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The invariant measure of a walking droplet in hydrodynamic pilot–wave theory 流体力学先导波理论中行走水滴的不变量度
IF 1.7 2区 数学
Nonlinearity Pub Date : 2024-07-18 DOI: 10.1088/1361-6544/ad5f6f
Hung D Nguyen and Anand U Oza
{"title":"The invariant measure of a walking droplet in hydrodynamic pilot–wave theory","authors":"Hung D Nguyen and Anand U Oza","doi":"10.1088/1361-6544/ad5f6f","DOIUrl":"https://doi.org/10.1088/1361-6544/ad5f6f","url":null,"abstract":"We study the long time statistics of a walker in a hydrodynamic pilot-wave system, which is a stochastic Langevin dynamics with an external potential and memory kernel. While prior experiments and numerical simulations have indicated that the system may reach a statistically steady state, its long-time behavior has not been studied rigorously. For a broad class of external potentials and pilot-wave forces, we construct the solutions as a dynamics evolving on suitable path spaces. Then, under the assumption that the pilot-wave force is dominated by the potential, we demonstrate that the walker possesses a unique statistical steady state. We conclude by presenting an example of such an invariant measure, as obtained from a numerical simulation of a walker in a harmonic potential.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"9 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743822","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
Prevention of infinite-time blowup by slightly super-linear degradation in a Keller–Segel system with density-suppressed motility 在具有密度抑制运动的凯勒-西格尔系统中，通过轻微的超线性降解防止无限时炸毁
IF 1.7 2区 数学
Nonlinearity Pub Date : 2024-07-17 DOI: 10.1088/1361-6544/ad6113
Yamin Xiao and Jie Jiang
{"title":"Prevention of infinite-time blowup by slightly super-linear degradation in a Keller–Segel system with density-suppressed motility","authors":"Yamin Xiao and Jie Jiang","doi":"10.1088/1361-6544/ad6113","DOIUrl":"https://doi.org/10.1088/1361-6544/ad6113","url":null,"abstract":"An initial-Neumann boundary value problem for a Keller–Segel system with density-suppressed motility and source terms is considered. Infinite-time blowup of the classical solution was previously observed for its source-free version when dimension . In this work, we prove that with any source term involving a slightly super-linear degradation effect on the density, of a growth order of at most, the classical solution is uniformly-in-time bounded when , thus preventing the infinite-time explosion detected in the source-free counter-part. The cornerstone of our proof lies in an improved comparison argument and a construction of an entropy inequality.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"34 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743746","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
Travelling pulses on three spatial scales in a Klausmeier-type vegetation-autotoxicity model 克劳斯迈尔型植被-自毒模型中三个空间尺度上的移动脉冲
IF 1.7 2区 数学
Nonlinearity Pub Date : 2024-07-17 DOI: 10.1088/1361-6544/ad6112
Paul Carter, Arjen Doelman, Annalisa Iuorio and Frits Veerman
{"title":"Travelling pulses on three spatial scales in a Klausmeier-type vegetation-autotoxicity model","authors":"Paul Carter, Arjen Doelman, Annalisa Iuorio and Frits Veerman","doi":"10.1088/1361-6544/ad6112","DOIUrl":"https://doi.org/10.1088/1361-6544/ad6112","url":null,"abstract":"Reaction-diffusion models describing interactions between vegetation and water reveal the emergence of several types of patterns and travelling wave solutions corresponding to structures observed in real-life. Increasing their accuracy by also considering the ecological factor known as autotoxicity has lead to more involved models supporting the existence of complex dynamic patterns. In this work, we include an additional carrying capacity for the biomass in a Klausmeier-type vegetation-water-autotoxicity model, which induces the presence of two asymptotically small parameters: ɛ, representing the usual scale separation in vegetation-water models, and δ, directly linked to autotoxicity. We construct three separate types of homoclinic travelling pulse solutions based on two different scaling regimes involving ɛ and δ, with and without a so-called superslow plateau. The relative ordering of the small parameters significantly influences the phase space geometry underlying the construction of the pulse solutions. We complement the analysis by numerical continuation of the constructed pulse solutions, and demonstrate their existence (and stability) by direct numerical simulation of the full partial differential equation model.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"56 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743745","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
On Liouville type results for the stationary MHD in R3 关于 R3 中静止 MHD 的柳维尔类型结果
IF 1.7 2区 数学
Nonlinearity Pub Date : 2024-07-17 DOI: 10.1088/1361-6544/ad6128
Dongho Chae and Jihoon Lee
{"title":"On Liouville type results for the stationary MHD in R3","authors":"Dongho Chae and Jihoon Lee","doi":"10.1088/1361-6544/ad6128","DOIUrl":"https://doi.org/10.1088/1361-6544/ad6128","url":null,"abstract":"This paper is concerned with the Liouville type theorems for the steady incompressible magnetohydrodynamics (MHD) equations. We establish that the solution to the steady MHD equations is identically zero under the integrability assumptions on (v, b). We show that, in particular, a combination of a strong integrability condition on the velocity of a fluid and a weak integrability condition on the magnetic field gives a sufficient condition on the Liouville type theorems. Furthermore, we show that the combination of the growth condition of the potential for the fluid velocity and the integrability condition for the magnetic field leads to the triviality of the solution.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"42 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141743747","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
L q -spectra of graph-directed planar non-conformal measures 图定向平面非共形度量的 L q谱
IF 1.7 2区 数学
Nonlinearity Pub Date : 2024-07-16 DOI: 10.1088/1361-6544/ad6055
Hua Qiu, Qi Wang and Shufang Wang
{"title":"L q -spectra of graph-directed planar non-conformal measures","authors":"Hua Qiu, Qi Wang and Shufang Wang","doi":"10.1088/1361-6544/ad6055","DOIUrl":"https://doi.org/10.1088/1361-6544/ad6055","url":null,"abstract":"We estimate the upper and lower Lq-spectra of measures generated by a class of graph-directed planar non-conformal iterated function systems. These systems are composed of contractions with lower triangular pointwise Jacobian. The estimation provides a criterion for the existence of the Lq-spectra in certain case. As an application, we derive the box-counting dimension of planar self-affine sets generated by lower triangular matrices, whose geometric construction satisfies a finite overlapping type condition.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"47 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719231","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
Scaling laws and exact results in turbulence * 湍流中的缩放定律和精确结果 *
IF 1.7 2区 数学
Nonlinearity Pub Date : 2024-07-16 DOI: 10.1088/1361-6544/ad6057
Matthew Novack
{"title":"Scaling laws and exact results in turbulence *","authors":"Matthew Novack","doi":"10.1088/1361-6544/ad6057","DOIUrl":"https://doi.org/10.1088/1361-6544/ad6057","url":null,"abstract":"In this note, we address the validity of certain exact results from turbulence theory in the deterministic setting. The main tools, inspired by the work of Duchon and Robert (2000 Nonlinearity13 249–55) and Eyink (2003 Nonlinearity16 137), are a number of energy balance identities for weak solutions of the incompressible Euler and Navier–Stokes equations. As a consequence, we show that certain weak solutions of the Euler and Navier–Stokes equations satisfy deterministic versions of Kolmogorov’s , , laws. We apply these computations to improve a recent result of Hofmanova et al (2023 arXiv:2304.14470), which shows that a construction of solutions of forced Navier–Stokes due to Bruè et al (2023 Commun. Pure Appl. Anal.) and exhibiting a form of anomalous dissipation satisfies asymptotic versions of Kolmogorov’s laws. In addition, we show that the globally dissipative 3D Euler flows recently constructed by Giri et al (2023 arXiv:2305.18509) satisfy the local versions of Kolmogorov’s laws.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"30 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719235","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
Stable/unstable holonomies, density of periodic points, and transitivity for continuum-wise hyperbolic homeomorphisms 连续双曲同构的稳定/不稳定整体性、周期点密度和反转性
IF 1.7 2区 数学
Nonlinearity Pub Date : 2024-07-16 DOI: 10.1088/1361-6544/ad6056
B Carvalho and E Rego
{"title":"Stable/unstable holonomies, density of periodic points, and transitivity for continuum-wise hyperbolic homeomorphisms","authors":"B Carvalho and E Rego","doi":"10.1088/1361-6544/ad6056","DOIUrl":"https://doi.org/10.1088/1361-6544/ad6056","url":null,"abstract":"We discuss different regularities on stable/unstable holonomies of cw-hyperbolic homeomorphisms and prove that if a cw-hyperbolic homeomorphism has continuous joint stable/unstable holonomies, then it has a dense set of periodic points in its non-wandering set. For that, we prove that the hyperbolic cw-metric (introduced in Artigue et al (2024 J. Differ. Equ.378 512–38)) can be adapted to be self-similar (as in Artigue (2018 Ergodic Theory Dyn. Syst.38 2422–46)) and, in this case, continuous joint stable/unstable holonomies are pseudo-isometric. We also prove transitivity of cw-hyperbolic homeomorphisms assuming that the stable/unstable holonomies are isometric. In the case the ambient space is a surface, we prove that a cwF-hyperbolic homeomorphism has continuous joint stable/unstable holonomies when every bi-asymptotic sector is regular.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"39 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719232","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
Relative equilibria of mechanical systems with rotational symmetry 具有旋转对称性的机械系统的相对平衡
IF 1.7 2区 数学
Nonlinearity Pub Date : 2024-07-14 DOI: 10.1088/1361-6544/ad4dfd
Philip Arathoon
{"title":"Relative equilibria of mechanical systems with rotational symmetry","authors":"Philip Arathoon","doi":"10.1088/1361-6544/ad4dfd","DOIUrl":"https://doi.org/10.1088/1361-6544/ad4dfd","url":null,"abstract":"We consider the task of classifying relative equilibria for mechanical systems with rotational symmetry. We divide relative equilibria into two natural groups: a generic class which we call normal, and a non-generic abnormal class. The eigenvalues of the locked inertia tensor descend to shape-space and endow it with the geometric structure of a three-web with the property that any normal relative equilibrium occurs as a critical point of the potential restricted to a leaf from the web. To demonstrate the utility of this web structure we show how the spherical three-body problem gives rise to a web of Cayley cubics on the three-sphere, and use this to fully classify the relative equilibria for the case of equal masses.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"38 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141719233","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
Amplitude equations for wave bifurcations in reaction–diffusion systems 反应扩散系统中波分岔的振幅方程
IF 1.7 2区 数学
Nonlinearity Pub Date : 2024-07-10 DOI: 10.1088/1361-6544/ad5e56
Edgardo Villar-Sepúlveda and Alan Champneys
{"title":"Amplitude equations for wave bifurcations in reaction–diffusion systems","authors":"Edgardo Villar-Sepúlveda and Alan Champneys","doi":"10.1088/1361-6544/ad5e56","DOIUrl":"https://doi.org/10.1088/1361-6544/ad5e56","url":null,"abstract":"A wave bifurcation is the counterpart to a Turing instability in reaction–diffusion systems, but where the critical wavenumber corresponds to a pure imaginary pair rather than a zero temporal eigenvalue. Such bifurcations require at least three components and give rise to patterns that are periodic in both space and time. Depending on boundary conditions, these patterns can comprise either rotating or standing waves. Restricting to systems in one spatial dimension, complete formulae are derived for the evaluation of the coefficients of the weakly nonlinear normal form of the bifurcation up to order five, including those that determine the criticality of both rotating and standing waves. The formulae apply to arbitrary n-component systems ( ) and their evaluation is implemented in software which is made available as supplementary material. The theory is illustrated on two different versions of three-component reaction–diffusion models of excitable media that were previously shown to feature super- and subcritical wave instabilities and on a five-component model of two-layer chemical reaction. In each case, two-parameter bifurcation diagrams are produced to illustrate the connection between complex dispersion relations and different types of Hopf, Turing, and wave bifurcations, including the existence of several codimension-two bifurcations.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"36 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141584632","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
Asymptotic stability of rarefaction wave and boundary layer for outflow problem on the viscous vasculogenesis model * 粘性血管生成模型上流出问题的稀释波和边界层的渐近稳定性*
IF 1.7 2区 数学
Nonlinearity Pub Date : 2024-07-10 DOI: 10.1088/1361-6544/ad5e2f
Qingqing Liu and Qian Yan
{"title":"Asymptotic stability of rarefaction wave and boundary layer for outflow problem on the viscous vasculogenesis model *","authors":"Qingqing Liu and Qian Yan","doi":"10.1088/1361-6544/ad5e2f","DOIUrl":"https://doi.org/10.1088/1361-6544/ad5e2f","url":null,"abstract":"In this paper, we are concerned with the outflow problem on a simplified viscous vasculogenesis model in the half-line . Firstly, we establish the global-in-time asymptotic stability of the rarefaction wave. Secondly, we obtain the unique existence and decay property of the boundary layer by using stable manifold theorem. Moreover, the asymptotic stability and convergence rates of solution towards boundary layer are obtained. The appearance of concentration makes the stationary problem more difficult than Navier–Stokes equations or Navier–Stokes–Poisson equations.","PeriodicalId":54715,"journal":{"name":"Nonlinearity","volume":"34 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141584875","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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