European Journal of Applied Mathematics最新文献

{"title":"Sufficiency of -cyclical monotonicity in a class of multi-marginal optimal transport problems","authors":"Luigi De Pascale, Anna Kausamo","doi":"10.1017/s0956792524000202","DOIUrl":"https://doi.org/10.1017/s0956792524000202","url":null,"abstract":"<p><span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240513153132896-0623:S0956792524000202:S0956792524000202_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$c$</span></span></img></span></span>-cyclical monotonicity is the most important optimality condition for an optimal transport plan. While the proof of necessity is relatively easy, the proof of sufficiency is often more difficult or even elusive. We present here a new approach, and we show how known results are derived in this new framework and how this approach allows to prove sufficiency in situations previously not treatable.</p>","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140933521","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":"Unified framework for the separation property in binary phase-segregation processes with singular entropy densities","authors":"Ciprian G. Gal, Andrea Poiatti","doi":"10.1017/s0956792524000196","DOIUrl":"https://doi.org/10.1017/s0956792524000196","url":null,"abstract":"This paper investigates the separation property in binary phase-segregation processes modelled by Cahn-Hilliard type equations with constant mobility, singular entropy densities and different particle interactions. Under general assumptions on the entropy potential, we prove the strict separation property in both two and three-space dimensions. Namely, in 2D, we notably extend the minimal assumptions on the potential adopted so far in the literature, by only requiring a mild growth condition of its first derivative near the singular points <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0956792524000196_inline1.png\"/> <jats:tex-math> $pm 1$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, without any pointwise additional assumption on its second derivative. For all cases, we provide a compact proof using De Giorgi’s iterations. In 3D, we also extend the validity of the asymptotic strict separation property to the case of fractional Cahn-Hilliard equation, as well as show the validity of the separation when the initial datum is close to an ‘energy minimizer’. Our framework offers insights into statistical factors like particle interactions, entropy choices and correlations governing separation, with broad applicability.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140933518","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":"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":"Modelling of the fluid flow in a thin domain with injection through permeable boundary","authors":"E. Marušić‐Paloka, Igor Pažanin","doi":"10.1017/s0956792524000123","DOIUrl":"https://doi.org/10.1017/s0956792524000123","url":null,"abstract":"\u0000 In this paper, we derive the effective model describing a thin-domain flow with permeable boundary through which the fluid is injected into the domain. We start with incompressible Stokes system and perform the rigorous asymptotic analysis. Choosing the appropriate scaling for the injection leads to a compressible effective model. In this paper, we derive the effective model describing a thin-domain flow with permeable boundary through which the fluid is injected into the domain. We start with incompressible Stokes system and perform the rigorous asymptotic analysis. Choosing the appropriate scaling for the injection leads to a compressible effective model.","PeriodicalId":51046,"journal":{"name":"European Journal of Applied Mathematics","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2024-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140656553","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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":"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":"<p>We consider heat or mass transport from a circular cylinder under a uniform crossflow at small Reynolds numbers, <span><span><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\"><span data-mathjax-type=\"texmath\"><span>$mathrm{Re}ll 1$</span></span></img></span></span>. 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 <span><span><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\"><span data-mathjax-type=\"texmath\"><span>$log mathrm{Re}$</span></span></img></span></span>. We here make use of the hybrid approximation of Kropinski, Ward &amp; Keller [(1995) SIAM <span>J. Appl. Math.</span> <span>55</span>, 1484], based upon a robust asymptotic expansion in powers of <span><span><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\"><span data-mathjax-type=\"texmath\"><span>$mathrm{Re}$</span></span></img></span></span>. In that approximation, the “inner” streamfunction is provided by the product of a pre-factor <span><span><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\"><span data-mathjax-type=\"texmath\"><span>$S$</span></span></img></span></span>, a slowly varying function of <span><span><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\"><span data-mathjax-type=\"texmath\"><span>$mathrm{Re}$</span></span></img></span></span>, with a <span><span><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\"><span data-mathjax-type=\"texmath\"><span>$mathrm{Re}$</span></span></img></span></span>-independent “canonical” solution of a simple mathematical form. The pre-factor, in turn, is determined as an implicit function of <span><span><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\"><span data-mathjax-type=\"texmath\"><span>$log mathrm{Re}$</span></span></img></span></span> 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":null,"pages":null},"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}