Physica D: Nonlinear Phenomena最新文献

英文中文

Entwining Yang–Baxter maps over Grassmann algebras

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134469

P. Adamopoulou , G. Papamikos

In this work we construct novel solutions to the set-theoretical entwining Yang–Baxter equation. These solutions are birational maps involving non-commutative dynamical variables which are elements of the Grassmann algebra of order

n

. The maps arise from refactorisation problems of Lax supermatrices associated to a nonlinear Schrödinger equation. In this non-commutative setting, we construct a spectral curve associated to each of the obtained maps using the characteristic function of its monodromy supermatrix. We find generating functions of invariants for the entwining Yang–Baxter maps from the moduli of the spectral curves. Moreover, we show that a hierarchy of birational entwining Yang–Baxter maps with commutative variables can be obtained by fixing the order

n

of the Grassmann algebra, and we present the cases

n = 1

(dual numbers) and

n = 2

. Then we discuss the integrability properties, such as Lax matrices, invariants, and measure preservation, for the obtained discrete dynamical systems.

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引用次数: 0

Properties of some dynamical systems for three collapsing inelastic particles

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134477

Théophile Dolmaire , Juan J.L. Velázquez

In this article we continue the study of the collapse of three inelastic particles in dimension

d \geq 2

, complementing the results we obtained in the companion paper (Dolmaire and Velázquez, 2024). We focus on the particular case of the nearly-linear inelastic collapse, when the order of collisions becomes eventually the infinite repetition of the period ⓪-①, ⓪-②, under the assumption that the relative velocities of the particles (with respect to the central particle ⓪) do not vanish at the time of collapse. Taking as starting point the full dynamical system that describes two consecutive collisions of the nearly-linear collapse, we derive formally a two-dimensional dynamical system, called the two-collision mapping. This mapping governs the evolution of the variables of the full dynamical system. We show in particular that in the so-called Zhou–Kadanoff regime, the orbits of the two-collision mapping can be described in full detail. We study rigorously the two-collision mapping, proving that the Zhou–Kadanoff regime is stable and locally attracting in a certain region of the phase space of the two-collision mapping. We describe all the fixed points of the two-collision mapping in the case when the norms of the relative velocities tend to the same positive limit. We establish conjectures to characterize the orbits that verify the Zhou–Kadanoff regime, motivated by numerical simulations, and we prove these conjectures for a simplified version of the two-collision mapping.

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引用次数: 0

Fold bifurcation identification through scientific machine learning

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134490

Giuseppe Habib , Ádám Horváth

This study employs scientific machine learning to identify transient time series of dynamical systems near a fold bifurcation of periodic solutions. The unique aspect of this work is that a convolutional neural network (CNN) is trained with a relatively small amount of data and on a single, very simple system, yet it is tested on much more complicated systems. This task requires strong generalization capabilities, which are achieved by incorporating physics-based information. This information is provided through a specific pre-processing of the input data, which includes transformation into polar coordinates, normalization, transformation into the logarithmic scale, and filtering through a moving mean. The results demonstrate that such data pre-processing enables the CNN to grasp the important features related to transient time-series near a fold bifurcation, namely, the trend of the oscillation amplitude, and disregard other characteristics that are not particularly relevant, such as the vibration frequency. The developed CNN was able to correctly classify transient trajectories near a fold for a mass-on-moving-belt system, a van der Pol-Duffing oscillator with an attached tuned mass damper, and a pitch-and-plunge wing profile. The results contribute to the progress towards the development of similar CNNs effective in real-life applications such as safety monitoring of dynamical systems.

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引用次数: 0

Data driven modeling for self-similar dynamics

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134505

Ruyi Tao , Ningning Tao , Yi-zhuang You , Jiang Zhang

Multiscale modeling of complex systems is crucial for understanding their intricacies. In recent years, data-driven multiscale modeling has emerged as a promising approach to tackle challenges associated with complex systems. Still, at present,this field is more focused on the prediction or control problems in specific fields, and there is no suitable framework to help us promote the establishment of complex system modeling theory. On the other hand, self-similarity is prevalent in complex systems, hinting that large-scale complex systems can be modeled at a reduced cost. In this paper, we introduce a multiscale neural network framework that incorporates self-similarity as prior knowledge, facilitating the modeling of self-similar dynamical systems. Our framework can discern whether the dynamics are self-similar to deterministic dynamics. For uncertain dynamics, it not only can judge whether it is self-similar or not, but also can compare and determine which parameter set is closer to self-similarity. The framework allows us to extract scale-invariant kernels from the dynamics for modeling at any scale. Moreover, our method can identify the power-law exponents in self-similar systems, providing valuable insights for the establishment of complex system modeling theory.

{"title":"Data driven modeling for self-similar dynamics","authors":"Ruyi Tao , Ningning Tao , Yi-zhuang You , Jiang Zhang","doi":"10.1016/j.physd.2024.134505","DOIUrl":"10.1016/j.physd.2024.134505","url":null,"abstract":"<div><div>Multiscale modeling of complex systems is crucial for understanding their intricacies. In recent years, data-driven multiscale modeling has emerged as a promising approach to tackle challenges associated with complex systems. Still, at present,this field is more focused on the prediction or control problems in specific fields, and there is no suitable framework to help us promote the establishment of complex system modeling theory. On the other hand, self-similarity is prevalent in complex systems, hinting that large-scale complex systems can be modeled at a reduced cost. In this paper, we introduce a multiscale neural network framework that incorporates self-similarity as prior knowledge, facilitating the modeling of self-similar dynamical systems. Our framework can discern whether the dynamics are self-similar to deterministic dynamics. For uncertain dynamics, it not only can judge whether it is self-similar or not, but also can compare and determine which parameter set is closer to self-similarity. The framework allows us to extract scale-invariant kernels from the dynamics for modeling at any scale. Moreover, our method can identify the power-law exponents in self-similar systems, providing valuable insights for the establishment of complex system modeling theory.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":"472 ","pages":"Article 134505"},"PeriodicalIF":2.7,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143163328","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Two-component stripe soliton states in spin-1/2 spin–orbit-coupled Bose–Einstein condensates

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2025.134540

Fei-Yan Liu , Qin Zhou

This work presents various types of stripe solitons of the one-dimensional two-component Gross–Pitaevskii (GP) equation, which can be used to describe the dynamic evolution of matter–waves in the spin-1/2 spin–orbit-coupled Bose–Einstein condensates (BECs). Firstly, in the absence of Rabi coupling, the approximate bright and dark stripe solitons are constructed by the multi-scale expansion method, which are formed by the linear superposition of two lowest symmetric states in its linear energy spectrum. Secondly, in the absence of Zeeman splitting, exact nondegenerate and degenerate bright stripe solitons as well as the degenerate dark stripe solitons of the integrable GP equation are obtained by the Hirota’s bilinear method. Finally, the transmission stability of stripe solitons and the interaction between two stripe solitons are discussed.

引用次数: 0

Localized synchronous patterns in weakly coupled bistable oscillator systems

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2025.134537

Erik Bergland , Jason J. Bramburger , Björn Sandstede

Motivated by numerical continuation studies of coupled mechanical oscillators, we investigate branches of localized time-periodic solutions of one-dimensional chains of coupled oscillators. We focus on Ginzburg–Landau equations with nonlinearities of Lambda-Omega type and establish the existence of localized synchrony patterns in the case of weak coupling and weak-amplitude dependence of the oscillator periods. Depending on the coupling, localized synchrony patterns lie on a discrete stack of isola branches or on a single connected snaking branch.

引用次数: 0

Turbulent transport regimes in the presence of an X-point magnetic configuration

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2025.134529

Fabio Moretti , Nakia Carlevaro , Francesco Cianfrani , Giovanni Montani

We analyze the transport properties of the two-dimensional electrostatic turbulence characterizing the edge of a Tokamak device from the study of test particles motion (passive fluid tracers) following the

E \times B

drift. We perform statistical tests on the tracer population in order to assess both the magnitude and the main features of transport. The role of other physical properties, such as viscosity and inverse energy cascade in the spectrum, is also considered. We outline that large scale eddies are responsible for greater transport coefficients, while the presence of an X-point magnetic field reduces the mean free path of the particles, however generating a larger outliers population with respect to a Gaussian profile.

引用次数: 0

Nonlinear q-voter model involving nonconformity on networks

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134508

NQZ Rinto Anugraha , Roni Muslim , Hariyanto Henokh Lugo , Fahrudin Nugroho , Idham Syah Alam , Muhammad Ardhi Khalif

The order–disorder phase transition is a fascinating phenomenon in opinion dynamics models within sociophysics. This transition emerges due to noise parameters, interpreted as social behaviors such as anticonformity and independence (nonconformity) in a social context. In this study, we examine the impact of nonconformist behaviors on the macroscopic states of the system. Both anticonformity and independence are parameterized by a probability

p

, with the model implemented on a complete graph and a scale-free network. Furthermore, we introduce a skepticism parameter

s

, which quantifies a voter’s propensity for nonconformity. Our analytical and simulation results reveal that the model exhibits continuous and discontinuous phase transitions for nonzero values of

s

at specific values of

q

. We estimate the critical exponents using finite-size scaling analysis to classify the model’s universality. The findings suggest that the model on the complete graph and the scale-free network share the same universality class as the mean-field Ising model. Additionally, we explore the scaling behavior associated with variations in

s

and assess the influence of

p

and

s

on the system’s opinion dynamics.

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引用次数: 0

On the convergence of Hermitian Dynamic Mode Decomposition

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134405

Nicolas Boullé , Matthew J. Colbrook

We study the convergence of Hermitian Dynamic Mode Decomposition (DMD) to the spectral properties of self-adjoint Koopman operators. Hermitian DMD is a data-driven method that approximates the Koopman operator associated with an unknown nonlinear dynamical system, using discrete-time snapshots. This approach preserves the self-adjointness of the operator in its finite-dimensional approximations. We prove that, under suitably broad conditions, the spectral measures corresponding to the eigenvalues and eigenfunctions computed by Hermitian DMD converge to those of the underlying Koopman operator. This result also applies to skew-Hermitian systems (after multiplication by

i

), applicable to generators of continuous-time measure-preserving systems. Along the way, we establish a general theorem on the convergence of spectral measures for finite sections of self-adjoint operators, including those that are unbounded, which is of independent interest to the wider spectral community. We numerically demonstrate our results by applying them to two-dimensional Schrödinger equations.

引用次数: 0

Unsupervised classification of non-linear dynamics in optical fiber propagation using intensity clustering

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena

Pub Date : 2025-02-01 DOI: 10.1016/j.physd.2024.134502

Anastasiia Sheveleva , Andrei V. Ermolaev , John M. Dudley , Christophe Finot

We demonstrate that centroid-based clustering of normalized intensity profiles is able to successfully isolate different classes of pulses associated with physically distinct regimes of nonlinear and dispersive propagation in optical fiber. Remarkable for its simplicity, this approach shows how analysis of only the temporal intensity profiles of propagating pulses, even at relatively limited sampling resolution, reveal sufficient similarities to allow physical classification of different classes of propagation behavior.

引用次数: 0

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