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Trend to Equilibrium for Run and Tumble Equations with Non-uniform Tumbling Kernels 具有非均匀翻滚内核的运行和翻滚方程的平衡趋势
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-05-14 DOI: 10.1007/s10440-024-00657-y
Josephine Evans, Havva Yoldaş
{"title":"Trend to Equilibrium for Run and Tumble Equations with Non-uniform Tumbling Kernels","authors":"Josephine Evans,&nbsp;Havva Yoldaş","doi":"10.1007/s10440-024-00657-y","DOIUrl":"10.1007/s10440-024-00657-y","url":null,"abstract":"<div><p>We study the long-time behaviour of a run and tumble model which is a kinetic-transport equation describing bacterial movement under the effect of a chemical stimulus. The experiments suggest that the non-uniform tumbling kernels are physically relevant ones as opposed to the uniform tumbling kernel which is widely considered in the literature to reduce the complexity of the mathematical analysis. We consider two cases: (i) the tumbling kernel depends on the angle between pre- and post-tumbling velocities, (ii) the velocity space is unbounded and the post-tumbling velocities follow the Maxwellian velocity distribution. We prove that the probability density distribution of bacteria converges to an equilibrium distribution with explicit (exponential for (i) and algebraic for (ii)) convergence rates, for any probability measure initial data. To the best of our knowledge, our results are the first results concerning the long-time behaviour of run and tumble equations with non-uniform tumbling kernels.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"191 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-024-00657-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141063724","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Reduced Variance Random Batch Methods for Nonlocal PDEs 非局部 PDE 的减方差随机批处理方法
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-05-09 DOI: 10.1007/s10440-024-00656-z
Lorenzo Pareschi, Mattia Zanella
{"title":"Reduced Variance Random Batch Methods for Nonlocal PDEs","authors":"Lorenzo Pareschi,&nbsp;Mattia Zanella","doi":"10.1007/s10440-024-00656-z","DOIUrl":"10.1007/s10440-024-00656-z","url":null,"abstract":"<div><p>Random Batch Methods (RBM) for mean-field interacting particle systems enable the reduction of the quadratic computational cost associated with particle interactions to a near-linear cost. The essence of these algorithms lies in the random partitioning of the particle ensemble into smaller batches at each time step. The interaction of each particle within these batches is then evolved until the subsequent time step. This approach effectively decreases the computational cost by an order of magnitude while increasing the amount of fluctuations due to the random partitioning. In this work, we propose a variance reduction technique for RBM applied to nonlocal PDEs of Fokker-Planck type based on a control variate strategy. The core idea is to construct a surrogate model that can be computed on the full set of particles at a linear cost while maintaining enough correlations with the original particle dynamics. Examples from models of collective behavior in opinion spreading and swarming dynamics demonstrate the great potential of the present approach.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"191 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-024-00656-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140934156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Alignment via Friction for Nonisothermal Multicomponent Fluid Systems 非等温多组分流体系统的摩擦对准
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-05-08 DOI: 10.1007/s10440-024-00655-0
Stefanos Georgiadis, Athanasios E. Tzavaras
{"title":"Alignment via Friction for Nonisothermal Multicomponent Fluid Systems","authors":"Stefanos Georgiadis,&nbsp;Athanasios E. Tzavaras","doi":"10.1007/s10440-024-00655-0","DOIUrl":"10.1007/s10440-024-00655-0","url":null,"abstract":"<div><p>The derivation of an approximate Class–I model for nonisothermal multicomponent systems of fluids, as the high-friction limit of a Class–II model is justified, by validating the Chapman–Enskog expansion performed from the Class–II model towards the Class–I model. The analysis proceeds by comparing two thermomechanical theories via relative entropy.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"191 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140934361","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
Quantum Hamiltonian Learning for the Fermi-Hubbard Model 费米-哈伯德模型的量子哈密顿学习
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-04-30 DOI: 10.1007/s10440-024-00651-4
Hongkang Ni, Haoya Li, Lexing Ying
{"title":"Quantum Hamiltonian Learning for the Fermi-Hubbard Model","authors":"Hongkang Ni,&nbsp;Haoya Li,&nbsp;Lexing Ying","doi":"10.1007/s10440-024-00651-4","DOIUrl":"10.1007/s10440-024-00651-4","url":null,"abstract":"<div><p>This work proposes a protocol for Fermionic Hamiltonian learning. For the Hubbard model defined on a bounded-degree graph, the Heisenberg-limited scaling is achieved while allowing for state preparation and measurement errors. To achieve <span>(epsilon )</span>-accurate estimation for all parameters, only <span>(tilde{mathcal{O}}(epsilon ^{-1}))</span> total evolution time is needed, and the constant factor is independent of the system size. Moreover, our method only involves simple one or two-site Fermionic manipulations, which is desirable for experiment implementation.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"191 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140828393","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
Polynomial Energy Decay Rate for the Wave Equation with Kinetic Boundary Condition 带动力学边界条件的波方程的多项式能量衰减率
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-04-22 DOI: 10.1007/s10440-024-00650-5
K. Laoubi, D. Seba
{"title":"Polynomial Energy Decay Rate for the Wave Equation with Kinetic Boundary Condition","authors":"K. Laoubi,&nbsp;D. Seba","doi":"10.1007/s10440-024-00650-5","DOIUrl":"10.1007/s10440-024-00650-5","url":null,"abstract":"<div><p>This paper concerns the polynomial decay of the dissipative wave equation subject to Kinetic boundary condition and non-neglected density in the square. After reformulating this problem into an abstract Cauchy problem, we show the existence and uniqueness of the solution. Then, by analyzing a family of eigenvalues of the corresponding operator, we prove that the rate of energy decay decreases in a polynomial way.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"191 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140677175","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
Indirect Boundary Controllability of Coupled Degenerate Wave Equations 耦合退化波方程的间接边界可控性
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-04-12 DOI: 10.1007/s10440-024-00649-y
Alhabib Moumni, Jawad Salhi, Mouhcine Tilioua
{"title":"Indirect Boundary Controllability of Coupled Degenerate Wave Equations","authors":"Alhabib Moumni,&nbsp;Jawad Salhi,&nbsp;Mouhcine Tilioua","doi":"10.1007/s10440-024-00649-y","DOIUrl":"10.1007/s10440-024-00649-y","url":null,"abstract":"<div><p>In this paper, we consider a system of two degenerate wave equations coupled through the velocities, only one of them being controlled. We assume that the coupling parameter is sufficiently small and we focus on null controllability problem. To this aim, using multiplier techniques and careful energy estimates, we first establish an indirect observability estimate for the corresponding adjoint system. Then, by applying the Hilbert Uniqueness Method, we show that the indirect boundary controllability of the original system holds for a sufficiently large time.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"190 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-024-00649-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140592140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Steady States of a Diffusive Population-Toxicant Model with Negative Toxicant-Taxis 具有负毒性-税收的扩散种群-毒素模型的稳定状态
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-04-12 DOI: 10.1007/s10440-024-00646-1
Jiawei Chu
{"title":"Steady States of a Diffusive Population-Toxicant Model with Negative Toxicant-Taxis","authors":"Jiawei Chu","doi":"10.1007/s10440-024-00646-1","DOIUrl":"10.1007/s10440-024-00646-1","url":null,"abstract":"<div><p>This paper is dedicated to studying the steady state problem of a population-toxicant model with negative toxicant-taxis, subject to homogeneous Neumann boundary conditions. The model captures the phenomenon in which the population migrates away from regions with high toxicant density towards areas with lower toxicant concentration. This paper establishes sufficient conditions for the non-existence and existence of non-constant positive steady state solutions. The results indicate that in the case of a small toxicant input rate, a strong toxicant-taxis mechanism promotes population persistence and engenders spatially heterogeneous coexistence (see, Theorem 2.3). Moreover, when the toxicant input rate is relatively high, the results unequivocally demonstrate that the combination of a strong toxicant-taxis mechanism and a high natural growth rate of the population fosters population persistence, which is also characterized by spatial heterogeneity (see, Theorem 2.4).</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"190 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-024-00646-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140591596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Global Classical Solutions to a Predator-Prey Model with Nonlinear Indirect Chemotaxis Mechanism 具有非线性间接趋化机制的捕食者-猎物模型的全局经典解法
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-04-10 DOI: 10.1007/s10440-024-00648-z
Chang-Jian Wang, Chun-Hai Ke
{"title":"Global Classical Solutions to a Predator-Prey Model with Nonlinear Indirect Chemotaxis Mechanism","authors":"Chang-Jian Wang,&nbsp;Chun-Hai Ke","doi":"10.1007/s10440-024-00648-z","DOIUrl":"10.1007/s10440-024-00648-z","url":null,"abstract":"<div><p>We deal with the following predator-prey model involving nonlinear indirect chemotaxis mechanism </p><div><div><span>$$ left { textstylebegin{array}{l@{quad }l} u_{t}=Delta u+xi nabla cdot (u nabla w)+a_{1}u(1-u^{r_{1}-1}-b_{1}v), &amp; xin Omega , t&gt;0, v_{t}=Delta v-chi nabla cdot (v nabla w)+a_{2}v(1-v^{r_{2}-1}+b_{2}u), &amp; xin Omega , t&gt;0, w_{t}=Delta w-w+z^{gamma }, &amp; xin Omega , t&gt;0, 0=Delta z-z+u^{alpha }+v^{beta }, &amp; xin Omega , t&gt;0 , end{array}displaystyle right . $$</span></div></div><p> under homogeneous Neumann boundary conditions in a bounded and smooth domain <span>(Omega subset mathbb{R}^{n})</span> (<span>(ngeq 1)</span>), where the parameters <span>(xi ,chi ,a_{1},a_{2},b_{1},b_{2},alpha ,beta ,gamma &gt;0)</span>. It has been shown that if <span>(r_{1}&gt;1)</span>, <span>(r_{2}&gt;2)</span> and <span>(gamma (alpha +beta )&lt;frac{2}{n})</span>, then there exist some suitable initial data such that the system has a global classical solution <span>((u,v,w,z))</span>, which is bounded in <span>(Omega times (0,infty ))</span>. Compared to the previous contributions, in this work, the boundedness criteria are only determined by the power exponents <span>(r_{1})</span>, <span>(r_{2})</span>, <span>(alpha )</span>, <span>(beta )</span>, <span>(gamma )</span> and spatial dimension <span>(n)</span> instead of the coefficients of the system and the sizes of initial data.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"190 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-024-00648-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140591841","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Efficient Numerical Schemes for a Two-Species Keller-Segel Model and Investigation of Its Blowup Phenomena in 3D 双物种凯勒-西格尔模型的高效数值方案及其三维爆破现象研究
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-04-10 DOI: 10.1007/s10440-024-00647-0
Xueling Huang, Jie Shen
{"title":"Efficient Numerical Schemes for a Two-Species Keller-Segel Model and Investigation of Its Blowup Phenomena in 3D","authors":"Xueling Huang,&nbsp;Jie Shen","doi":"10.1007/s10440-024-00647-0","DOIUrl":"10.1007/s10440-024-00647-0","url":null,"abstract":"<div><p>We consider in this paper numerical approximation and simulation of a two-species Keller-Segel model. The model enjoys an energy dissipation law, mass conservation and bound or positivity preserving for the population density of two species. We construct a class of very efficient numerical schemes based on the generalized scalar auxiliary variable with relaxation which preserve unconditionally the essential properties of the model at the discrete level. We conduct a sequence of numerical tests to validate the properties of these schemes, and to study the blow-up phenomena of the model in a three-dimensional domain in parabolic-elliptic form and parabolic-parabolic form.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"190 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-024-00647-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140591845","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A New Blowup Criterion to the Cauchy Problem for the Three-Dimensional Compressible Viscous Micropolar Fluids with Vacuum 带真空的三维可压缩粘性微极性流体考奇问题的新吹胀准则
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-04-04 DOI: 10.1007/s10440-024-00642-5
Xiaofeng Hou, Yinjie Xu
{"title":"A New Blowup Criterion to the Cauchy Problem for the Three-Dimensional Compressible Viscous Micropolar Fluids with Vacuum","authors":"Xiaofeng Hou,&nbsp;Yinjie Xu","doi":"10.1007/s10440-024-00642-5","DOIUrl":"10.1007/s10440-024-00642-5","url":null,"abstract":"<div><p>In this paper, we prove a new blowup criterion for the strong solution to the Cauchy problem of three-dimensional micropolar fluid equation with vacuum. Specifically, we establish a blowup criterion in terms of <span>(L_{t}^{infty }L_{x}^{q})</span> of the density, where <span>(1&lt; q&lt;infty )</span>, and it is independent on the velocity of rotation of the microscopic particles.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"190 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140591546","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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