SIAM Journal on Applied Mathematics最新文献_第2页

A Numerical Scheme and Validation of the Asymptotic Energy Release Rate Formula for a 2D Gel Thin-Film Debonding Problem 二维凝胶薄膜脱粘问题的数值方案和渐近能量释放率公式验证

IF 1.9 4区数学

SIAM Journal on Applied Mathematics Pub Date : 2024-08-13 DOI: 10.1137/23m1579042

Maria Carme Calderer, Duvan Henao, Manuel A. Sánchez, Ronald A. Siegel, Sichen Song

{"title":"A Numerical Scheme and Validation of the Asymptotic Energy Release Rate Formula for a 2D Gel Thin-Film Debonding Problem","authors":"Maria Carme Calderer, Duvan Henao, Manuel A. Sánchez, Ronald A. Siegel, Sichen Song","doi":"10.1137/23m1579042","DOIUrl":"https://doi.org/10.1137/23m1579042","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1766-1791, August 2024. Abstract. This article presents a numerical scheme for the variational model formulated by Calderer et al. [J. Elast., 141 (2020), pp. 51–73] for the debonding of a hydrogel film from a rigid substrate upon exposure to solvent, in the two-dimensional case of a film placed between two parallel walls. It builds upon the scheme introduced by Song et al. [J. Elast., 153 (2023), pp. 651–679] for completely bonded gels, which fails to be robust in the case of gels that are already debonded. The new scheme is used to compute the energy release rate function, based on which predictions are offered for the threshold thickness below which the gel/substrate system is stable against debonding. This study, in turn, makes it possible to validate a theoretical estimate for the energy release rate obtained in the cited works, which is based on a thin-film asymptotic analysis and which, due to its explicit nature, is potentially valuable in medical device development. An existence theorem and rigorous justifications of some approximations made in our numerical scheme are also provided.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"24 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142219287","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

Global Dynamics of Reaction-Diffusion Systems with a Time-Varying Domain 具有时变域的反应-扩散系统的全局动力学

IF 1.9 4区数学

SIAM Journal on Applied Mathematics Pub Date : 2024-08-13 DOI: 10.1137/23m1582990

King-Yeung Lam, Xiao-Qiang Zhao, Min Zhu

{"title":"Global Dynamics of Reaction-Diffusion Systems with a Time-Varying Domain","authors":"King-Yeung Lam, Xiao-Qiang Zhao, Min Zhu","doi":"10.1137/23m1582990","DOIUrl":"https://doi.org/10.1137/23m1582990","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1742-1765, August 2024. Abstract. This paper is devoted to the study of the global dynamics for a large class of reaction-diffusion systems with a time-varying domain. By appealing to the theories of asymptotically autonomous and periodic semiflows, we establish the threshold-type results on the long-time behavior of solutions for such a system in the cases of asymptotically bounded and periodic domains, respectively. To investigate the model system in the case of asymptotically unbounded domain, we first prove the global attractivity for nonautonomous reaction-diffusion systems with asymptotically vanishing diffusion coefficients via the method of sub- and supersolutions and then use the comparison arguments to obtain the threshold dynamics. We also apply these analytical results to a reaction-diffusion model of dengue fever transmission to investigate the effect of time-varying domain on the basic reproduction number. It turns out that the basic reproduction numbers with dengue fever transmission for the asymptotically bounded and unbounded domains are always less than that for the spatially homogeneous case, and under appropriate conditions, the basic reproduction numbers for asymptotically bounded and periodic domains are larger than or equal to that for the stationary bounded domain.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"111 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142219288","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

Bayesian Experimental Design for Head Imaging by Electrical Impedance Tomography 电阻抗断层扫描头部成像的贝叶斯实验设计

IF 1.9 4区数学

SIAM Journal on Applied Mathematics Pub Date : 2024-08-05 DOI: 10.1137/23m1624634

N. Hyvönen, A. Jääskeläinen, R. Maity, A. Vavilov

{"title":"Bayesian Experimental Design for Head Imaging by Electrical Impedance Tomography","authors":"N. Hyvönen, A. Jääskeläinen, R. Maity, A. Vavilov","doi":"10.1137/23m1624634","DOIUrl":"https://doi.org/10.1137/23m1624634","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1718-1741, August 2024. Abstract. This work considers the optimization of electrode positions in head imaging by electrical impedance tomography. The study is motivated by maximizing the sensitivity of electrode measurements to conductivity changes when monitoring the condition of a stroke patient, which justifies adopting a linearized version of the complete electrode model as the forward model. The algorithm is based on finding a (locally) A-optimal measurement configuration via gradient descent with respect to the electrode positions. The efficient computation of the needed derivatives of the complete electrode model is one of the focal points. Two algorithms are introduced and numerically tested on a three-layer head model. The first one assumes a region of interest and a Gaussian prior for the conductivity in the brain, and it can be run offline, i.e., prior to taking any measurements. The second algorithm first computes a reconstruction of the conductivity anomaly caused by the stroke with an initial electrode configuration by combining lagged diffusivity iteration with sequential linearizations, which can be interpreted to produce an approximate Gaussian probability density for the conductivity perturbation. It then resorts to the first algorithm to find new, more informative positions for the available electrodes with the constructed density as the prior.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"135 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141942528","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 the Non-Hermitian Skin Effect in One Dimension 一维非赫米提皮肤效应的稳定性

IF 1.9 4区数学

SIAM Journal on Applied Mathematics Pub Date : 2024-08-05 DOI: 10.1137/23m1610537

Habib Ammari, Silvio Barandun, Bryn Davies, Erik Orvehed Hiltunen, Ping Liu

{"title":"Stability of the Non-Hermitian Skin Effect in One Dimension","authors":"Habib Ammari, Silvio Barandun, Bryn Davies, Erik Orvehed Hiltunen, Ping Liu","doi":"10.1137/23m1610537","DOIUrl":"https://doi.org/10.1137/23m1610537","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1697-1717, August 2024. Abstract. This paper shows both analytically and numerically that the skin effect in systems of non-Hermitian subwavelength resonators is robust with respect to random imperfections in the system. The subwavelength resonators are highly contrasting material inclusions that resonate in a low-frequency regime. The non-Hermiticity is due to the introduction of a directional damping term (motivated by an imaginary gauge potential), which leads to a skin effect that is manifested by the system’s eigenmodes accumulating at one edge of the structure. We elucidate the topological protection of the associated (real) eigenfrequencies and illustrate numerically the competition between the two different localization effects present when the system is randomly perturbed: the non-Hermitian skin effect and the disorder-induced Anderson localization. We show numerically that, as the strength of the disorder increases, more and more eigenmodes become localized in the bulk. Our results are based on an asymptotic matrix model for subwavelength physics and can be generalized also to tight-binding models in condensed matter theory.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"45 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141942440","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 and Transient Dynamics of a Stoichiometric Algal Growth Model with Two-Stage Phosphate Uptake 具有两阶段磷酸盐吸收的定量藻类生长模型的渐近和瞬态动力学分析

IF 1.9 4区数学

SIAM Journal on Applied Mathematics Pub Date : 2024-08-02 DOI: 10.1137/23m1611750

Shufei Gao, Sanling Yuan, Anglu Shen, Hao Wang

{"title":"Asymptotic and Transient Dynamics of a Stoichiometric Algal Growth Model with Two-Stage Phosphate Uptake","authors":"Shufei Gao, Sanling Yuan, Anglu Shen, Hao Wang","doi":"10.1137/23m1611750","DOIUrl":"https://doi.org/10.1137/23m1611750","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1668-1696, August 2024. Abstract. Exploring the mechanism of phosphate ([math]) uptake by algae is essential to accurate prediction and a comprehensive understanding of harmful algal blooms (HABs). Previous experimental studies have revealed the existence of two distinct [math] pools, namely the surface-adsorbed [math] pool and the intracellular [math] pool, in certain species of algae. Motivated by these observations, a novel stoichiometric model, which incorporates a two-stage [math] uptake process, is proposed and analyzed to investigate the impact of these [math] pools on algal growth. Model validation results show that with proper parameterizations, this model can accurately capture algal growth dynamics in the laboratory and in the field. The asymptotic dynamics are explored through a complete mathematical analysis and the transient dynamics are explored through multiscale analysis, revealing the driving mechanism of different growth phases of algae. Furthermore, we derive an approximate formula for estimating the switching time from high to low growth rate in algae, which can serve as a valuable tool for predicting the duration of HABs. These findings contribute to the strengthening of prediction and improving understanding of HABs.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"52 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141885388","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

Prandtl–Batchelor Flow in a Cylindrical Domain 圆柱形域中的普朗特-巴歇尔流

IF 1.9 4区数学

SIAM Journal on Applied Mathematics Pub Date : 2024-07-31 DOI: 10.1137/24m1637313

Emmanuel Dormy, H. Keith Moffatt

引用次数: 0

A Stable Imaging Functional for Anisotropic Periodic Media in Electromagnetic Inverse Scattering 电磁反向散射中各向异性周期介质的稳定成像函数

IF 1.9 4区数学

SIAM Journal on Applied Mathematics Pub Date : 2024-07-29 DOI: 10.1137/23m1577080

Dinh-Liem Nguyen, Trung Truong

引用次数: 0

Pseudodifferential Models for Ultrasound Waves with Fractional Attenuation 具有分数衰减的超声波伪微分模型

IF 1.9 4区数学

SIAM Journal on Applied Mathematics Pub Date : 2024-07-26 DOI: 10.1137/24m1634011

Sebastian Acosta, Jesse Chan, Raven Johnson, Benjamin Palacios

{"title":"Pseudodifferential Models for Ultrasound Waves with Fractional Attenuation","authors":"Sebastian Acosta, Jesse Chan, Raven Johnson, Benjamin Palacios","doi":"10.1137/24m1634011","DOIUrl":"https://doi.org/10.1137/24m1634011","url":null,"abstract":"SIAM Journal on Applied Mathematics, Volume 84, Issue 4, Page 1609-1630, August 2024. Abstract. To strike a balance between modeling accuracy and computational efficiency for simulations of ultrasound waves in soft tissues, we derive a pseudodifferential factorization of the wave operator with fractional attenuation. This factorization allows us to approximately solve the Helmholtz equation via one-way (transmission) or two-way (transmission and reflection) sweeping schemes tailored to high-frequency wave fields. We provide explicitly the three highest order terms of the pseudodifferential expansion to incorporate the well-known square-root first order symbol for wave propagation, the zeroth order symbol for amplitude modulation due to changes in wave speed and damping, and the next symbol to model fractional attenuation. We also propose wide-angle Padé approximations for the pseudodifferential operators corresponding to these three highest order symbols. Our analysis provides insights regarding the role played by the frequency and the Padé approximations in the estimation of error bounds. We also provide a proof-of-concept numerical implementation of the proposed method and test the error estimates numerically.","PeriodicalId":51149,"journal":{"name":"SIAM Journal on Applied Mathematics","volume":"58 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141778882","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

Joint Impact of Maturation Delay and Fear Effect on the Population Dynamics of a Predator-Prey System 成熟延迟和恐惧效应对捕食者-猎物系统种群动态的共同影响

IF 1.9 4区数学

SIAM Journal on Applied Mathematics Pub Date : 2024-07-22 DOI: 10.1137/23m1596569

Xiaoke Ma, Ying Su, Xingfu Zou

引用次数: 0

Uniform Asymptotic Approximations for the Phase Plane Trajectories of the SIR Model with Vital Dynamics 具有生命动力学的 SIR 模型相平面轨迹的均匀渐近法

IF 1.9 4区数学

SIAM Journal on Applied Mathematics Pub Date : 2024-07-22 DOI: 10.1137/23m1576050

Todd L. Parsons, David J. D. Earn

引用次数: 0