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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
A Tension Spline Based Numerical Algorithm for Singularly Perturbed Partial Differential Equations on Non-uniform Discretization 基于张力样条的非均匀离散奇异扰动偏微分方程数值算法
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-04-03 DOI: 10.1007/s10440-024-00645-2
Murali Mohan Kumar P., Ravi Kanth A.S.V.
{"title":"A Tension Spline Based Numerical Algorithm for Singularly Perturbed Partial Differential Equations on Non-uniform Discretization","authors":"Murali Mohan Kumar P.,&nbsp;Ravi Kanth A.S.V.","doi":"10.1007/s10440-024-00645-2","DOIUrl":"10.1007/s10440-024-00645-2","url":null,"abstract":"<div><p>The present study investigates an algorithm numerically for finding the solution of partial differential equation with differences involved singular perturbation parameter(SPPDE) on non-uniform grid. Taylor series expansion provides a close approximation of the delay and advance terms in the convection-diffusion terms. After the approximations in shift containing terms, we applied the Crank-Nicolson application on uniform grid in the vertical direction. Subsequently, the resultant system is employed by the method of tension spline on a piece-wise uniform grid. Empirical evidence has shown that the suggested approach exhibits second-order characteristics in both the spatial and temporal dimensions. The effectiveness of derived scheme demonstrated through the solution of examples and the results are compared with existed methods. In the conclusion section, we will discuss the effect of shift parameters behavior for various singular perturbation parameter.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"190 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140591705","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
Threshold Dynamics for Diffusive Age-Structured Model over Unbounded Domains: Age-Dependent Death and Diffusion Rates 无界域上扩散年龄结构模型的阈值动力学：依赖年龄的死亡和扩散率
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-03-28 DOI: 10.1007/s10440-024-00643-4
Mohammadkheer AlJararha
{"title":"Threshold Dynamics for Diffusive Age-Structured Model over Unbounded Domains: Age-Dependent Death and Diffusion Rates","authors":"Mohammadkheer AlJararha","doi":"10.1007/s10440-024-00643-4","DOIUrl":"10.1007/s10440-024-00643-4","url":null,"abstract":"<div><p>The global dynamics of the typical age-structured model with age-dependent mortality and diffusion rates on unbounded domains have been established. On the one hand, we showed that a positive and constant state solution of the mature population is globally asymptotically stable with respect to the compact-open topology; on the other hand, we showed that the trivial solution is globally asymptotically stable with respect to the usual supremum norm. As an application of our result, we applied the result to birth functions appearing in biology. In addition to the theoretical results, we also present a numerical simulation.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"190 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140325843","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 Error Bounds for the Extended Vertical Linear Complementarity Problems of CKV-Type Matrices and CKV-Type (B)-Matrices CKV 型矩阵和 CKV 型 $B$ - 矩阵的扩展垂直线性互补问题的全局误差约束
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-03-28 DOI: 10.1007/s10440-024-00644-3
Lei Gao, Xiudan Jia, Xia Jing, Yi Liu
{"title":"Global Error Bounds for the Extended Vertical Linear Complementarity Problems of CKV-Type Matrices and CKV-Type (B)-Matrices","authors":"Lei Gao,&nbsp;Xiudan Jia,&nbsp;Xia Jing,&nbsp;Yi Liu","doi":"10.1007/s10440-024-00644-3","DOIUrl":"10.1007/s10440-024-00644-3","url":null,"abstract":"<div><p>Some global error bounds with undetermined parameters, which are not always valid, for the extended vertical linear complementarity problems (LCP) of CKV-type matrices and CKV-type <span>(B)</span>-matrices, are presented by Yan and Wang (Jpn. J. Ind. Appl. Math. 41:129–150, 2024). In this paper, new global error bounds for the extended vertical LCP of CKV-type matrices and CKV-type <span>(B)</span>-matrices are given, which depend only on the entries of the involved matrices. Numerical examples show that the new bounds are better than those provided in Zhang et al. (Comput. Optim. Appl. 42(3):335–352, 2009) and Wang et al. (Comput. Appl. Math. 40:148, 2021) in some cases.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"190 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140325685","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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