Journal of Nonlinear Science最新文献

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Charge Transport Systems with Fermi-Dirac Statistics for Memristors.
IF 2.6 2区 数学
Journal of Nonlinear Science Pub Date : 2025-01-01 Epub Date: 2025-02-18 DOI: 10.1007/s00332-025-10140-z
Maxime Herda, Ansgar Jüngel, Stefan Portisch
{"title":"Charge Transport Systems with Fermi-Dirac Statistics for Memristors.","authors":"Maxime Herda, Ansgar Jüngel, Stefan Portisch","doi":"10.1007/s00332-025-10140-z","DOIUrl":"10.1007/s00332-025-10140-z","url":null,"abstract":"<p><p>An instationary drift-diffusion system for the electron, hole, and oxygen vacancy densities, coupled to the Poisson equation for the electric potential, is analyzed in a bounded domain with mixed Dirichlet-Neumann boundary conditions. The electron and hole densities are governed by Fermi-Dirac statistics, while the oxygen vacancy density is governed by Blakemore statistics. The equations model the charge carrier dynamics in memristive devices used in semiconductor technology. The global existence of weak solutions is proved in up to three space dimensions. The proof is based on the free energy inequality, an iteration argument to improve the integrability of the densities, and estimations of the Fermi-Dirac integral. Under a physically realistic elliptic regularity condition, it is proved that the densities are bounded.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"35 2","pages":"44"},"PeriodicalIF":2.6,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11836105/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143469817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
The Port-Hamiltonian Structure of Continuum Mechanics.
IF 2.6 2区 数学
Journal of Nonlinear Science Pub Date : 2025-01-01 Epub Date: 2025-01-28 DOI: 10.1007/s00332-025-10130-1
Ramy Rashad, Stefano Stramigioli
{"title":"The Port-Hamiltonian Structure of Continuum Mechanics.","authors":"Ramy Rashad, Stefano Stramigioli","doi":"10.1007/s00332-025-10130-1","DOIUrl":"https://doi.org/10.1007/s00332-025-10130-1","url":null,"abstract":"<p><p>In this paper, we present a novel approach to the geometric formulation of solid and fluid mechanics within the port-Hamiltonian framework, which extends the standard Hamiltonian formulation to non-conservative and open dynamical systems. Leveraging Dirac structures, instead of symplectic or Poisson structures, this formalism allows the incorporation of energy exchange within the spatial domain or through its boundary, which allows for a more comprehensive description of continuum mechanics. Building upon our recent work in describing nonlinear elasticity using exterior calculus and bundle-valued differential forms, this paper focuses on the systematic derivation of port-Hamiltonian models for solid and fluid mechanics in the material, spatial, and convective representations using Hamiltonian reduction theory. This paper also discusses constitutive relations for stress within this framework including hyper-elasticity, for both finite and infinitesimal strains, as well as viscous fluid flow governed by the Navier-Stokes equations.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"35 2","pages":"35"},"PeriodicalIF":2.6,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11775082/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143069304","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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
Biologically Inspired Pectoral Propulsors with Flapping and Rowing Control for a Specified Stroke Plane Angle 具有特定冲程平面角度的拍打和划船控制功能的生物启发胸桨
IF 3 2区 数学
Journal of Nonlinear Science Pub Date : 2024-09-17 DOI: 10.1007/s00332-024-10078-8
Bing Luo, Wei Li
{"title":"Biologically Inspired Pectoral Propulsors with Flapping and Rowing Control for a Specified Stroke Plane Angle","authors":"Bing Luo, Wei Li","doi":"10.1007/s00332-024-10078-8","DOIUrl":"https://doi.org/10.1007/s00332-024-10078-8","url":null,"abstract":"<p>Many flying and swimming creatures have morphing pectoral propulsors (wings or fins) for propulsion, typically with flapping, rowing, and pitching motions; flapping and rowing motions are responsible for the <i>stroke plane angle</i> that is important for a broader performance space of the propulsor, while the stroke plane angle has been less characterized and implemented by artificial propulsors of biomimetic vehicles and thus has lack of stroke plane angle control. In this paper, we consider robotic pectoral propulsors with combined flapping and rowing motions for a stroke plane angle that can be generally specified. We consider two possible rotation axes configurations (i.e., the dependence of the rotation axes for flapping and rowing). For each rotation axes configuration, we propose the kinematic relations between the flapping and rowing motions for a generally specified stroke plane angle and provide the general flapping (or rowing) kinematics as a function of the rowing (or flapping) kinematics, which have not been characterized previously. These results serve as the reference trajectories of the propulsor for specified stroke plane angles and have implications for stroke plane angle control and thus have implications to achieve a broader performance space for biomimetic propulsors.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"77 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142269337","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
Critical Transitions for Asymptotically Concave or d-Concave Nonautonomous Differential Equations with Applications in Ecology 渐近凹或 d-Concave 非自治微分方程的临界转换及其在生态学中的应用
IF 3 2区 数学
Journal of Nonlinear Science Pub Date : 2024-09-16 DOI: 10.1007/s00332-024-10088-6
Jesús Dueñas, Carmen Núñez, Rafael Obaya
{"title":"Critical Transitions for Asymptotically Concave or d-Concave Nonautonomous Differential Equations with Applications in Ecology","authors":"Jesús Dueñas, Carmen Núñez, Rafael Obaya","doi":"10.1007/s00332-024-10088-6","DOIUrl":"https://doi.org/10.1007/s00332-024-10088-6","url":null,"abstract":"<p>The occurrence of tracking or tipping situations for a transition equation <span>(x'=f(t,x,Gamma (t,x)))</span> with asymptotic limits <span>(x'=f(t,x,Gamma _pm (t,x)))</span> is analyzed. The approaching condition is just <span>(lim _{trightarrow pm infty }(Gamma (t,x)-Gamma _pm (t,x))=0)</span> uniformly on compact real sets, and so there is no restriction to the dependence on time of the asymptotic equations. The hypotheses assume concavity in <i>x</i> either of the maps <span>(xmapsto f(t,x,Gamma _pm (t,x)))</span> or of their derivatives with respect to the state variable (d-concavity), but not of <span>(xmapsto f(t,x,Gamma (t,x)))</span> nor of its derivative. The analysis provides a powerful tool to analyze the occurrence of critical transitions for one-parametric families <span>(x'=f(t,x,Gamma ^c(t,x)))</span>. The new approach significatively widens the field of application of the results, since the evolution law of the transition equation can be essentially different from those of the limit equations. Among these applications, some scalar population dynamics models subject to nontrivial predation and migration patterns are analyzed, both theoretically and numerically. Some key points in the proofs are: to understand the transition equation as part of an orbit in its hull which approaches the -limit and <img alt=\"\" src=\"//media.springernature.com/lw17/springer-static/image/art%3A10.1007%2Fs00332-024-10088-6/MediaObjects/332_2024_10088_IEq8_HTML.gif\" style=\"width:17px;max-width:none;\"/>-limit sets; to observe that these sets concentrate all the ergodic measures; and to prove that in order to describe the dynamical possibilities of the equation it is sufficient that the concavity or d-concavity conditions hold for a complete measure subset of the equations of the hull.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"77 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142257205","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 Resonant Lyapunov Centre Theorem with an Application to Doubly Periodic Travelling Hydroelastic Waves 共振李亚普诺夫中心定理在双周期水弹性游波中的应用
IF 3 2区 数学
Journal of Nonlinear Science Pub Date : 2024-09-14 DOI: 10.1007/s00332-024-10073-z
R. Ahmad, M. D. Groves, D. Nilsson
{"title":"A Resonant Lyapunov Centre Theorem with an Application to Doubly Periodic Travelling Hydroelastic Waves","authors":"R. Ahmad, M. D. Groves, D. Nilsson","doi":"10.1007/s00332-024-10073-z","DOIUrl":"https://doi.org/10.1007/s00332-024-10073-z","url":null,"abstract":"<p>We present a Lyapunov centre theorem for an antisymplectically reversible Hamiltonian system exhibiting a nondegenerate 1 : 1 or <span>(1:-1)</span> semisimple resonance as a detuning parameter is varied. The system can be finite- or infinite-dimensional (and quasilinear) and have a non-constant symplectic structure. We allow the origin to be a ‘trivial’ eigenvalue arising from a translational symmetry or, in an infinite-dimensional setting, to lie in the continuous spectrum of the linearised Hamiltonian vector field provided a compatibility condition on its range is satisfied. As an application, we show how Kirchgässner’s spatial dynamics approach can be used to construct doubly periodic travelling waves on the surface of a three-dimensional body of water (of finite or infinite depth) beneath a thin ice sheet (‘hydroelastic waves’). The hydrodynamic problem is formulated as a reversible Hamiltonian system in which an arbitrary horizontal spatial direction is the time-like variable, and the infinite-dimensional phase space consists of wave profiles which are periodic (with fixed period) in a second, different horizontal direction. Applying our Lyapunov centre theorem at a point in parameter space associated with a 1 : 1 or <span>(1:-1)</span> semisimple resonance yields a periodic solution of the spatial Hamiltonian system corresponding to a doubly periodic hydroelastic wave.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"18 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142257206","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
Solitary-Wave Solutions of the Fractional Nonlinear Schrödinger Equation: I—Existence and Numerical Generation 分数非线性薛定谔方程的孤波解:I-存在性与数值生成
IF 3 2区 数学
Journal of Nonlinear Science Pub Date : 2024-09-11 DOI: 10.1007/s00332-024-10086-8
Angel Durán, Nuria Reguera
{"title":"Solitary-Wave Solutions of the Fractional Nonlinear Schrödinger Equation: I—Existence and Numerical Generation","authors":"Angel Durán, Nuria Reguera","doi":"10.1007/s00332-024-10086-8","DOIUrl":"https://doi.org/10.1007/s00332-024-10086-8","url":null,"abstract":"<p>The present paper is the first part of a project devoted to the fractional nonlinear Schrödinger (fNLS) equation. It is concerned with the existence and numerical generation of the solitary-wave solutions. For the first point, some conserved quantities of the problem are used to search for solitary-wave solutions from a constrained critical point problem and the application of the concentration-compactness theory. Several properties of the waves, such as the regularity and the asymptotic decay in some cases, are derived from the existence result. Some other properties, such as the monotone behavior and the speed-amplitude relation, will be explored computationally. To this end, a numerical procedure for the generation of the profiles is proposed. The method is based on a Fourier pseudospectral approximation of the differential system for the profiles and the use of Petviashvili’s iteration with extrapolation.\u0000</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"10 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206260","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
Chaotic Dynamics at the Boundary of a Basin of Attraction via Non-transversal Intersections for a Non-global Smooth Diffeomorphism 通过非全局光滑衍射的非横向交叉在吸引盆地边界的混沌动力学
IF 3 2区 数学
Journal of Nonlinear Science Pub Date : 2024-09-11 DOI: 10.1007/s00332-024-10079-7
Ernest Fontich, Antonio Garijo, Xavier Jarque
{"title":"Chaotic Dynamics at the Boundary of a Basin of Attraction via Non-transversal Intersections for a Non-global Smooth Diffeomorphism","authors":"Ernest Fontich, Antonio Garijo, Xavier Jarque","doi":"10.1007/s00332-024-10079-7","DOIUrl":"https://doi.org/10.1007/s00332-024-10079-7","url":null,"abstract":"<p>In this paper, we give analytic proofs of the existence of transversal homoclinic points for a family of non-globally smooth diffeomorphisms having the origin as a fixed point which come out as a truncated map governing the local dynamics near a critical period three-cycle associated with the Secant map. Using Moser’s version of Birkhoff–Smale’s theorem, we prove that the boundary of the basin of attraction of the origin contains a Cantor-like invariant subset such that the restricted dynamics to it is conjugate to the full shift of <i>N</i>-symbols for any integer <span>(Nge 2)</span> or infinity.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"13 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206261","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
Stability and Bifurcation Analysis of a Reaction–Diffusion SIRS Epidemic Model with the General Saturated Incidence Rate 具有一般饱和发病率的反应-扩散 SIRS 流行模型的稳定性和分岔分析
IF 3 2区 数学
Journal of Nonlinear Science Pub Date : 2024-09-04 DOI: 10.1007/s00332-024-10081-z
Gaoyang She, Fengqi Yi
{"title":"Stability and Bifurcation Analysis of a Reaction–Diffusion SIRS Epidemic Model with the General Saturated Incidence Rate","authors":"Gaoyang She, Fengqi Yi","doi":"10.1007/s00332-024-10081-z","DOIUrl":"https://doi.org/10.1007/s00332-024-10081-z","url":null,"abstract":"<p>In this paper, we are concerned with the dynamics of a reaction–diffusion SIRS epidemic model with the general saturated nonlinear incidence rates. Firstly, we show the global existence and boundedness of the in-time solutions for the parabolic system. Secondly, for the ODEs system, we analyze the existence and stability of the disease-free equilibrium solution, the endemic equilibrium solutions as well as the bifurcating periodic solution. In particular, in the language of the basic reproduction number, we are able to address the existence of the saddle-node-like bifurcation and the secondary bifurcation (Hopf bifurcation). Our results also suggest that the ODEs system has a Allee effect, i.e., one can expect either the coexistence of a stable disease-free equilibrium and a stable endemic equilibrium solution, or the coexistence of a stable disease-free equilibrium solution and a stable periodic solution. Finally, for the PDEs system, we are capable of deriving the Turing instability criteria in terms of the diffusion rates for both the endemic equilibrium solutions and the Hopf bifurcating periodic solution. The onset of Turing instability can bring out multi-level bifurcations and manifest itself as the appearance of new spatiotemporal patterns. It seems also interesting to note that <i>p</i> and <i>k</i>, appearing in the saturated incidence rate <span>(kSI^p/(1+alpha I^p))</span>, tend to play far reaching roles in the spatiotemporal pattern formations.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"185 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206262","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
Measure-Valued Structured Deformations 量值结构变形
IF 3 2区 数学
Journal of Nonlinear Science Pub Date : 2024-09-03 DOI: 10.1007/s00332-024-10076-w
Stefan Krömer, Martin Kružík, Marco Morandotti, Elvira Zappale
{"title":"Measure-Valued Structured Deformations","authors":"Stefan Krömer, Martin Kružík, Marco Morandotti, Elvira Zappale","doi":"10.1007/s00332-024-10076-w","DOIUrl":"https://doi.org/10.1007/s00332-024-10076-w","url":null,"abstract":"<p>Measure-valued structured deformations are introduced to present a unified theory of deformations of continua. The energy associated with a measure-valued structured deformation is defined via relaxation departing either from energies associated with classical deformations or from energies associated with structured deformations. A concise integral representation of the energy functional is provided both in the unconstrained case and under Dirichlet conditions on a part of the boundary.\u0000</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"20 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206280","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
The Dynamics of Periodic Traveling Interfacial Electrohydrodynamic Waves: Bifurcation and Secondary Bifurcation 周期性行进的界面电流体动力波的动力学:分岔和二次分岔
IF 3 2区 数学
Journal of Nonlinear Science Pub Date : 2024-09-02 DOI: 10.1007/s00332-024-10085-9
Guowei Dai, Fei Xu, Yong Zhang
{"title":"The Dynamics of Periodic Traveling Interfacial Electrohydrodynamic Waves: Bifurcation and Secondary Bifurcation","authors":"Guowei Dai, Fei Xu, Yong Zhang","doi":"10.1007/s00332-024-10085-9","DOIUrl":"https://doi.org/10.1007/s00332-024-10085-9","url":null,"abstract":"<p>In this paper, we consider two-dimensional periodic capillary-gravity waves traveling under the influence of a vertical electric field. The full system is a nonlinear, two-layered, free boundary problem. The interface dynamics are derived by coupling Euler equations for the velocity field of the fluid with voltage potential equations governing the electric field. We first introduce the naive flattening technique to transform the free boundary problem into a fixed boundary problem. We then prove the existence of small-amplitude electrohydrodynamic waves with constant vorticity using local bifurcation theory. Moreover, we show that these electrohydrodynamic waves are formally stable in the linearized sense. Furthermore, we obtain a secondary bifurcation curve that emerges from the primary branch, consisting of ripple solutions on the interface. As far as we know, such solutions in electrohydrodynamics are established for the first time. It is worth noting that the electric field <span>(E_0)</span> plays a key role in controlling the shapes and types of waves on the interface.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"8 1","pages":""},"PeriodicalIF":3.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142206263","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
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