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Symplectic Structures on the Space of Space Curves. 空间曲线空间上的辛结构。
IF 2.6 2区 数学
Journal of Nonlinear Science Pub Date : 2026-01-01 Epub Date: 2026-04-15 DOI: 10.1007/s00332-026-10266-8
Martin Bauer, Sadashige Ishida, Peter W Michor
{"title":"Symplectic Structures on the Space of Space Curves.","authors":"Martin Bauer, Sadashige Ishida, Peter W Michor","doi":"10.1007/s00332-026-10266-8","DOIUrl":"10.1007/s00332-026-10266-8","url":null,"abstract":"<p><p>We present symplectic structures on the shape space of unparameterized space curves that generalize the classical Marsden-Weinstein structure. Our method integrates the Liouville 1-form of the Marsden-Weinstein structure with Riemannian structures that have been introduced in mathematical shape analysis. We also derive Hamiltonian vector fields for several classical Hamiltonian functions with respect to these new symplectic structures.</p><p><strong>Supplementary information: </strong>The online version contains supplementary material available at 10.1007/s00332-026-10266-8.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"36 2","pages":"45"},"PeriodicalIF":2.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13083510/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147724183","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
Evolution Equations on Co-evolving Graphs: Long-Time Behaviour and the Graph-Continuity Equation. 协同演化图的演化方程：长时间行为和图连续性方程。
IF 2.6 2区 数学
Journal of Nonlinear Science Pub Date : 2026-01-01 Epub Date: 2026-03-05 DOI: 10.1007/s00332-026-10248-w
José Antonio Carrillo, Antonio Esposito, László Mikolás
{"title":"Evolution Equations on Co-evolving Graphs: Long-Time Behaviour and the Graph-Continuity Equation.","authors":"José Antonio Carrillo, Antonio Esposito, László Mikolás","doi":"10.1007/s00332-026-10248-w","DOIUrl":"10.1007/s00332-026-10248-w","url":null,"abstract":"<p><p>We focus on evolution equations on co-evolving infinite graphs and establish a rigorous link with a class of nonlinear continuity equations, whose vector fields depend on the graphs considered. More precisely, weak solutions of the so-called graph-continuity equation are shown to be the push-forward of their initial datum through the flow map solving the associated characteristics' equation, which depends on the co-evolving graph considered. This connection can be used to prove contractions in a suitable distance, although the flow on the graphs requires a too limiting assumption on the overall flux. Therefore, we consider upwinding dynamics on graphs with pointwise and monotonic velocity and prove long-time convergence of the solutions towards the uniform mass distribution.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"36 2","pages":"31"},"PeriodicalIF":2.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12963218/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147379197","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
Decomposable and Essentially Univariate Mass-Action Systems: Extensions of the Deficiency One Theorem. 可分解和本质上的单变量质量作用系统：亏一定理的推广。
IF 2.6 2区 数学
Journal of Nonlinear Science Pub Date : 2026-01-01 Epub Date: 2026-06-02 DOI: 10.1007/s00332-026-10278-4
Abhishek Deshpande, Stefan Müller
{"title":"Decomposable and Essentially Univariate Mass-Action Systems: Extensions of the Deficiency One Theorem.","authors":"Abhishek Deshpande, Stefan Müller","doi":"10.1007/s00332-026-10278-4","DOIUrl":"10.1007/s00332-026-10278-4","url":null,"abstract":"<p><p>The classical and extended deficiency one theorems by Feinberg apply to reaction networks with mass-action kinetics that have independent linkage classes or subnetworks, each with a deficiency of at most one and exactly one absorbing strong component. The theorems assume the existence of a positive equilibrium and guarantee the existence of a unique positive equilibrium in every stoichiometric compatibility class. In our work, we use the <i>monomial dependency</i> which extends the concept of deficiency. First, we provide a dependency one theorem for parametrized systems of polynomial equations that are essentially univariate and decomposable. As our main result, we present a corresponding theorem for mass-action systems, which permits subnetworks with arbitrary deficiency and arbitrary number of absorbing strong components. Finally, to complete the picture, we derive the extended deficiency one theorem as a special case of our more general dependency one theorem.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"36 3","pages":"66"},"PeriodicalIF":2.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13230314/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148165504","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
A fourth-order C-bracket scheme for nonlinear shallow-water sloshing in an oscillating tank with non-periodic inflow-outflow boundary conditions and biharmonic dissipation. 具有非周期进流-流出边界条件和双谐波耗散的振荡槽非线性浅水晃动的四阶c -支架格式。
IF 2.6 2区 数学
Journal of Nonlinear Science Pub Date : 2026-01-01 Epub Date: 2026-08-14 DOI: 10.1007/s00332-026-10317-0
Hamid Alemi Ardakani
{"title":"A fourth-order C-bracket scheme for nonlinear shallow-water sloshing in an oscillating tank with non-periodic inflow-outflow boundary conditions and biharmonic dissipation.","authors":"Hamid Alemi Ardakani","doi":"10.1007/s00332-026-10317-0","DOIUrl":"https://doi.org/10.1007/s00332-026-10317-0","url":null,"abstract":"<p><p>The second-order energy- and potential-enstrophy-conserving numerical scheme introduced by Arakawa & Lamb (1981) for the shallow-water equations with <i>periodic</i> boundary conditions, and extended by Salmon (2004) in the context of Hamiltonian Poisson-bracket discretisation, is further extended to a <i>fourth-order discretisation</i> for the problem of <i>nonlinear shallow-water sloshing</i> over a <i>corrugated bottom surface</i> in a rectangular rigid basin, with <i>symmetric and non-symmetric porous solid side walls</i> and <i>periodic and non-periodic prescribed inflow-outflow boundary conditions</i>, undergoing a prescribed <i>coupled surge-sway motion</i>. Adaptation to a finite domain with periodic and non-periodic inflow-outflow boundary conditions requires a new approach to the boundary conditions at <i>porous</i> solid boundaries, and the ghost cell grid point approximations in the context of the fourth-order finite-difference discretisation on the Arakawa C-grid. Theoretical Poisson-bracket arguments are used to define the required boundary conditions. In addition, standard <i>biharmonic dissipation</i> is incorporated into the numerical modelling to prevent potential enstrophy from accumulating at the smallest resolved scales, which improves the quality and stability of the approximate solutions, enabling long-term integrations to be carried out. The scheme is implemented, shown to preserve the total mass, energy, and potential enstrophy over <i>long-time</i> integration with bounded fluctuations. The presented <i>higher-order C-bracket sloshing integrator</i> provides a robust, stable, fast and precise building block for long-time computational modelling of floating ocean wave energy devices with <i>flexible</i> components, like a flexible bottom surface or membrane for wave energy extraction.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"36 5","pages":"98"},"PeriodicalIF":2.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13476303/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148764580","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
Softening Locally Polyhedral Tilings. 软化局部多面体瓷砖。
IF 2.6 2区 数学
Journal of Nonlinear Science Pub Date : 2026-01-01 Epub Date: 2026-09-18 DOI: 10.1007/s00332-026-10320-5
Gergely Ambrus, Dorottya Dancsó
{"title":"Softening Locally Polyhedral Tilings.","authors":"Gergely Ambrus, Dorottya Dancsó","doi":"10.1007/s00332-026-10320-5","DOIUrl":"10.1007/s00332-026-10320-5","url":null,"abstract":"<p><p>We call a cell <math><mrow><mi>C</mi> <mo>⊂</mo> <msup><mrow><mi>R</mi></mrow> <mi>d</mi></msup> </mrow> </math> <i>soft</i> if every point of its boundary lies on a smooth curve contained in <math><mrow><mi>∂</mi> <mi>C</mi></mrow> </math> . A tiling of the space is called <i>completely soft</i> if all of its cells are soft. In their 2024 article, Domokos, Goriely, G. Horváth and Regős conjectured that every polyhedral tiling of <math> <msup><mrow><mi>R</mi></mrow> <mn>3</mn></msup> </math> satisfying mild regularity assumptions can be locally deformed into a completely soft tiling. By constructing an algorithm that first bends the edges emanating from each vertex and then extends this transformation to a sufficiently smooth deformation, they proved the conjecture for polyhedral tilings satisfying a certain combinatorial condition. In the present paper, we precisely describe a new edge-bending algorithm that establishes a more general version of this conjecture: every <i>locally polyhedral</i> tiling of <math> <msup><mrow><mi>R</mi></mrow> <mn>3</mn></msup> </math> can be completely softened. We also give a short proof of an earlier result of Domokos, G. Horváth, and Regős stating that every suitably nondegenerate polygonic tiling of the plane has, on average, at least two points per cell at which the softness criterion is violated.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"36 5","pages":"105"},"PeriodicalIF":2.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13585884/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149009214","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
Charge Transport Systems with Fermi-Dirac Statistics for Memristors. 忆阻器的费米-狄拉克统计电荷输运系统。
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 Inheritance of Local Bifurcations in Mass Action Networks. 群体行动网络中局部分岔的继承性。
IF 2.6 2区 数学
Journal of Nonlinear Science Pub Date : 2025-01-01 Epub Date: 2025-05-17 DOI: 10.1007/s00332-025-10165-4
Murad Banaji, Balázs Boros, Josef Hofbauer
{"title":"The Inheritance of Local Bifurcations in Mass Action Networks.","authors":"Murad Banaji, Balázs Boros, Josef Hofbauer","doi":"10.1007/s00332-025-10165-4","DOIUrl":"10.1007/s00332-025-10165-4","url":null,"abstract":"<p><p>We consider local bifurcations of equilibria in dynamical systems arising from chemical reaction networks with mass action kinetics. In particular, given any mass action network admitting a local bifurcation of equilibria, assuming only a general transversality condition, we list some enlargements of the network which preserve its capacity for the bifurcation. These results allow us to identify bifurcations in reaction networks from examination of their subnetworks, extending and complementing previous results on the inheritance of nontrivial dynamical behaviours amongst mass action networks. A number of examples are presented to illustrate applicability of the results.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"35 4","pages":"72"},"PeriodicalIF":2.6,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12085349/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144102915","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. 连续介质力学的port - hamilton结构。
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
Robust Heteroclinic Cycles in Pluridimensions. 多维鲁棒异斜周期。
IF 2.6 2区 数学
Journal of Nonlinear Science Pub Date : 2025-01-01 Epub Date: 2025-06-11 DOI: 10.1007/s00332-025-10175-2
Sofia B S D Castro, Alastair M Rucklidge
{"title":"Robust Heteroclinic Cycles in Pluridimensions.","authors":"Sofia B S D Castro, Alastair M Rucklidge","doi":"10.1007/s00332-025-10175-2","DOIUrl":"10.1007/s00332-025-10175-2","url":null,"abstract":"<p><p>Heteroclinic cycles are sequences of equilibria along with trajectories that connect them in a cyclic manner. We investigate a class of robust heteroclinic cycles that do not satisfy the usual condition that all connections between equilibria lie in flow-invariant subspaces of equal dimension. We refer to these as robust heteroclinic cycles in pluridimensions. The stability of these cycles cannot be expressed in terms of ratios of contracting and expanding eigenvalues in the usual way because, when the subspace dimensions increase, the equilibria fail to have contracting eigenvalues. We develop the stability theory for robust heteroclinic cycles in pluridimensions, allowing for the absence of contracting eigenvalues. We present four new examples, each with four equilibria and living in four dimensions, that illustrate the stability calculations. Potential applications include modelling the dynamics of evolving populations when there are transitions between equilibria corresponding to mixed populations with different numbers of species.</p>","PeriodicalId":50111,"journal":{"name":"Journal of Nonlinear Science","volume":"35 4","pages":"80"},"PeriodicalIF":2.6,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12159117/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144303452","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
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