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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
{"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}
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. <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}
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
{"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}
引用次数: 0
Realistic Pattern Formations on Surfaces by Adding Arbitrary Roughness 通过添加任意粗糙度在表面形成逼真图案
IF 1.9 4区 数学
SIAM Journal on Applied Mathematics Pub Date : 2024-06-03 DOI: 10.1137/22m1518001
Siqing Li, Leevan Ling, Steven J. Ruuth, Xuemeng Wang
{"title":"Realistic Pattern Formations on Surfaces by Adding Arbitrary Roughness","authors":"Siqing Li, Leevan Ling, Steven J. Ruuth, Xuemeng Wang","doi":"10.1137/22m1518001","DOIUrl":"https://doi.org/10.1137/22m1518001","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 1163-1185, June 2024. <br/> Abstract. We are interested in generating surfaces with arbitrary roughness and forming patterns on the surfaces. Two methods are applied to construct rough surfaces. In the first method, some superposition of wave functions with random frequencies and angles of propagation are used to get periodic rough surfaces with analytic parametric equations. The amplitude of such surfaces is also an important variable in the provided eigenvalue analysis for the Laplace–Beltrami operator and in the generation of pattern formation. Numerical experiments show that the patterns become irregular as the amplitude and frequency of the rough surface increase. For the sake of easy generalization to closed manifolds, we propose a second construction method for rough surfaces, which uses random nodal values and discretized heat filters. We provide numerical evidence that both surface construction methods yield comparable patterns to those observed in real-life animals.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"418 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141259022","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
Optimal Bacterial Resource Allocation Strategies in Batch Processing 批处理中的最佳细菌资源分配策略
IF 1.9 4区 数学
SIAM Journal on Applied Mathematics Pub Date : 2024-05-31 DOI: 10.1137/22m1506328
Agustín Gabriel Yabo, Jean-Baptiste Caillau, Jean-Luc Gouzé
{"title":"Optimal Bacterial Resource Allocation Strategies in Batch Processing","authors":"Agustín Gabriel Yabo, Jean-Baptiste Caillau, Jean-Luc Gouzé","doi":"10.1137/22m1506328","DOIUrl":"https://doi.org/10.1137/22m1506328","url":null,"abstract":"SIAM Journal on Applied Mathematics, Ahead of Print. <br/> Abstract. The study of living microorganisms using resource allocation models has been key in elucidating natural behaviors of bacteria, by allowing allocation of microbial resources to be represented through optimal control strategies. The approach can also be applied to research in microbial cell factories, to investigate the optimal production of value-added compounds regulated by an external control. The latter is the subject of this paper, in which we study batch bioprocessing from a resource allocation perspective. Based on previous works, we propose a simple bacterial growth model accounting for the dynamics of the bioreactor and intracellular composition, and we analyze its asymptotic behavior and stability. Using optimization and optimal control theory, we study the production of biomass and metabolites of interest for infinite- and finite-time horizons. The resulting optimal control problems are studied using Pontryagin’s maximum principle and numerical methods, and the solutions found are characterized by the presence of the Fuller phenomenon (producing an infinite set of switching points occurring in a finite-time window) at the junctions with a second-order singular arc. The approach, inspired by biotechnological engineering, aims to shed light upon the role of cellular composition and resource allocation during batch processing and, at the same time, poses very interesting and challenging mathematical problems.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"34 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141196806","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
First Hitting Time of a One-Dimensional Lévy Flight to Small Targets 一维莱维飞行对小目标的首次命中时间
IF 1.9 4区 数学
SIAM Journal on Applied Mathematics Pub Date : 2024-05-29 DOI: 10.1137/23m1586239
Daniel Gomez, Sean D. Lawley
{"title":"First Hitting Time of a One-Dimensional Lévy Flight to Small Targets","authors":"Daniel Gomez, Sean D. Lawley","doi":"10.1137/23m1586239","DOIUrl":"https://doi.org/10.1137/23m1586239","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 1140-1162, June 2024. <br/> Abstract. First hitting times (FHTs) describe the time it takes a random “searcher” to find a “target” and are used to study timescales in many applications. FHTs have been well-studied for diffusive search, especially for small targets, which is called the narrow capture or narrow escape problem. In this paper, we study the FHT to small targets for a one-dimensional superdiffusive search described by a Lévy flight. By applying the method of matched asymptotic expansions to a fractional differential equation we obtain an explicit asymptotic expansion for the mean FHT (MFHT). For fractional order [math] (describing a [math]-stable Lévy flight whose squared displacement scales as [math] in time [math]) and targets of radius [math], we show that the MFHT is order one for [math] and diverges as [math] for [math] and [math] for [math]. We then use our asymptotic results to identify the value of [math] which minimizes the average MFHT and find that (a) this optimal value of [math] vanishes for sparse targets and (b) the value [math] (corresponding to an inverse square Lévy search) is optimal in only very specific circumstances. We confirm our results by comparison to both deterministic numerical solutions of the associated fractional differential equation and stochastic simulations.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"72 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141259062","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
Asymptotic Analysis and Simulation of Mean First Passage Time for Active Brownian Particles in 1-D 一维活动布朗粒子平均首次通过时间的渐近分析与模拟
IF 1.9 4区 数学
SIAM Journal on Applied Mathematics Pub Date : 2024-05-17 DOI: 10.1137/23m1593917
Sarafa A. Iyaniwura, Zhiwei Peng
{"title":"Asymptotic Analysis and Simulation of Mean First Passage Time for Active Brownian Particles in 1-D","authors":"Sarafa A. Iyaniwura, Zhiwei Peng","doi":"10.1137/23m1593917","DOIUrl":"https://doi.org/10.1137/23m1593917","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 1079-1095, June 2024. <br/> Abstract. Active Brownian particles (ABPs) are a model for nonequilibrium systems in which the constituent particles are self-propelled in addition to their Brownian motion. Compared to the well-studied mean first passage time (MFPT) of passive Brownian particles, the MFPT of ABPs is much less developed. In this paper, we study the MFPT for ABPs in a 1-D domain with absorbing boundary conditions at both ends of the domain. To reveal the effect of swimming on the MFPT, we consider an asymptotic analysis in the weak-swimming or small Péclet ([math]) number limit. In particular, analytical expressions for the survival probability and the MFPT are developed up to [math]. We explore the effects of the starting positions and starting orientations on the MFPT. Our analysis shows that if the starting orientations are biased towards one side of the domain, the MFPT as a function of the starting position becomes asymmetric about the center of the domain. The analytical results were confirmed by the numerical solutions of the full PDE model.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"24 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141061644","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 of a Capillary Circular Cylinder between Two Parallel Cylinders 两个平行圆柱体之间毛细管圆柱体的稳定性
IF 1.9 4区 数学
SIAM Journal on Applied Mathematics Pub Date : 2024-05-14 DOI: 10.1137/23m1602139
Rafael López
{"title":"Stability of a Capillary Circular Cylinder between Two Parallel Cylinders","authors":"Rafael López","doi":"10.1137/23m1602139","DOIUrl":"https://doi.org/10.1137/23m1602139","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 1039-1059, June 2024. <br/> Abstract. Consider a system of two parallel solid cylinders of equal radius made of a homogeneous material. We study the stability of a liquid bridge of circular cylinder shape between both solid cylinders. It is proved that if the circular cylinder liquid is concave, then it is stable. If the circular cylinder liquid is convex, we establish conditions on the radius of the cylinder liquid and the contact angle that ensure that long convex circular cylinders are not stable. Estimates for the length of these convex cylinders are given.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"36 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925364","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Modeling of Electronic Dynamics in Twisted Bilayer Graphene 扭曲双层石墨烯电子动力学建模
IF 1.9 4区 数学
SIAM Journal on Applied Mathematics Pub Date : 2024-05-14 DOI: 10.1137/23m1595941
Tianyu Kong, Diyi Liu, Mitchell Luskin, Alexander B. Watson
{"title":"Modeling of Electronic Dynamics in Twisted Bilayer Graphene","authors":"Tianyu Kong, Diyi Liu, Mitchell Luskin, Alexander B. Watson","doi":"10.1137/23m1595941","DOIUrl":"https://doi.org/10.1137/23m1595941","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 1011-1038, June 2024. <br/> Abstract. We consider the problem of numerically computing the quantum dynamics of an electron in twisted bilayer graphene. The challenge is that atomic-scale models of the dynamics are aperiodic for generic twist angles because of the incommensurability of the layers. The Bistritzer–MacDonald PDE model, which is periodic with respect to the bilayer’s moiré pattern, has recently been shown to rigorously describe these dynamics in a parameter regime. In this work, we first prove that the dynamics of the tight-binding model of incommensurate twisted bilayer graphene can be approximated by computations on finite domains. The main ingredient of this proof is a speed of propagation estimate proved using Combes–Thomas estimates. We then provide extensive numerical computations, which clarify the range of validity of the Bistritzer–MacDonald model.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"21 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Local Perception and Learning Mechanisms in Resource-Consumer Dynamics 资源-消费者动态中的局部感知和学习机制
IF 1.9 4区 数学
SIAM Journal on Applied Mathematics Pub Date : 2024-05-13 DOI: 10.1137/23m1598593
Qingyan Shi, Yongli Song, Hao Wang
{"title":"Local Perception and Learning Mechanisms in Resource-Consumer Dynamics","authors":"Qingyan Shi, Yongli Song, Hao Wang","doi":"10.1137/23m1598593","DOIUrl":"https://doi.org/10.1137/23m1598593","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 3, Page 988-1010, June 2024. <br/> Abstract. Spatial memory is key in animal movement modeling, but it has been challenging to explicitly model learning to describe memory acquisition. In this paper, we study novel cognitive consumer-resource models with different consumer learning mechanisms and investigate their dynamics. These models consist of two PDEs in composition with one ODE such that the spectrum of the corresponding linearized operator at a constant steady state is unclear. We describe the spectra of the linearized operators and analyze the eigenvalue problems to determine the stability of the constant steady states. We then perform bifurcation analysis by taking the perceptual diffusion rate as the bifurcation parameter. It is found that steady-state and Hopf bifurcations can both occur in these systems, and the bifurcation points are given so that the stability region can be determined. Moreover, rich spatial and spatiotemporal patterns can be generated in such systems via different types of bifurcation. Our effort establishes a new approach to tackling a hybrid model of PDE-ODE composition and provides a deeper understanding of cognitive movement-driven consumer-resource dynamics.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"21 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925136","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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