Physica D: Nonlinear Phenomena最新文献

英文中文

Alignment of geophysical fields: A differential geometry perspective 地球物理场对准：微分几何视角

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-01 Epub Date: 2025-10-30 DOI: 10.1016/j.physd.2025.134997

Yicun Zhen , Valentin Resseguier , Bertrand Chapron

To estimate the displacements of physical state variables, the physics principles that govern the state variables must be considered. Technically, for a certain class of state variables, each state variable is associated to a tensor field. Ways displacement maps act on different state variables will then differ according to their associated different tensor field definitions. Displacement procedures can then explicitly ensure the conservation of certain physical quantities (total mass, total vorticity, total kinetic energy, etc.), and a differential-geometry-based optimization formulated. Morphing with the correct physics, it is reasonable to apply the estimated displacement map to unobserved state variables, as long as the displacement maps are strongly correlated. This leads to a new nudging strategy using all-available observations to infer displacements of both observed and unobserved state variables. Using the proposed nudging method before applying ensemble data assimilation, numerical results show improved preservation of the intrinsic structure of underlying physical processes.

为了估计物理状态变量的位移，必须考虑控制状态变量的物理原理。从技术上讲，对于某一类状态变量，每个状态变量都与一个张量场相关联。位移映射作用于不同状态变量的方式将根据它们相关的不同张量场定义而有所不同。位移过程可以明确地确保某些物理量（总质量、总涡量、总动能等）的守恒，并制定了基于微分几何的优化公式。根据正确的物理变形，只要位移映射是强相关的，就可以合理地将估计的位移映射应用于未观察到的状态变量。这导致了一种新的推动策略，使用所有可用的观察来推断观察到的和未观察到的状态变量的位移。在集成数据同化之前使用所提出的助推方法，数值结果表明底层物理过程的内在结构得到了更好的保存。

引用次数: 0

Hydrodynamic stability of convection in porous medium with chemical reaction effect and generalised boundary conditions 具有化学反应效应和广义边界条件的多孔介质对流流体动力稳定性

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-01 Epub Date: 2025-10-24 DOI: 10.1016/j.physd.2025.135007

Sanaa L. Khalaf, Akil J. Harfash

We study solutal convection in a Brinkman porous layer with generalised Robin boundary conditions for solute concentration and two-sided Navier slip for velocity. The linear onset threshold (

R a_{L}

) and the global energy threshold (

R a_{E}

) are determined using a new Chebyshev collocation algorithm coupled to a pseudoinverse–eigenvalue formulation and a golden–section search. Accuracy is assessed through residual evaluation, as no analytical solutions are available for this problem. The results reveal that the Brinkman coefficient

λ

exerts a nearly linear stabilising influence on both

R a_{L}

and

R a_{E}

, while the slip coefficients

N_{L}

and

N_{U}

act asymmetrically to destabilise the system. In addition, the interaction between the reaction parameter

ζ

and the concentration ratio

η

produces non-monotonic shifts in the stability thresholds. These findings clarify how reaction, solute exchange, and interfacial slip reshape both linear and nonlinear stability boundaries in Brinkman porous media, and they establish a high-accuracy computational framework for analysing stability regimes relevant to reactive transport.

我们研究了Brinkman多孔层中的溶质对流，溶质浓度采用广义Robin边界条件，速度采用双面Navier滑移。线性起始阈值（RaL）和全局能量阈值（RaE）采用一种新的Chebyshev配置算法，结合伪特征值反公式和黄金分割搜索来确定。准确性是通过残差评价来评估的，因为这个问题没有可用的解析解。结果表明，Brinkman系数λ对RaL和RaE都具有近似线性的稳定作用，而滑移系数NL和NU则具有不对称的不稳定作用。此外，反应参数ζ与浓度比η之间的相互作用产生了稳定性阈值的非单调位移。这些发现阐明了反应、溶质交换和界面滑移如何重塑Brinkman多孔介质中的线性和非线性稳定性边界，并为分析与反应输运相关的稳定性体系建立了高精度的计算框架。

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引用次数: 0

A new mathematical model for cell motility with nonlocal repulsion from saturated areas 饱和区非局部排斥作用下细胞运动的新数学模型

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-01 Epub Date: 2025-10-22 DOI: 10.1016/j.physd.2025.134973

Carlo Giambiagi Ferrari, Francisco Guillén-González, Mayte Pérez-Llanos, Antonio Suárez

The main purpose of this work is the mathematical modelling of large populations of cells under different deterministic interactions among themselves, in balance with random diffusion. We focus on cell–cell interaction mechanisms for a single population confined to an isolated domain. We derive a macroscopic mathematical model including a nonlocal saturation coefficient depending on a crowding capacity, as part of a nonlocal drift term. Then, this capacity acts as a threshold above which repulsion effects appear. This macroscopic model is approached using two different microscopic discrete models based on Eulerian or Lagrangian reference systems, respectively.

这项工作的主要目的是在不同确定性相互作用下的大量细胞的数学建模，以平衡随机扩散。我们专注于细胞-细胞相互作用机制的单一种群限制在一个孤立的领域。我们推导了一个宏观数学模型，包括一个依赖于拥挤容量的非局部饱和系数，作为非局部漂移项的一部分。然后，这种能力作为一个阈值，超过这个阈值，排斥力效应就会出现。该宏观模型分别采用基于欧拉或拉格朗日参照系的两种不同的微观离散模型。

引用次数: 0

On the Hamiltonian structure of the intrinsic evolution of a closed vortex sheet 闭涡片内禀演化的哈密顿结构

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-01 Epub Date: 2025-10-15 DOI: 10.1016/j.physd.2025.134978

Banavara N. Shashikanth

Motivated by the work of previous authors on vortex sheets and their applications, the intrinsic inviscid evolution equations of a closed vortex sheet in a plane, separating two piecewise constant density fluids, and their Hamiltonian form are investigated. The model has potential applications to problems involving the dynamics of interfaces of two immiscible fluids. A boundary Poisson bracket, which appears to be new and related to the KdV bracket, is obtained containing the curve-tangential derivative

\partial / \partial s

. Lagrangian invariants of the sheet motion by its self-induced velocity–the Cauchy principal value of the Biot–Savart integral–are also derived.

在前人研究涡旋片及其应用的基础上，研究了分离两段等密度流体的平面上封闭涡旋片的固有无粘演化方程及其哈密顿形式。该模型对涉及两种非混相流体界面动力学的问题具有潜在的应用价值。得到了一个边界泊松括号，它看起来是新的，并且与KdV括号相关，它包含曲线切向导数∂/∂s。本文还推导了薄片运动的自诱导速度的拉格朗日不变量——Biot-Savart积分的柯西主值。

引用次数: 0

Flexible evolution of flocking tracking for a nonlinear collective migration model with heterogeneous transmission delays 具有异构传输延迟的非线性群体迁移模型的柔性演化

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-01 Epub Date: 2025-09-12 DOI: 10.1016/j.physd.2025.134927

Yipeng Chen, Yicheng Liu, Xiao Wang

Division of labour and cooperation in animal groups is an external manifestation of swarm intelligence, such as leaders and followers in collective migration of animals. In this paper, we propose a nonlinear multi-agent system named collective migration model and try to build a more realistic dynamic leader–follower structure that facilitates flexible evolution of flocking tracking. The model highlights individual heterogeneity, especially including heterogeneous transmission delays among agents and heterogeneous parameters called tracking strategies that establish a trade-off between alignment and tracking for each agent, and essentially determine the leader–follower structure of the system. By constructing dynamic upper bounds of velocity, setting tracking periods and partitioning state space, a time-varying tracking strategy vector is designed to produce a dynamic leader–follower structure in which the system has a flexible configuration and can achieve flocking tracking for any initial state. The increase of transmission delay prolongs the switching cycle of leader–follower structure, and decreases the convergence speed of the system. An algorithm of the tracking strategy vector and several numerical simulations are provided to verify our results.

动物群体的分工合作是群体智能的外在表现，如动物集体迁徙中的领导者和追随者。本文提出了一种非线性多智能体系统的集体迁移模型，并试图建立一个更真实的动态领导者-追随者结构，以促进群体跟踪的灵活进化。该模型突出了个体异质性，特别是包括代理之间的异构传输延迟和称为跟踪策略的异构参数，这些参数在每个代理的校准和跟踪之间建立了权衡，并从本质上确定了系统的领导-追随者结构。通过构造动态速度上界、设置跟踪周期和划分状态空间，设计时变跟踪策略向量，生成具有灵活配置的动态leader-follower结构，使系统在任意初始状态下都能实现集群跟踪。传输时延的增大延长了导从动结构的切换周期，降低了系统的收敛速度。给出了跟踪策略向量的一种算法和几个数值仿真来验证我们的结果。

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引用次数: 0

Magnus exponential integrators for stiff time-varying stochastic systems 刚性时变随机系统的Magnus指数积分器

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-01 Epub Date: 2025-11-11 DOI: 10.1016/j.physd.2025.135034

Dev Jasuja , P.J. Atzberger

We introduce exponential numerical integration methods for handling stiff stochastic dynamical systems having time-varying dissipative operators and fluctuations. Time-dependence presents challenges for exponentiation to obtain tractable expressions for evaluation, especially when the dissipative operators do not commute in time. We introduce approaches based on statistical mechanics and Magnus expansions to obtain stochastic integration methods that exhibit fluctuation–dissipation balance and other properties that facilitate computations. We show how practical computational methods can be developed to approximate and evaluate the contributions of the resulting stochastic expressions. We demonstrate our methods on several examples, including time-varying SDEs that arise in particle simulations and for SPDEs that model fluctuations in concentration fields of spatially-extended systems. Our introduced approaches provide methods for preserving statistical structures and other properties to obtain exponential numerical integrators for handling stiffness in time-varying stochastic dynamical systems.

本文引入指数数值积分方法来处理具有时变耗散算子和波动的刚性随机动力系统。当耗散算子不随时间交换时，时间依赖性给幂运算获得易于处理的求值表达式带来了挑战。我们引入了基于统计力学和Magnus展开的方法来获得具有波动-耗散平衡和其他便于计算的特性的随机积分方法。我们展示了如何开发实用的计算方法来近似和评估所得随机表达式的贡献。我们在几个例子上展示了我们的方法，包括在粒子模拟中出现的时变SDEs和在空间扩展系统的浓度场中模拟波动的SPDEs。我们介绍的方法提供了保留统计结构和其他性质的方法，以获得指数数值积分器，用于处理时变随机动力系统的刚度。

引用次数: 0

Quadruplet form of water waves kinetic equation 水波动力学方程的四重态形式

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-01 Epub Date: 2025-10-14 DOI: 10.1016/j.physd.2025.134977

V. Geogjaev

We present the quadruplet form of the kinetic equation for deep water surface waves (the Hasselmann equation). This formulation explicitly utilizes quadruplets of interacting waves. We define the integration over the quadruplets and rewrite the interaction integral using this definition. We use our construction to study the kinetic equation, in particular, we calculate the Kolmogorov constants for the Zakharov–Filonenko spectra.

我们提出了深水表面波动力学方程的四重态形式（哈塞曼方程）。这个公式明确地利用了相互作用波的四重波。我们定义了四元组的积分，并用这个定义重写了交互积分。我们用我们的构造研究了动力学方程，特别是计算了Zakharov-Filonenko谱的Kolmogorov常数。

引用次数: 0

Hamiltonian Monte Carlo with asymmetrical momentum distributions 具有不对称动量分布的哈密顿蒙特卡罗

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-01 Epub Date: 2025-09-27 DOI: 10.1016/j.physd.2025.134952

Soumyadip Ghosh, Yingdong Lu, Tomasz Nowicki

Existing rigorous convergence guarantees for the Hamiltonian Monte Carlo (HMC) algorithm use Gaussian auxiliary momentum variables, which are crucially symmetrically distributed. We present a novel convergence analysis for HMC utilizing new dynamical and probabilistic arguments. The convergence is rigorously established under significantly weaker conditions, which among others allow for general auxiliary distributions. In our framework, we show that plain HMC with asymmetrical momentum distributions breaks a key self-adjointness requirement. We propose a modified version of HMC, that we call the Alternating Direction HMC (AD-HMC), which overcomes this difficulty. Sufficient conditions are established under which AD-HMC exhibits geometric convergence in Wasserstein distance. The geometric convergence analysis is extended to when the Hamiltonian motion is approximated by the leapfrog symplectic integrator, where an additional Metropolis–Hastings rejection step is required. Numerical experiments suggest that AD-HMC can generalize a popular dynamic auxiliary scheme to show improved performance over HMC with Gaussian auxiliaries.

现有的Hamiltonian Monte Carlo （HMC）算法的严格收敛保证使用高斯辅助动量变量，这些辅助动量变量是关键对称分布的。利用新的动力学和概率参数，提出了一种新的HMC收敛分析方法。在较弱的条件下严格地建立了收敛性，其中包括一般辅助分布。在我们的框架中，我们证明了具有不对称动量分布的普通HMC打破了一个关键的自伴随性要求。我们提出了一种改进的HMC，我们称之为交替方向HMC (AD-HMC)，它克服了这个困难。建立了AD-HMC在Wasserstein距离上呈现几何收敛的充分条件。将几何收敛分析推广到用跳越型辛积分器逼近哈密顿运动时，其中需要增加一个Metropolis-Hastings抑制步骤。数值实验表明，AD-HMC可以推广一种流行的动态辅助方案，以提高具有高斯辅助的HMC的性能。

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引用次数: 0

Unraveling multiple 1:1 entrainment regions in the Arnold onion diagram: A study of the circadian Novak–Tyson model 在阿诺德洋葱图中解开多个1:1的携带区域：昼夜节律诺瓦克-泰森模型的研究

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-01 Epub Date: 2025-09-24 DOI: 10.1016/j.physd.2025.134949

Emel Khan , Lawan Wijayasooriya , Pejman Sanaei

The entrainment of biological oscillators is a fundamental problem in studying dynamical systems and synchronization. The Arnold onion diagram is a key tool for visualizing entrainment patterns in a two-dimensional parameter space, defined by period (

T

) and photoperiod (

χ

). This paper investigates the entrainment behavior of various oscillatory regimes in the Novak–Tyson (NT) model. While previous studies have documented the presence of Arnold onions featuring a single 1:1 entrainment region, our work introduces the novel emergence of multiple disconnected 1:1 entrainment regions within these diagrams. Through the analysis of dynamical systems, we show that multiple Arnold onions emerge for an unforced system near the Hopf bifurcation, which behaves as a damped oscillator. These findings offer new insights into the complex mechanisms underlying circadian seasonality and its dependence on intrinsic oscillator dynamics.

生物振子的夹带是研究动力系统和同步的一个基本问题。阿诺德洋葱图是在二维参数空间中可视化夹带模式的关键工具，由周期(T)和光周期（χ）定义。本文研究了Novak-Tyson （NT）模型中不同振荡状态的夹带行为。虽然以前的研究已经记录了阿诺德洋葱具有单个1:1夹带区域的存在，但我们的工作在这些图中引入了多个不连接的1:1夹带区域的新出现。通过对动力系统的分析，我们证明了在Hopf分岔附近的非强制系统存在多个Arnold onion，其表现为阻尼振荡器。这些发现为昼夜节律季节性的复杂机制及其对内在振荡器动力学的依赖提供了新的见解。

引用次数: 0

Particle, kinetic and hydrodynamic models for sea ice floes, Part I: Non-rotating floes 海洋浮冰的颗粒、动力和水动力模型，第一部分：非旋转浮冰

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-01 Epub Date: 2025-09-24 DOI: 10.1016/j.physd.2025.134951

Quanling Deng , Seung-Yeal Ha

We introduce a comprehensive modeling framework for the dynamics of sea ice floes using particle, kinetic, and hydrodynamic approaches. Building upon the foundational work of Ha and Tadmor on the Cucker–Smale model for flocking, we derive a Vlasov-type kinetic formulation and a corresponding hydrodynamic description. The particle model incorporates essential physical properties of sea ice floes, including size, position, velocity, and interactions governed by Newtonian mechanics. By extending these principles, the kinetic model captures large-scale features through the phase-space distribution, and we also present a hydrodynamic model using the velocity moments and a suitable closure condition. In this paper, as an idea-introductory step, we assume that ice floes are non-rotating and focus on the linear velocity dynamics. Our approach highlights the role of contact forces, ocean drag effects, and conservation laws in the multiscale description of sea ice dynamics, offering a potential pathway for the improved understanding and prediction of sea ice behaviors in changing climatic conditions.

我们介绍了一个综合的建模框架，海冰的动力学使用粒子，动力学和水动力学的方法。在Ha和Tadmor对cucker - small群集模型的基础工作的基础上，我们推导了vlasov型动力学公式和相应的流体动力学描述。粒子模型结合了海洋浮冰的基本物理特性，包括大小、位置、速度和由牛顿力学控制的相互作用。通过扩展这些原理，动力学模型通过相空间分布捕获了大尺度特征，并且我们还提出了一个使用速度矩和合适的闭合条件的水动力模型。在本文中，作为一个思想的介绍步骤，我们假设浮冰是不旋转的，并专注于线速度动力学。我们的方法强调了接触力、海洋阻力效应和守恒定律在海冰动力学多尺度描述中的作用，为提高对气候条件变化下海冰行为的理解和预测提供了一条潜在的途径。

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