Journal of Nonlinear Science最新文献_第3页

Mathematical Models for the Large Spread of a Contact-Based Infection: A Statistical Mechanics Approach 接触性感染大规模传播的数学模型：统计力学方法

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-07-08 DOI: 10.1007/s00332-024-10062-2

Marzia Bisi, Silvia Lorenzani

{"title":"Mathematical Models for the Large Spread of a Contact-Based Infection: A Statistical Mechanics Approach","authors":"Marzia Bisi, Silvia Lorenzani","doi":"10.1007/s00332-024-10062-2","DOIUrl":"https://doi.org/10.1007/s00332-024-10062-2","url":null,"abstract":"In this work, we derive a system of Boltzmann-type equations to describe the spread of contact-based infections, such as SARS-CoV-2 virus, at the microscopic scale, that is, by modeling the human-to-human mechanisms of transmission. To this end, we consider two populations, characterized by specific distribution functions, made up of individuals without symptoms (population 1) and infected people with symptoms (population 2). The Boltzmann operators model the interactions between individuals within the same population and among different populations with a probability of transition from one to the other due to contagion or, vice versa, to recovery. In addition, the influence of innate and adaptive immune systems is taken into account. Then, starting from the Boltzmann microscopic description we derive a set of evolution equations for the size and mean state of each population considered. Mathematical properties of such macroscopic equations, as equilibria and their stability, are investigated, and some numerical simulations are performed in order to analyze the ability of our model to reproduce the characteristic features of Covid-19 type pandemics.","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"368 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141571720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 Generalized $$Gamma $$ -Convergence Concept for a Class of Equilibrium Problems 一类均衡问题的广义 $$Gamma $$ 收敛概念

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-07-05 DOI: 10.1007/s00332-024-10059-x

Michael Hintermüller, Steven-Marian Stengl

引用次数: 0

Well-Posedness of a Viscoelastic Resistive Force Theory and Applications to Swimming 粘弹性阻力理论的良好拟合及其在游泳中的应用

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-07-03 DOI: 10.1007/s00332-024-10051-5

Laurel Ohm

{"title":"Well-Posedness of a Viscoelastic Resistive Force Theory and Applications to Swimming","authors":"Laurel Ohm","doi":"10.1007/s00332-024-10051-5","DOIUrl":"https://doi.org/10.1007/s00332-024-10051-5","url":null,"abstract":"We propose and analyze a simple model for the evolution of an immersed, inextensible filament which incorporates linear viscoelastic effects of the surrounding fluid. The model is a closed-form system of equations along the curve only which includes a ‘memory’ term due to viscoelasticity. For a planar filament, given a forcing in the form of a preferred curvature, we prove well-posedness of the fiber evolution as well as the existence of a unique time-periodic solution in the case of time-periodic forcing. Moreover, we obtain an expression for the swimming speed of the filament in terms of the preferred curvature. The swimming speed depends in a complicated way on the viscoelastic parameters corresponding to the fluid relaxation time and additional polymeric viscosity. We study this expression in detail, accompanied by numerical simulations, and show that this simple model can capture complex effects of viscoelasticity on swimming. In particular, the viscoelastic swimmer is shown to be faster than its Newtonian counterpart in some situations and slower in others. Strikingly, we even find an example where viscoelastic effects may lead to a reversal in swimming direction from the Newtonian setting, although this occurs when the displacement for both the Newtonian and viscoelastic swimmers is practically negligible.","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"30 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141527974","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Complex Fluid Models of Mixed Quantum–Classical Dynamics 量子-经典混合动力学的复杂流体模型

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-07-02 DOI: 10.1007/s00332-024-10044-4

François Gay-Balmaz, Cesare Tronci

{"title":"Complex Fluid Models of Mixed Quantum–Classical Dynamics","authors":"François Gay-Balmaz, Cesare Tronci","doi":"10.1007/s00332-024-10044-4","DOIUrl":"https://doi.org/10.1007/s00332-024-10044-4","url":null,"abstract":"Several methods in nonadiabatic molecular dynamics are based on Madelung’s hydrodynamic description of nuclear motion, while the electronic component is treated as a finite-dimensional quantum system. In this context, the quantum potential leads to severe computational challenges and one often seeks to neglect its contribution, thereby approximating nuclear motion as classical. The resulting model couples classical hydrodynamics for the nuclei to the quantum motion of the electronic component, leading to the structure of a complex fluid system. This type of mixed quantum–classical fluid models has also appeared in solvation dynamics to describe the coupling between liquid solvents and the quantum solute molecule. While these approaches represent a promising direction, their mathematical structure requires a certain care. In some cases, challenging higher-order gradients make these equations hardly tractable. In other cases, these models are based on phase-space formulations that suffer from well-known consistency issues. Here, we present a new complex fluid system that resolves these difficulties. Unlike common approaches, the current system is obtained by applying the fluid closure at the level of the action principle of the original phase-space model. As a result, the system inherits a Hamiltonian structure and retains energy/momentum balance. After discussing some of its structural properties and dynamical invariants, we illustrate the model in the case of pure-dephasing dynamics. We conclude by presenting some invariant planar models.","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"7 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141527973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Breaking Consensus in Kinetic Opinion Formation Models on Graphons 打破石墨上动能舆论形成模型的共识

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-07-01 DOI: 10.1007/s00332-024-10060-4

Bertram Düring, Jonathan Franceschi, Marie-Therese Wolfram, Mattia Zanella

引用次数: 0

Towards a Classification of Steady-State Bifurcations for Networks with Asymmetric Inputs 为非对称输入网络的稳态分岔分类而努力

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-07-01 DOI: 10.1007/s00332-024-10061-3

Manuela Aguiar, Ana Dias, Pedro Soares

引用次数: 0

Oscillatory Motions of Multiple Spikes in Three-Component Reaction–Diffusion Systems 三分量反应-扩散系统中多个尖峰的振荡运动

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-06-28 DOI: 10.1007/s00332-024-10058-y

Shuangquan Xie, Wen Yang, Jiaojiao Zhang

{"title":"Oscillatory Motions of Multiple Spikes in Three-Component Reaction–Diffusion Systems","authors":"Shuangquan Xie, Wen Yang, Jiaojiao Zhang","doi":"10.1007/s00332-024-10058-y","DOIUrl":"https://doi.org/10.1007/s00332-024-10058-y","url":null,"abstract":"For three specific singular perturbed three-component reaction–diffusion systems that admit N-spike solutions in one of the components on a finite domain, we present a detailed analysis for the dynamics of temporal oscillations in the spike positions. The onset of these oscillations is induced by N Hopf bifurcations with respect to the translation modes that are excited nearly simultaneously. To understand the dynamics of N spikes in the vicinity of Hopf bifurcations, we combine the center manifold reduction and the matched asymptotic method to derive a set of ordinary differential equations (ODEs) of dimension 2N describing the spikes’ locations and velocities, which can be recognized as normal forms of multiple Hopf bifurcations. The reduced ODE system then is represented in the form of linear oscillators with weakly nonlinear damping. By applying the multiple-time method, the leading order of the oscillation amplitudes is further characterized by an N-dimensional ODE system of the Stuart–Landau type. Although the leading order dynamics of these three systems are different, they have the same form after a suitable transformation. On the basis of the reduced systems for the oscillation amplitudes, we prove that there are at most (lfloor N/2 rfloor +1) stable equilibria, corresponding to (lfloor N /2 rfloor +1) types of different oscillations. This resolves an open problem proposed by Xie et al. (Nonlinearity 34(8):5708–5743, 2021) for a three-component Schnakenberg system and generalizes the results to two other classic systems. Numerical simulations are presented to verify the analytic results.\u0000","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"80 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Higher-Order Network Interactions Through Phase Reduction for Oscillators with Phase-Dependent Amplitude 通过相位缩减实现振幅随相位变化的振荡器的高阶网络互动

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-06-24 DOI: 10.1007/s00332-024-10053-3

Christian Bick, Tobias Böhle, Christian Kuehn

{"title":"Higher-Order Network Interactions Through Phase Reduction for Oscillators with Phase-Dependent Amplitude","authors":"Christian Bick, Tobias Böhle, Christian Kuehn","doi":"10.1007/s00332-024-10053-3","DOIUrl":"https://doi.org/10.1007/s00332-024-10053-3","url":null,"abstract":"Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction—the reduction of the dynamics onto an invariant torus—captures the emergence of collective dynamical phenomena, such as synchronization. While a first-order approximation of the dynamics on the torus may be appropriate in some situations, higher-order phase reductions become necessary, for example, when the coupling strength increases. However, these are generally hard to compute and thus they have only been derived in special cases: This includes globally coupled Stuart–Landau oscillators, where the limit cycle of the uncoupled nonlinear oscillator is circular as the amplitude is independent of the phase. We go beyond this restriction and derive second-order phase reductions for coupled oscillators for arbitrary networks of coupled nonlinear oscillators with phase-dependent amplitude, a scenario more reminiscent of real-world oscillations. We analyze how the deformation of the limit cycle affects the stability of important dynamical states, such as full synchrony and splay states. By identifying higher-order phase interaction terms with hyperedges of a hypergraph, we obtain natural classes of coupled phase oscillator dynamics on hypergraphs that adequately capture the dynamics of coupled limit cycle oscillators.\u0000","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"38 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141503469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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

Smooth Subsonic and Transonic Spiral Flows with Nonzero Vorticity to Steady Euler–Poisson System in Concentric Cylinders 同心圆柱体中具有非零涡度的平稳亚音速和跨音速螺旋流动与稳定欧拉-泊松系统

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-06-24 DOI: 10.1007/s00332-024-10057-z

Shangkun Weng, Wengang Yang, Na Zhang

引用次数: 0

The Hanging Chain Problem in the Sphere and in the Hyperbolic Plane 球面和双曲面中的悬链问题

IF 3 2区数学

Journal of Nonlinear Science Pub Date : 2024-06-19 DOI: 10.1007/s00332-024-10056-0

Rafael López

引用次数: 0