相关论文: Weakly versus highly nonlinear dynamics in 1D syst…
A detailed qualitative analysis and numerical modeling of the evolution of cosmological models based on nonlinear classical and phantom scalar fields with self-action are performed. Complete phase portraits of the corresponding dynamical…
Conserved growth models that exhibit a nonlinear instability in which the height (depth) of isolated pillars (grooves) grows in time are studied by numerical integration and stochastic simulation. When this instability is controlled by the…
The cosmology of flat FLRW universes dominated by a single scalar field is discussed. General features of the evolution of the universe and the scalar field are illustrated by specific examples. In particular the role of critical points,…
We use the dynamical analysis to study the evolution of the universe at late time for the model in which the interaction between dark energy and dark matter is inspired by disformal transformation. We extend the analysis in the existing…
Based on the hyperboloidal framework, we research the dynamical process of charged de Sitter black holes scattered by a charged scalar field. From the linear perturbation analysis, with the coupling strength within a critical interval, the…
The main objectives of this article are two-fold. First, we study the effect of the nonlinear Onsager mobility on the phase transition and on the well-posedness of the Cahn-Hilliard equation modeling a binary system. It is shown in…
Pattern formation has been extensively studied in the context of evolving (time-dependent) domains in recent years, with domain growth implicated in ameliorating problems of pattern robustness and selection, in addition to more realistic…
We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…
Nonequilibrium statistical mechanics exhibit a variety of complex phenomena far from equilibrium. It inherits challenges of equilibrium, including accurately describing the joint distribution of a large number of configurations, and also…
Modelling is an essential procedure in analyzing and controlling a given logical dynamic system (LDS). It has been proved that deterministic LDS can be modeled as a linear-like system using algebraic state space representation. However, due…
We consider the dynamics of thin two-dimensional viscous droplets on chemically heterogeneous surfaces moving under the combined effects of slip, mass transfer and capillarity. The resulting long-wave evolution equation for the droplet…
In this paper we study the dynamics of nonlinear random walks. While typical random walks on networks consist of standard Markov chains whose static transition probabilities dictate the flow of random walkers through the network, nonlinear…
Simple Hartree-type equations lead to dynamics of a subsystem that is not completely positive in the sense accepted in mathematical literature. In the linear case this would imply that negative probabilities have to appear for some system…
The work deals with homogeneous and isotropic, flat FRW model of the universe which is filled up with non-interacting dark matter and dark energy to compatible with recent observational evidences. By choosing the dark energy in the form of…
We describe a mechanism that results in the nonlinear instability of stationary states even in the case where the stationary states are linearly stable. This instability is due to the nonlinearity-induced coupling of the linearization's…
Understanding the structural evolution of granular systems is a long-standing problem. A recently proposed theory for such dynamics in two dimensions predicts that steady states of very dense systems satisfy detailed-balance. We analyse…
The study of stochastic systems has received considerable interest over the years. Their dynamics can describe many equilibrium and nonequilibrium fluctuating systems. At the same time, nonequilibrium constraints interact with the time…
Using dynamical systems methods, we describe the evolution of a minimally coupled scalar field and a Friedmann-Lemaitre-Robertson-Walker universe in the context of general relativity, which is relevant for inflation and late-time…
Phase transitions and critical behavior of driven systems are reviewed. Models exhibiting phase transitions, spontaneous symmetry breaking, phase separation and coarsening processes in d=1 dimension are discussed.
Scalar fields in the early Universe are mostly discussed in two limits: either in equilibrium or completely decoupled. In this work we discuss scenarios where there are scalar fields that are not in equilibrium, but for which the coupling…