore the effect of advection on the spectral stability of the fronts to long wavelength perturbations in two spatial dimensions. We find that for suitably large advection coefficient [math], the fronts are stable to such perturbations, while they can be unstable for smaller values of [math]. In this case, a critical asymptotic scaling [math] is obtained at which the onset of instability occurs. The results are applied to a family of traveling fronts in a dryland ecosystem model.
{"title":"A Stabilizing Effect of Advection on Planar Interfaces in Singularly Perturbed Reaction-Diffusion Equations","authors":"Paul Carter","doi":"10.1137/23m1610872","DOIUrl":"https://doi.org/10.1137/23m1610872","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 1227-1253, June 2024. <br/> Abstract. We consider planar traveling fronts between stable steady states in two-component singularly perturbed reaction-diffusion-advection equations, where a small quantity [math] represents the ratio of diffusion coefficients. The fronts under consideration are large amplitude and contain a sharp interface, induced by traversing a fast heteroclinic orbit in a suitable slow-fast framework. We explore the effect of advection on the spectral stability of the fronts to long wavelength perturbations in two spatial dimensions. We find that for suitably large advection coefficient [math], the fronts are stable to such perturbations, while they can be unstable for smaller values of [math]. In this case, a critical asymptotic scaling [math] is obtained at which the onset of instability occurs. The results are applied to a family of traveling fronts in a dryland ecosystem model.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"17 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141508786","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 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.
SIAM 应用数学杂志》，第 84 卷第 3 期，第 1204-1226 页，2024 年 6 月。 摘要单个细胞中的随机振荡通常以具有振荡自相关函数的非单调功率谱为特征。在此，我们开发了一种分析方法，用于研究随机基因表达的最小混合模型中的随机振荡，该模型包括启动子状态切换、蛋白质合成和降解以及遗传反馈回路。在我们的模型中观察到的振荡是由噪声引起的，因为确定性理论预测了稳定的固定点。蛋白质浓度波动的自相关函数、功率谱和稳态分布是以封闭形式计算的。利用精确可解模型，我们说明了持续振荡是由基因状态切换引起的沿随机滞后环的圆周运动。随着负反馈强度的增加，会出现三相随机分岔，这揭示了随机突发是如何演变成随机振荡的。在我们的模型中，振荡往往发生在蛋白质相对稳定、基因转换相对缓慢的时候。我们发现，翻译猝发增强了随机振荡的稳健性，并扩大了随机振荡的区域。这些结果为 R. Thomas 关于单细胞基因表达动力学的两个猜想提供了更深入的见解。
{"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. <br/> 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}
SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 1186-1203, June 2024. Abstract. We consider longitudinal shear flows over a superhydrophobic grating made up of a periodic array of grooves separated by infinitely thin slats, addressing the case where the liquid partially invades the grooves. We allow for curved menisci, specified via a depression angle at the contact line. We focus on the limit of small solid fractions where the length of the wetted portion of the slat is small compared with the period. Following an earlier analysis of the comparable flow over noninvaded grooves [O. Schnitzer, J. Fluid Mech., 820 (2017), pp. 580–603], this singular limit is treated using matched asymptotic expansions, with an outer region on the scale of a single period and an inner region on the scale of the wetted portion of the slat. The flow problem in both regions is solved using conformal mappings. Asymptotic matching yields a closed-form approximation for the slip length as a function of the solid fraction and depression angle.
{"title":"Longitudinal Shear Flow over a Superhydrophobic Grating with Partially Invaded Grooves and Curved Menisci","authors":"Ehud Yariv","doi":"10.1137/23m1616522","DOIUrl":"https://doi.org/10.1137/23m1616522","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 1186-1203, June 2024. <br/> Abstract. We consider longitudinal shear flows over a superhydrophobic grating made up of a periodic array of grooves separated by infinitely thin slats, addressing the case where the liquid partially invades the grooves. We allow for curved menisci, specified via a depression angle at the contact line. We focus on the limit of small solid fractions where the length of the wetted portion of the slat is small compared with the period. Following an earlier analysis of the comparable flow over noninvaded grooves [O. Schnitzer, J. Fluid Mech., 820 (2017), pp. 580–603], this singular limit is treated using matched asymptotic expansions, with an outer region on the scale of a single period and an inner region on the scale of the wetted portion of the slat. The flow problem in both regions is solved using conformal mappings. Asymptotic matching yields a closed-form approximation for the slip length as a function of the solid fraction and depression angle.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"34 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141552943","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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