European Journal of Applied Mathematics最新文献

{"title":"Threshold dynamics scenario of a plants-pollinators cooperative system with impulsive effect on a periodically evolving domain","authors":"Jie Wang, Ruirui Yang, Jian Wang, Jianxiong Cao","doi":"10.1017/s0956792524000135","DOIUrl":"https://doi.org/10.1017/s0956792524000135","url":null,"abstract":"Flowering plants depend on some animals for pollination and contribute to nourish the animals in natural environments. We call these animals pollinators and build a plants-pollinators cooperative model with impulsive effect on a periodically evolving domain. Next, we define the ecological reproduction index for single plant model and plants-pollinators system, respectively, whose threshold dynamics, including the extinction, persistence and coexistence, is established by the method of upper and lower solutions. Theoretical analysis shows that a large domain evolution rate has a positive influence on the survival of pollinators whether or not the impulsive effect occurs, and the pulse eliminates the pollinators even when the evolution rate is high. Moreover, some selective numerical simulations are still performed to explain our theoretical results.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"11 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140834661","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}

{"title":"Emergent behaviours of a non-abelian quantum synchronisation model over the unitary group","authors":"Dohyun Kim, Jeongho Kim","doi":"10.1017/s095679252400010x","DOIUrl":"https://doi.org/10.1017/s095679252400010x","url":null,"abstract":"We introduce a new non-abelian quantum synchronisation model over the unitary group, represented as a gradient flow, where state matrices asymptotically converge to a common one up to phase translation. We provide a sufficient framework leading to quantum synchronisation based on Riccati-type differential inequalities. In addition, uniform time-delayed interaction is considered for modelling realistic communication, and we demonstrate that quantum synchronisation is persistent when a small time delay is allowed. Finally, numerical simulation is performed to visualise qualitative behaviours and support theoretical results.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"208 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140834658","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}

{"title":"Flocking dynamics of agents moving with a constant speed and a randomly switching topology","authors":"Hyunjin Ahn, Woojoo Shim","doi":"10.1017/s0956792524000214","DOIUrl":"https://doi.org/10.1017/s0956792524000214","url":null,"abstract":"In this paper, we present a sufficient framework to exhibit the sample path-wise asymptotic flocking dynamics of the Cucker–Smale model with unit-speed constraint and the randomly switching network topology. We employ a matrix formulation of the given equation, which allows us to evaluate the diameter of velocities with respect to the adjacency matrix of the network. Unlike the previous result on the randomly switching Cucker–Smale model, the unit-speed constraint disallows the system to be considered as a nonautonomous linear ordinary differential equation on velocity vector, which forces us to get a weaker form of the flocking estimate than the result for the original Cucker–Smale model.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"46 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140842452","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}

{"title":"Uniform propagation of chaos for a dollar exchange econophysics model","authors":"Fei Cao, Roberto Cortez","doi":"10.1017/s0956792524000184","DOIUrl":"https://doi.org/10.1017/s0956792524000184","url":null,"abstract":"We study the poor-biased model for money exchange introduced in Cao &amp; Motsch ((2023) <jats:italic>Kinet. Relat. Models</jats:italic> 16(5), 764–794.): agents are being randomly picked at a rate proportional to their current wealth, and then the selected agent gives a dollar to another agent picked uniformly at random. Simulations of a stochastic system of finitely many agents as well as a rigorous analysis carried out in Cao &amp; Motsch ((2023) <jats:italic>Kinet. Relat. Models</jats:italic> 16(5), 764–794.), Lanchier ((2017) <jats:italic>J. Stat. Phys.</jats:italic> 167(1), 160–172.) suggest that, when both the number of agents and time become large enough, the distribution of money among the agents converges to a Poisson distribution. In this manuscript, we establish a uniform-in-time propagation of chaos result as the number of agents goes to infinity, which justifies the validity of the mean-field deterministic infinite system of ordinary differential equations as an approximation of the underlying stochastic agent-based dynamics.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"23 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-04-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140637166","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}

{"title":"Macroscopic limit of a Fokker-Planck model of swarming rigid bodies","authors":"Pierre Degond, Amic Frouvelle","doi":"10.1017/s0956792524000111","DOIUrl":"https://doi.org/10.1017/s0956792524000111","url":null,"abstract":"We consider self-propelled rigid bodies interacting through local body-attitude alignment modelled by stochastic differential equations. We derive a hydrodynamic model of this system at large spatio-temporal scales and particle numbers in any dimension <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0956792524000111_inline1.png\" /> <jats:tex-math> $n geq 3$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. This goal was already achieved in dimension <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0956792524000111_inline2.png\" /> <jats:tex-math> $n=3$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> or in any dimension <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0956792524000111_inline3.png\" /> <jats:tex-math> $n geq 3$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> for a different system involving jump processes. However, the present work corresponds to huge conceptual and technical gaps compared with earlier ones. The key difficulty is to determine an auxiliary but essential object, the generalised collision invariant. We achieve this aim by using the geometrical structure of the rotation group, namely its maximal torus, Cartan subalgebra and Weyl group as well as other concepts of representation theory and Weyl’s integration formula. The resulting hydrodynamic model appears as a hyperbolic system whose coefficients depend on the generalised collision invariant.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"12 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140630596","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}

{"title":"A finite-volume scheme for fractional diffusion on bounded domains","authors":"Rafael Bailo, José A. Carrillo, Stefano Fronzoni, David Gómez-Castro","doi":"10.1017/s0956792524000172","DOIUrl":"https://doi.org/10.1017/s0956792524000172","url":null,"abstract":"<p>We propose a new fractional Laplacian for bounded domains, expressed as a conservation law and thus particularly suited to finite-volume schemes. Our approach permits the direct prescription of no-flux boundary conditions. We first show the well-posedness theory for the fractional heat equation. We also develop a numerical scheme, which correctly captures the action of the fractional Laplacian and its anomalous diffusion effect. We benchmark numerical solutions for the Lévy–Fokker–Planck equation against known analytical solutions. We conclude by numerically exploring properties of these equations with respect to their stationary states and long-time asymptotics.</p>","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"47 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140576039","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}

{"title":"Slow passage through the Busse balloon – predicting steps on the Eckhaus staircase","authors":"Anna Asch, Montie Avery, Anthony Cortez, Arnd Scheel","doi":"10.1017/s0956792524000160","DOIUrl":"https://doi.org/10.1017/s0956792524000160","url":null,"abstract":"<p>Motivated by the impact of worsening climate conditions on vegetation patches, we study dynamic instabilities in an idealised Ginzburg–Landau model. Our main results predict time instances of sudden drops in wavenumber and the resulting target states. The changes in wavenumber correspond to the annihilation of individual vegetation patches when resources are scarce and cannot support the original number of patches. Drops happen well after the primary pattern has destabilised at the Eckhaus boundary and key to distinguishing between the disappearance of 1,2 or more patches during the drop are complex spatio-temporal resonances in the linearisation at the unstable pattern. We support our results with numerical simulations and expect our results to be conceptually applicable universally near the Eckhaus boundary, in particular in more realistic models.</p>","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"6 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140576038","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}

{"title":"Large Péclet number forced convection from a circular wire in a uniform stream: hybrid approximations at small Reynolds numbers","authors":"Ehud Yariv","doi":"10.1017/s0956792524000147","DOIUrl":"https://doi.org/10.1017/s0956792524000147","url":null,"abstract":"&lt;p&gt;We consider heat or mass transport from a circular cylinder under a uniform crossflow at small Reynolds numbers, &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240415115644043-0058:S0956792524000147:S0956792524000147_inline1.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$mathrm{Re}ll 1$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt;. This problem has been thwarted in the past by limitations inherent in the classical analyses of the singular flow problem, which have used asymptotic expansions in inverse powers of &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240415115644043-0058:S0956792524000147:S0956792524000147_inline2.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$log mathrm{Re}$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt;. We here make use of the hybrid approximation of Kropinski, Ward &amp; Keller [(1995) SIAM &lt;span&gt;J. Appl. Math.&lt;/span&gt; &lt;span&gt;55&lt;/span&gt;, 1484], based upon a robust asymptotic expansion in powers of &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240415115644043-0058:S0956792524000147:S0956792524000147_inline3.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$mathrm{Re}$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt;. In that approximation, the “inner” streamfunction is provided by the product of a pre-factor &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240415115644043-0058:S0956792524000147:S0956792524000147_inline4.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$S$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt;, a slowly varying function of &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240415115644043-0058:S0956792524000147:S0956792524000147_inline5.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$mathrm{Re}$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt;, with a &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240415115644043-0058:S0956792524000147:S0956792524000147_inline6.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$mathrm{Re}$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt;-independent “canonical” solution of a simple mathematical form. The pre-factor, in turn, is determined as an implicit function of &lt;span&gt;&lt;span&gt;&lt;img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240415115644043-0058:S0956792524000147:S0956792524000147_inline7.png\"&gt;&lt;span data-mathjax-type=\"texmath\"&gt;&lt;span&gt;$log mathrm{Re}$&lt;/span&gt;&lt;/span&gt;&lt;/img&gt;&lt;/span&gt;&lt;/span&gt; via asymptotic matching with a numerical solution of the nonlinear single-scaled “outer” problem, where the cylinder appears as a point singularity. We exploit the hybrid approximation to analyse","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"122 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140602836","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}

{"title":"Consensus-based optimisation with truncated noise","authors":"Massimo Fornasier, Peter Richtárik, Konstantin Riedl, Lukang Sun","doi":"10.1017/s095679252400007x","DOIUrl":"https://doi.org/10.1017/s095679252400007x","url":null,"abstract":"Consensus-based optimisation (CBO) is a versatile multi-particle metaheuristic optimisation method suitable for performing non-convex and non-smooth global optimisations in high dimensions. It has proven effective in various applications while at the same time being amenable to a theoretical convergence analysis. In this paper, we explore a variant of CBO, which incorporates truncated noise in order to enhance the well-behavedness of the statistics of the law of the dynamics. By introducing this additional truncation in the noise term of the CBO dynamics, we achieve that, in contrast to the original version, higher moments of the law of the particle system can be effectively bounded. As a result, our proposed variant exhibits enhanced convergence performance, allowing in particular for wider flexibility in choosing the noise parameter of the method as we confirm experimentally. By analysing the time evolution of the Wasserstein-<jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S095679252400007X_inline1.png\" /> <jats:tex-math> $2$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> distance between the empirical measure of the interacting particle system and the global minimiser of the objective function, we rigorously prove convergence in expectation of the proposed CBO variant requiring only minimal assumptions on the objective function and on the initialisation. Numerical evidences demonstrate the benefit of truncating the noise in CBO.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"84 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140576290","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}

{"title":"Measuring multidimensional heterogeneity in emergent social phenomena","authors":"Giuseppe Toscani","doi":"10.1017/s0956792524000081","DOIUrl":"https://doi.org/10.1017/s0956792524000081","url":null,"abstract":"Measuring inequalities in a multidimensional framework is a challenging problem, which is common to most field of science and engineering. Nevertheless, despite the enormous amount of researches illustrating the fields of application of inequality indices, and of the Gini index in particular, very few consider the case of a multidimensional variable. In this paper, we consider in some details a new inequality index, based on the Fourier transform, that can be fruitfully applied to measure the degree of inhomogeneity of multivariate probability distributions. This index exhibits a number of interesting properties that make it very promising in quantifying the degree of inequality in datasets of complex and multifaceted social phenomena.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":"49 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140301840","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}