Physica D: Nonlinear Phenomena最新文献

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The amplitude equation for the space-fractional Swift–Hohenberg equation

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2025.134531

Christian Kuehn , Sebastian Throm

Non-local reaction–diffusion partial differential equations (PDEs) involving the fractional Laplacian have arisen in a wide variety of applications. One common tool to analyze the dynamics of classical local PDEs very close to instability is to derive local amplitude/modulation multiscale approximations, which provide local normal forms classifying the onset of a wide variety of pattern-formation phenomena. In this work, we study amplitude equations for the space-fractional Swift–Hohenberg equation. The Swift–Hohenberg equation is a basic model problem motivated by pattern formation in fluid dynamics and has served as one of the main PDEs to develop general techniques to derive amplitude equations. We prove that there exists near the first bifurcation point an approximation by a (real) Ginzburg–Landau equation. Interestingly, this Ginzburg–Landau equation is a local PDE, which provides a rigorous justification of the physical conjecture that suitably localized unstable modes can out-compete superdiffusion and re-localize a PDE near instability. Our main technical contributions are to provide a suitable function space setting for the approximation problem, and to then bound the residual between the original PDE and its amplitude equation, i.e., to rigorously prove a multiscale decomposition between the leading critical modes and the higher-order remainder terms.

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引用次数: 0

A diffusion–advection epidemic model with mass action infection mechanism and birth–death effect

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134467

Xiaodan Chen, Renhao Cui

This paper is concerned with a reaction–diffusion–advection SIS (susceptible–infected–susceptible) epidemic model with mass action infection mechanism and linear birth–death effect. We derive a variational expression of the basic reproduction number

R_{0}

and establish its threshold role between disease extinction and persistence. More importantly, we investigate asymptotic profiles of endemic equilibrium with respect to large advection or small motility of susceptible/infected individuals. Compared with three other closely related modeling systems in previous works, it turns out that our model is not only mathematically more difficult to tackle, but also the theoretical findings reveal rather different phenomena concerning spreading and spatial distribution of infectious diseases. These results may bring some prospective applications in disease control strategies.

引用次数: 0

Fractured alliances in a four-species cyclic ecological system

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134479

E.Y. Siegfried, A. Bayliss, V.A. Volpert

We consider two Lotka–Volterra type models for ecological communities exhibiting a modified form of cyclic competition. The first governs a four-species ecological system. When each species competes only with one other species cyclically, then, it is known that, for strong competition the system evolves to one of two alliances of non-competing species.

We consider the case when there is internal competition and predation within one of the alliances. This leads to an embedded three-species rock–paper–scissors (

R P S

) community, which can be dynamically unstable — leading to attracting heteroclinic cycles within the four-species system. We show that, even for vanishingly small fracturing, other outcomes are also possible. We identify all possible physical steady states, their stabilities and bifurcations which can occur between them (eight bifurcations in all).

For our second model, we consider the case of two ecological communities within a heterogeneous environment. The communities are coupled, allowing information exchange between them. We prove that for strong coupling the two communities will form a unified state corresponding to one with averaged ecological parameters. For the case of dynamically unstable communities (i.e., heteroclinic cycles), we develop a method to characterize the averaged heteroclinic cycle based on the rate of expansion of trajectory visits to the appropriate saddle. Information exchange can allow small ecological heterogeneities to lead to very major changes in the steady state. In particular, information exchange can quench heteroclinic cycles within both communities or conversely can allow for heteroclinic cycles where none would occur for each community in isolation.

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引用次数: 0

The integrable Ermakov structure and elliptic vortex solution in the inviscid gas-liquid two-phase flow

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134495

Hongli An , Manwai Yuen , Haixing Zhu

The inviscid gas-liquid two-phase flow is an important physical model, which has a wide range of applications in natural, engineering and biomedicine. In this paper, we propose a novel elliptic vortex ansatz and thereby reduce the gas-liquid two-phase flow to a set of nonlinear dynamical system. The latter is shown to not only admit the Lax pair formulation and associated integrable stationary nonlinear Schrödinger connection, but also possess the integrable Ermakov structure of Hamiltonian type which exists both in the density parameters and mixed velocity of the two-phase flow. In addition, we construct a class of vortex solutions termed pulsrodons corresponding to pulsating elliptic warm-core rings and discuss its dynamical behaviors. Such solutions have recently found applications in geography, tidal oscillations, oceanic and atmospheric dynamics.

引用次数: 0

Stripe patterns for Gierer–Meinhard model in spatially varying thin domains

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134480

Leila Mohammadi , Theodore Kolokolnikov , David Iron , Tamara A. Franz-Odendaal

We explore pattern formation for the GM model on thin domains. If the domain is sufficiently thin, the pattern consists of stripes which are nearly one-dimensional. We analyze patterns consisting of one, two or many stripes. We find that a single stripe can be located either at the thickest or thinnest part of the channel, depending on the choice of parameters. In the limit of many stripes, we derive an effective pattern density description of the equilibrium state. The effective density is easily computable as a solution of a first order ODE subject to an integral constraint. Depending on problem parameters, the resulting pattern can be either global spanning the entire domain, or can be clustered near either thickest or thinnest part of the domain. In addition, instability thresholds are derived from the continuum density limit of many stripes. Full two-dimensional numerical simulations are performed and are shown to be in agreement with the asymptotic results.

引用次数: 0

Scaling invariance for the diffusion coefficient in a dissipative standard mapping

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134513

Edson D. Leonel , Célia M. Kuwana , Diego F.M. Oliveira

The unbounded diffusion observed for the standard mapping in a regime of high nonlinearity is suppressed by dissipation due to the violation of Liouville’s theorem. The diffusion coefficient becomes important for the description of scaling invariance particularly for the suppression of the unbounded action diffusion. When the dynamics start in the regime of low action, the diffusion coefficient remains constant for a long time, guaranteeing the diffusion for an ensemble of particles. Eventually, it evolves into a regime of decay, marking the suppression of particle action growth. We prove it is scaling invariant for the control parameters and the crossover time identifying the changeover from the constant domain, leading to diffusion, for a regime of decay marking the saturation of the diffusion, scales with the same critical exponent

z = - 1

for a transition from bounded to unbounded diffusion in a dissipative time dependent billiard system.

引用次数: 0

Sampling error mitigation through spectrum smoothing: First experiments with ensemble transform Kalman filters and Lorenz models

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134436

Bosu Choi , Yoonsang Lee

In data assimilation, an ensemble provides a way to propagate the probability density of a system described by a nonlinear prediction model. Although a large ensemble size is required for statistical accuracy, the ensemble size is typically limited to a small number due to the computational cost of running the prediction model, which leads to a sampling error. Several methods, such as localization and inflation, exist to mitigate the sampling error, often requiring problem-dependent fine-tuning and design. This work introduces a nonintrusive sampling error mitigation method that modifies the ensemble to ensure a smooth turbulent spectrum. It turns out that the ensemble modification to satisfy the smooth spectrum leads to inhomogeneous localization and inflation, which apply spatially varying localization and inflation levels at different locations. The efficacy of the new idea is validated through a suite of stringent test regimes of the Lorenz 96 turbulent model.

引用次数: 0

Thermocapillary weak viscoelastic film flows on a rotating substrate

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134493

Souradip Chattopadhyay, Hangjie Ji

We analyze the dynamics and stability of a thin viscoelastic film on a rotating, nonuniformly heated inclined plane, assuming weak rotation and a region far from the axis. The centrifugal force’s effect on instability is a key focus, with Walter’s B

^{''}

rheology used for the viscoelastic liquid. By applying the long-wave approximation, we derive a nonlinear evolution equation for the local film thickness, capturing the interplay of viscoelasticity, rotation, thermocapillarity, and gravity in the low Reynolds number regime. Linear stability analysis shows that the linear growth rate of disturbances is influenced by the viscoelastic parameter, centrifugal force, and Marangoni stresses, while the linear wave speed is affected by rotation and thermocapillarity, but not viscoelasticity. A weakly nonlinear stability analysis reveals distinct instability regions, with both supercritical stable and subcritical unstable zones governed by rotation, thermocapillarity, and viscoelasticity. Numerical studies show that rotation enhances wave height, and viscoelasticity and thermal effects further amplify it. Additionally, viscoelasticity, rotation, and thermal effects impact nonlinear wave speed, though nonuniform heating reduces wave propagation. Full numerical simulations confirm the results from linear and weakly nonlinear analyses.

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引用次数: 0

Adaptive dynamic social networks using an agent-based model to study the role of social awareness in infectious disease spread

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2025.134530

Leonardo López , Leonardo Giovanini

The synergy between the spread of infectious diseases, individual behavior, and group dynamics is widely recognized by epidemiologists and researchers. Our pioneering methodology introduces a model based on agents embedded within adaptive temporal networks, providing a nuanced portrayal of daily interactions through an agent-based paradigm. Each agent encapsulates the interactions of individuals, with external stimuli and environmental cues influencing their behavior. Comprising three intertwined elements — individual behavior, social dynamics, and epidemiological factors — the model has been validated against real-world influenza outbreaks, demonstrating superior performance compared to traditional methodologies. Our framework exhibits extensive versatility and applicability by encapsulating individual-level dynamics through elementary rules and simulating complex social behaviors such as social consciousness.

引用次数: 0

Soliton resolution and asymptotic stability of N-soliton solutions for the defocusing mKdV equation with a non-vanishing background

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2025.134526

Zechuan Zhang, Taiyang Xu, Engui Fan

We analytically study the large-time asymptotics of the solution of the defocusing modified Korteweg–de Vries (mKdV) equation under a symmetric non-vanishing background, which supports the emergence of solitons. It is demonstrated that the asymptotic expansion of the solution at the large time could verify the renowned soliton resolution conjecture. Moreover, the asymptotic stability of

N

-soliton solution is also exhibited in the present work. We establish our results by performing a

\bar{\partial}

-nonlinear steepest descent analysis to the associated Riemann–Hilbert (RH) problem.

引用次数: 0

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