We show a quantitative analysis of the perturbed electric field of a 3D anisotropic conductive rod geometry embedded in homogeneous background, which is an extension of the work in 2D case. The solution to the perturbed problem is presented by layer potential techniques, and dedicated asymptotic analysis is employed for characterization of the density function. The asymptotic result shows that near the high curvature boundary of the rod, the electric field is much strong, compared with other parts adjacent to the rod.
{"title":"Quantitative analysis for rod-shaped inclusion in three-dimensional conductivity problem","authors":"Youjun Deng, Ghadir Shokor","doi":"10.1002/mma.10541","DOIUrl":"https://doi.org/10.1002/mma.10541","url":null,"abstract":"<p>We show a quantitative analysis of the perturbed electric field of a 3D anisotropic conductive rod geometry embedded in homogeneous background, which is an extension of the work in 2D case. The solution to the perturbed problem is presented by layer potential techniques, and dedicated asymptotic analysis is employed for characterization of the density function. The asymptotic result shows that near the high curvature boundary of the rod, the electric field is much strong, compared with other parts adjacent to the rod.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 4","pages":"4212-4231"},"PeriodicalIF":2.1,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143380062","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we propose a new numerical method to simulate acoustic scattering problems in two-dimensional periodic structures with non-periodic incident fields. Applying the Floquet-Bloch transform to the scattering problem yields a family of quasi-periodic boundary value problems dependent on the Floquet-Bloch parameter. Consequently, the solution of the original scattering problem is written as the inverse Floquet-Bloch transform of the solutions to these boundary value problems. The key step in our method is the numerical approximation of this integral transform by a quadrature rule with a nonuniform choice of quadrature points adapted to the regularity of the family of quasi-periodic solutions. This achieved by a graded subdivision of the full interval for the Floquet-Bloch parameter and applying a Gauss-Legrendre quadrature rule on each subinterval. We prove that the numerical method converges exponentially with respect to both the number of subintervals and the number of Gaussian quadrature points. Some numerical experiments are provided to illustrate the results.
{"title":"A nonuniform mesh method in the Floquet parameter domain for wave scattering by periodic surfaces","authors":"Tilo Arens, Ruming Zhang","doi":"10.1002/mma.10548","DOIUrl":"https://doi.org/10.1002/mma.10548","url":null,"abstract":"<p>In this paper, we propose a new numerical method to simulate acoustic scattering problems in two-dimensional periodic structures with non-periodic incident fields. Applying the Floquet-Bloch transform to the scattering problem yields a family of quasi-periodic boundary value problems dependent on the Floquet-Bloch parameter. Consequently, the solution of the original scattering problem is written as the inverse Floquet-Bloch transform of the solutions to these boundary value problems. The key step in our method is the numerical approximation of this integral transform by a quadrature rule with a nonuniform choice of quadrature points adapted to the regularity of the family of quasi-periodic solutions. This achieved by a graded subdivision of the full interval for the Floquet-Bloch parameter and applying a Gauss-Legrendre quadrature rule on each subinterval. We prove that the numerical method converges exponentially with respect to both the number of subintervals and the number of Gaussian quadrature points. Some numerical experiments are provided to illustrate the results.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 4","pages":"4289-4309"},"PeriodicalIF":2.1,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/mma.10548","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143380067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper investigates a stochastic two predators–one prey system with ratio-dependent functional response under regime switching. The stochastic extinction of species and the existence of ergodic stationary distribution for the system are established, and the transition probability of the solution converging to the stationary distribution also is obtained. To illustrate our theoretical results, the numerical examples and simulations are presented. Our findings also demonstrate that the stationary distribution and extinction of species for the stochastic two predators–one prey system are affected by random perturbations, leading to an imbalance in ecology.
{"title":"Global dynamics in a stochastic two predators–one prey system with regime-switching and ratio-dependent functional response","authors":"Nafeisha Tuerxun, Zhidong Teng","doi":"10.1002/mma.10586","DOIUrl":"https://doi.org/10.1002/mma.10586","url":null,"abstract":"<p>This paper investigates a stochastic two predators–one prey system with ratio-dependent functional response under regime switching. The stochastic extinction of species and the existence of ergodic stationary distribution for the system are established, and the transition probability of the solution converging to the stationary distribution also is obtained. To illustrate our theoretical results, the numerical examples and simulations are presented. Our findings also demonstrate that the stationary distribution and extinction of species for the stochastic two predators–one prey system are affected by random perturbations, leading to an imbalance in ecology.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 4","pages":"4952-4979"},"PeriodicalIF":2.1,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143379942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Quantum graphs model processes in complex systems represented as spatial networks in various fields of natural science and technology. An example is the oscillations of elastic string networks, the nodes of which, besides the continuity conditions, also obey the Kirchhoff conditions, expressing the balance of tensions. In this paper, we propose a new look at quantum graphs as temporal networks, which means that the variable parametrizing the edges of a graph is interpreted as time, while each internal vertex is a branching point giving several different scenarios for the further trajectory of a process. Then Kirchhoff-type conditions may also arise. Namely, they will be satisfied by such a trajectory of the process that is optimal with account of all the scenarios simultaneously. By employing the recent concept of global delay, we extend the problem of damping a first-order control system with aftereffect, considered earlier only on an interval, to an arbitrary tree graph. The first means that the delay, imposed starting from the initial moment of time, associated with the root of the tree, propagates through all internal vertices. Bringing the system into the equilibrium and minimizing the energy functional with account of the anticipated probability of each scenario, we come to a variational problem. Then, we establish its equivalence to a self-adjoint boundary value problem on the tree for some second-order equations involving both the global delay and the global advance. The unique solvability of both problems is proved. We also illustrate that the interval case when the coefficients of the equation are discrete stochastic processes in discrete time can be viewed as the extension to a tree.
{"title":"On damping a control system with global aftereffect on quantum graphs: Stochastic interpretation","authors":"Sergey Buterin","doi":"10.1002/mma.10549","DOIUrl":"https://doi.org/10.1002/mma.10549","url":null,"abstract":"<p>Quantum graphs model processes in complex systems represented as spatial networks in various fields of natural science and technology. An example is the oscillations of elastic string networks, the nodes of which, besides the continuity conditions, also obey the Kirchhoff conditions, expressing the balance of tensions. In this paper, we propose a new look at quantum graphs as <i>temporal</i> networks, which means that the variable parametrizing the edges of a graph is interpreted as time, while each internal vertex is a branching point giving several different scenarios for the further trajectory of a process. Then Kirchhoff-type conditions may also arise. Namely, they will be satisfied by such a trajectory of the process that is optimal with account of all the scenarios simultaneously. By employing the recent concept of global delay, we extend the problem of damping a first-order control system with aftereffect, considered earlier only on an interval, to an arbitrary tree graph. The first means that the delay, imposed starting from the initial moment of time, associated with the root of the tree, propagates through all internal vertices. Bringing the system into the equilibrium and minimizing the energy functional with account of the anticipated probability of each scenario, we come to a variational problem. Then, we establish its equivalence to a self-adjoint boundary value problem on the tree for some second-order equations involving both the global delay and the global advance. The unique solvability of both problems is proved. We also illustrate that the interval case when the coefficients of the equation are discrete stochastic processes in discrete time can be viewed as the extension to a tree.</p>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 4","pages":"4310-4331"},"PeriodicalIF":2.1,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143380068","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let Y be a random variable whose moment generating function exists in some neighborhood of the origin. The aim of this paper is to study probabilistic versions of the degenerate Whitney numbers of the second kind and those of the degenerate Dowling polynomials, namely, the probabilistic degenerate Whitney numbers of the second kind associated with