Physica D: Nonlinear Phenomena最新文献

英文中文

MHD Front and rear stagnation-point flow of a moving permeable flat surface 移动透水平面前后滞止点流动

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-11 DOI: 10.1016/j.physd.2025.135075

Mustafa Turkyilmazoglu , Abdulaziz Alotaibi

This study investigates the unsteady stagnation-point flow around a permeable flat body, where the body’s motion relative to the impinging flow can vary with time. Additionally, the surface is subjected to a time-varying magnetic field. We first transform the governing equations of unsteady motion into a similarity form using specific forms of time-dependent variables. This allows us to explore potential exact solutions, leading to the identification of special exponential solutions applicable to both front and rear stagnation-point flows. To further comprehend the interplay of magnetic field, wall transpiration, and wall movement on the stagnation-point flow development, we conduct comprehensive numerical simulations. These simulations clarify the boundaries of unique and multiple solution regimes influenced by these physical parameters. Furthermore, we identify distinct regimes of separated and attached stagnant flow, which hold significant relevance in flow control applications in fluid mechanics and industrial engineering fields. Wall suction acts to regularize the upper branch solutions, and magnetic field enhances the domain of dual solutions, with further enlarging the separated flow zone for the front stagnation-point flow. However, for the rear stagnation-point flow, the upper and lower branches of solutions are linked by the magnetic field.

本文研究了可渗透平面体周围的非定常滞点流动，其中物体相对于撞击流的运动可以随时间变化。此外，表面受到时变磁场的影响。首先利用特定形式的时变变量将非定常运动控制方程转化为相似形式。这使我们能够探索潜在的精确解，从而确定适用于前后停滞点流动的特殊指数解。为了进一步了解磁场、壁面蒸腾和壁面运动对停滞点流动发展的相互作用，我们进行了全面的数值模拟。这些模拟阐明了受这些物理参数影响的唯一解和多重解的边界。此外，我们还确定了分离和附着滞流的不同形式，这在流体力学和工业工程领域的流动控制应用中具有重要意义。壁面吸力对上部支路解有规整作用，磁场增强了对偶解的域，进一步扩大了前停滞点流的分离流区。而对于后滞点流，解的上下分支被磁场连接。

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引用次数: 0

Characterization of the dynamics of free and excited Grudzinski-Zebrowski (GZ) oscillator using mathematical methods and microcontroller simulation experiment 用数学方法和微控制器仿真实验表征自由和受激格鲁津斯基-泽布罗斯基（GZ）振荡器的动力学

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-09 DOI: 10.1016/j.physd.2025.135077

Ulrich Simo Domguia , Vinod V , Bipin Balaram , Paul Woafo

In this work, we consider the Grudzinski-Zebrowski oscillator excited periodically and analyze its dynamical behaviors with reference to the effects of external stimuli on electric node of the heart. Mathematical analysis, numerical and microcontroller simulations are employed. The nonlinear differential equation of the GZ oscillator is solved both analytically and numerically using averaging and the four-order Runge-Kutta methods. The results obtained are shown in terms of asymptotic solution, bifurcation diagrams, corresponding Lyapunov exponents variation and time histories. The bifurcation diagrams reveal the presence of winding number, chaos, bursting, spiking and pulse oscillations. The analytical calculations match well with the numerical results. These behaviors are exhibited experimentally using microcontroller simulations with a good qualitative agreement.

本文考虑周期性激发的Grudzinski-Zebrowski振荡器，结合外界刺激对心脏电结的影响，分析了其动力学行为。采用数学分析、数值模拟和单片机仿真。采用平均法和四阶龙格-库塔法对GZ振子的非线性微分方程进行了解析和数值求解。得到的结果用渐近解、分岔图、相应的Lyapunov指数变化和时程来表示。分岔图揭示了圈数、混沌、爆发、尖峰和脉冲振荡的存在。解析计算结果与数值结果吻合较好。这些行为在实验中使用微控制器模拟显示，具有良好的定性一致性。

引用次数: 0

Discrete Local Active Memristive HR and FHN Coupled Neuron Model and FPGA Implementation 离散局部有源记忆电阻HR和FHN耦合神经元模型及FPGA实现

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-09 DOI: 10.1016/j.physd.2025.135078

Jialong Wang, Shaohui Yan, Jiandong Zhang

This parper introduces an innovative discrete local active memristor and demonstrates its local active characteristics using DC V-I curves. The proposed memristor simulates the function of biological synapses, and further constructs a discrete coupled Hindmarsh-Rose and FitzHugh-Nagumo (HR-FHN) neuron model. It calculates and analyzes its fixed points and Hamiltonian energy, clarifying the energy dynamics and equilibrium point mechanism of firing model conversion in this system. At the same time, theoretical analysis and numerical simulation show that it can generate multiple firing models under the influence of local active memristors. In addition, complex chaotic behaviors are observed, such as the coexistence of different firing models, transient chaos, and offset boosting. It is implemented as a digital circuit using Field-Programmable Gate Array (FPGA), demonstrating the dynamic control and physical reliability of the discrete local active memristive neuron model.

本文介绍了一种新型的离散型局部有源忆阻器，并利用直流V-I曲线证明了其局部有源特性。所提出的忆阻器模拟了生物突触的功能，并进一步构建了一个离散耦合的Hindmarsh-Rose和FitzHugh-Nagumo （HR-FHN）神经元模型。对其不动点和哈密顿能量进行了计算和分析，阐明了该系统发射模型转换的能量动力学和平衡点机理。同时，理论分析和数值模拟表明，在局部有源忆阻器的影响下，该方法可以生成多种点火模型。此外，还观察到不同发射模式共存、瞬态混沌和偏移助推等复杂混沌行为。利用现场可编程门阵列（FPGA）将其实现为数字电路，验证了离散局部有源记忆神经元模型的动态控制和物理可靠性。

引用次数: 0

Dynamic entrainment of neuronal spiking: A phase plane analysis and a data-driven approach 神经元尖峰的动态夹带：相平面分析和数据驱动的方法

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-08 DOI: 10.1016/j.physd.2025.135071

Lawan Wijayasooriya , Soheil Saghafi , Emel Khan , Pejman Sanaei

Precise timing in neuronal spiking is important for effective signal processing and transmission in excitable systems. Disruptions to the timing accuracy of neuronal synchronization can impair brain function and contribute to neurodegenerative diseases such as Huntington’s disease. In this work, we employ a technique called “dynamic entrainment” to determine the optimal time gap between successive input pulses required to bring and maintain the system in a 1:1 entrainment regime. Unlike the previous study that applied dynamic entrainment to the four-dimensional Hodgkin-Huxley model, we adopt the approach for the two-dimensional Morris-Lecar model. The reduced dimensionality of Morris-Lecar makes it computationally efficient while still capturing essential features of excitability. It also facilitates straightforward phase plane analysis providing geometric insights into the success of dynamic entrainment. It demonstrates that dynamic entrainment allows achieving and sustaining 1:1 entrainment when fixed periodic forcing fails. We also explore the use of dynamic entrainment at higher-order resonances within the Arnold tongue. By dynamically changing the inter-pulse interval, we achieved 1:1 entrainment, and the effective period of the selected point shifted to an originally 1:1 region.

在可兴奋系统中，神经元峰值的精确定时对有效的信号处理和传输至关重要。破坏神经元同步的时间准确性会损害大脑功能，并导致神经退行性疾病，如亨廷顿氏病。在这项工作中，我们采用了一种称为“动态夹带”的技术来确定连续输入脉冲之间的最佳时间间隔，以使系统保持在1:1夹带状态。与之前将动态夹带应用于四维Hodgkin-Huxley模型的研究不同，我们采用了二维Morris-Lecar模型的方法。Morris-Lecar的降维使其在计算效率高的同时仍然捕捉到兴奋性的基本特征。它还有助于直接相平面分析，为动态夹带的成功提供几何见解。它表明，动态夹带允许实现和维持1:1夹带时，固定的周期性强迫失败。我们还探讨了在阿诺德舌的高阶共振中动态夹带的使用。通过动态改变脉冲间间隔，实现了1:1的夹带，并将所选点的有效周期移至原来1:1的区域。

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引用次数: 0

Exploring complexity of a Frenkel-Kontorova-Type atomic chain 探索frenkel - kontorova型原子链的复杂性

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-08 DOI: 10.1016/j.physd.2025.135072

Ozgur Afsar , Sevda Saltik , Fatimat Bughluyeva

Spatially ordered patterns that may emerge in various natural phenomena as the result of an evolution cause an increasing order within the system until forming a stationary state. One of special types of such patterns, highly complex cantor sets, arises as a result of successive bifurcations of trajectories of a dynamical system throughout its evolution in the control parameter space. It is well known that evolution towards such ordered structures requires a decrease in the entropy of the system, which can lead to an increase in the degree of complexity of the phase space. Although there are many entropy-based complexity measures in the literature, exploring the appropriate entropy that is capable of explaining such an evolution process and defining the degree of complexity of the structure of the physical system is one of the main research topics in complexity science. We evaluated possible total energy values of Frenkel-Kontorova-type independent chains with a free boundary condition at static equilibrium. We show that the ensemble of the total energies represents period doublings and chaotic band-mergings if one changes the control parameter, which is the value of the amplitude of the substrate potential. The periods of the total energies accumulate at a critical value, causing the emergence of self-similar and spatially organized fractal patterns. Using the energy distributions in the control parameter space, we also calculate entropy-based complexity measures: Shannon, Kullback-Leibler and q-Renormalized entropies. We show that the q-renormalized entropy behaves according to the well-known low-entropy criteria of self-organization, whereas the Shannon and Kullback-Leibler entropies cannot. This implies that the q-renormalized entropy is an appropriate entropy to explore the emergence and disappearance of spatially organized fractal energy patterns and to evaluate their complexities.

空间有序模式可能出现在各种自然现象中，作为进化的结果，导致系统内的秩序增加，直到形成一个稳定状态。这种模式的一种特殊类型，高度复杂的康托集，是由于动力系统在控制参数空间的整个演化过程中轨迹的连续分叉而产生的。众所周知，向这种有序结构的演化需要系统熵的减少，这可能导致相空间复杂性的增加。虽然文献中有许多基于熵的复杂性度量，但探索能够解释这种演化过程并定义物理系统结构复杂程度的适当熵是复杂性科学的主要研究课题之一。我们计算了在静态平衡下具有自由边界条件的frenkel - kontorova型独立链可能的总能值。我们表明，如果改变控制参数，即基底电位的幅值，则总能量的集合表示周期加倍和混沌带合并。总能量的周期累积在一个临界值，导致自相似和空间组织的分形模式的出现。利用控制参数空间中的能量分布，我们还计算了基于熵的复杂度度量：Shannon、Kullback-Leibler和q-重整化熵。我们证明了q重整熵的行为符合众所周知的自组织的低熵准则，而香农和库伦巴克-莱伯勒熵则不能。这意味着q重正化熵是探索空间组织分形能量模式的出现和消失以及评估其复杂性的合适熵。

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引用次数: 0

IADNet: A neural network for discovering particle interactions from trajectory data 从轨迹数据中发现粒子相互作用的神经网络

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-04 DOI: 10.1016/j.physd.2025.135057

Ru Geng , Yixian Gao , Jian Zu , Hong-Kun Zhang

Deciphering interparticle interactions remains fundamental to unraveling complex systems across physics, chemistry, and biological sciences. Conventional approaches often suffer from prior knowledge reliance or insufficient interpretability in characterizing interactions. To overcome these limitations, this study proposes the Interaction Discovery Neural Network (IADNet), which integrates graph structure learning with physics-constrained strategies to directly reconstruct interaction graph topologies from particle trajectories while establishing explicit mapping relationships with actual physical system configurations. To validate its universality, we tested IADNet across four different systems spanning classical mechanics, molecular chemistry, biological models, and lattice systems. Experimental results demonstrate that IADNet can accurately reconstruct spring connection topologies and estimate elastic coefficient ratios, effectively identify chemical bonds in molecules, reveal hidden long-range interactions in DNA models and restore base sequence arrangements, and detect anomalous patterns in lattice systems. These findings underscore IADNet’s potential in multiparticle system research.

破译粒子间的相互作用仍然是解开物理、化学和生物科学复杂系统的基础。传统方法在描述相互作用时往往存在先验知识依赖或可解释性不足的问题。为了克服这些限制，本研究提出了交互发现神经网络（IADNet），该网络将图结构学习与物理约束策略相结合，直接从粒子轨迹重建交互图拓扑，同时建立与实际物理系统配置的显式映射关系。为了验证其通用性，我们在四个不同的系统中测试了IADNet，包括经典力学、分子化学、生物模型和晶格系统。实验结果表明，IADNet可以准确地重建弹簧连接拓扑并估计弹性系数比，有效地识别分子中的化学键，揭示DNA模型中隐藏的远程相互作用并恢复碱基序列排列，并检测晶格系统中的异常模式。这些发现强调了IADNet在多粒子系统研究中的潜力。

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引用次数: 0

Copula-based analytical results of horizontal visibility graphs for correlated time series 相关时间序列水平可见性图的copula分析结果

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-03 DOI: 10.1016/j.physd.2025.135058

Jeong-Min Lee , Hang-Hyun Jo

The visibility graph (VG) algorithm and its variants have been extensively studied in the time series analysis as they transform the time series into the network of nodes and links, enabling to characterize the time series in terms of network measures such as degree distributions. Despite numerous practical applications of VGs in various disciplines, analytical, rigorous understanding of VGs for the correlated time series is still far from complete due to the lack of mathematical tools for modeling the correlation structure in the time series in a tractable form. In this work, we adopt the Farlie-Gumbel-Morgenstern (FGM) copula method to derive the analytical solutions of degree distributions of the horizontal visibility graph (HVG) and its directed version (DHVG) for the correlated time series. Our analytical results show exactly how the correlation between consecutive data points affects the degree distributions of HVGs and DHVGs up to the first order of the correlation parameter in the FGM copula. Thus, our findings shed light on the rigorous understanding of the VG algorithms.

可见性图（VG）算法及其变体在时间序列分析中得到了广泛的研究，因为它们将时间序列转换为节点和链路的网络，从而能够根据度分布等网络度量来表征时间序列。尽管VGs在各个学科中有许多实际应用，但由于缺乏以易于处理的形式对时间序列中的相关结构进行建模的数学工具，对相关时间序列的VGs的分析性，严格的理解仍然远远不够。本文采用Farlie-Gumbel-Morgenstern (FGM) copula方法，推导了相关时间序列水平可见性图（HVG）及其有向性图（DHVG）度分布的解析解。我们的分析结果准确地显示了连续数据点之间的相关性如何影响hvg和dhvg的度分布，直至FGM联结中相关参数的一阶。因此，我们的发现揭示了对VG算法的严格理解。

引用次数: 0

Assessment of averaged 1D models for column adsorption with 3D computational experiments 用三维计算实验评价柱吸附的平均一维模型

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-03 DOI: 10.1016/j.physd.2025.135064

Maria Aguareles , Francesc Font

We present a 3D mathematical model for contaminant capture in an adsorption column. The novelty of our approach involves the description of mass transfer by adsorption via a nonlinear evolution equation on the porous media surface, while Stokes flow and an advection-diffusion equation model contaminant transport through the interstices. Simulations with varying microstructures but identical porosity show minimal microstructure impact on contaminant distribution, especially in the radial direction. Using homogenization theory and a periodic microstructure, we derive a 1D adsorption model with two effective coefficients, dispersion and permeability, that explicitly incorporate microstructural details. The 1D model closely reproduces 3D results, including concentration profiles and outlet breakthrough curves. The 3D simulations converge to the 1D model as the microstructure is refined. Our model provides a theoretical foundation for the widely used 1D model, confirming its reliability for investigating, optimising, and designing column adsorption processes.

我们提出了吸附柱中污染物捕获的三维数学模型。我们的方法的新颖之处在于通过多孔介质表面的非线性演化方程来描述吸附传质，而Stokes流和平流扩散方程模型通过间隙来模拟污染物的传输。不同微观结构但孔隙率相同的模拟表明，微观结构对污染物分布的影响最小，尤其是在径向上。利用均质化理论和周期微观结构，我们推导了一个一维吸附模型，该模型具有两个有效系数，即分散度和渗透率，明确地包含了微观结构细节。一维模型可以很好地再现三维结果，包括浓度分布和出口突破曲线。随着微观结构的细化，三维模拟向一维模型收敛。我们的模型为广泛使用的一维模型提供了理论基础，证实了其在柱吸附过程研究、优化和设计中的可靠性。

引用次数: 0

Coupling of different solvable ensembles of random matrices II. Series over fat partitions: matrix models and discrete ensembles 随机矩阵不同可解集合的耦合II。胖分区上的级数：矩阵模型和离散集成

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-02 DOI: 10.1016/j.physd.2025.135061

A. Yu Orlov

We consider series over Young diagrams of products of Schur functions s_{λ ∪ λ}, marked with “fat partitions” λ ∪ λ, which appear in matrix models associated with ensembles of symplectic and orthogonal matrices and quaternion Ginibre ensembles. We consider mixed matrix models that also contain complex Ginibre ensembles labeled by graphs and the three ensembles mentioned above. Cases are identified when a series of perturbations in coupling constants turn out to be tau functions of the DKP hierarchy introduced by the Kyoto school. This topic relates matrix models to random partitions - discrete symplectic ensemble and its modifications.

我们考虑舒尔函数sλ∪λ积的Young图上的级数，用“fat partitions”λ∪λ标记，它出现在与辛矩阵和正交矩阵的集合以及四元数Ginibre集合相关的矩阵模型中。我们考虑混合矩阵模型，其中也包含由图标记的复杂Ginibre集成和上述三种集成。当耦合常数的一系列扰动被证明是京都学派引入的DKP层次的tau函数时，确定了一些情况。本课题将矩阵模型与随机分区-离散辛系综及其修正联系起来。

引用次数: 0

Spectral instability of peakons for a class of cubic quasilinear shallow-water equations 一类三次拟线性浅水方程峰的谱不稳定性

IF 2.9 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-12-02 DOI: 10.1016/j.physd.2025.135060

Qinwei Huang, Juan Huang

This paper focuses on a model with homogeneous cubic nonlinearity, which can be derived from classical shallow water theory as an asymptotic model. It is known as the mCH-Novikov equation, as it combines the integrable modified Camassa-Holm (mCH) equation and the Novikov equation. We systematically characterize the point spectrum of the peakon solutions and aim to prove spectral and linear instability on

L^{2} (R)

of peakons. To this end, we extend the corresponding linearized operator from

H^{1} (R)

to the larger space

L^{2} (R)

, since unstable eigenfunctions may reside in

L^{2} (R) ∖ H^{1} (R)

, and

L^{2} (R)

provides the natural framework for spectral instability analysis. Subsequently, we numerically verify these theoretical findings through spectral stability analysis and time-stepping numerical simulations of the model across different parameter regimes. Specifically, we analyze the parametric dependence of spectral stability to investigate how the mCH and Novikov terms affect the dynamics of the evolution equations.

本文研究了一个由经典浅水理论导出的具有齐次三次非线性的渐近模型。它被称为mCH-Novikov方程，因为它结合了可积修正Camassa-Holm （mCH）方程和Novikov方程。我们系统地描述了峰值解的点谱，目的是证明峰值在L2(R)上的谱和线性不稳定性。为此，我们将相应的线性化算子从H1(R)扩展到更大的空间L2(R)，因为不稳定特征函数可能存在于L2(R)∈H1(R)中，并且L2(R)为谱不稳定性分析提供了自然的框架。随后，我们通过谱稳定性分析和模型跨不同参数范围的时步数值模拟对这些理论发现进行了数值验证。具体来说，我们分析了谱稳定性的参数依赖性，以研究mCH和Novikov项如何影响演化方程的动力学。

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引用次数: 0

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