Related papers: Spatio-temporal dynamics induced by competing inst…
We investigate the dynamical formation of nonlinear patterns in one-dimensional ring condensates under bichromatic periodic modulation of the interaction strength. The stability phase diagram of the condensate's homogeneous density state is…
We numerically study a one-dimensional conserved growth equation with competing linear (Ehrlich-Schwoebel) and nonlinear instabilities. As a control parameter is varied, this model exhibits a non-equilibrium phase transition between two…
The processes in nonequilibrium dissipative media caused by coherent structure formation and lead to the complicated dynamics are of interest for nonlinear physics. Here we consider a model of the flow of interacting electronics patterns.…
Instabilities and pattern formation is the rule in nonequilibrium systems. Selection of a persistent lengthscale, or coarsening (increase of the lengthscale with time) are the two major alternatives. When and under which conditions one…
Many systems exhibit a phase where the order parameter is spatially modulated. These patterns can be the result of a frustration caused by the competition between interaction forces with opposite effects. In all models with local…
Localized patterns are coherent structures embedded in a quiescent state and occur in both discrete and continuous media across a wide range of applications. While it is well-understood how domain covering patterns (for example stripes and…
We investigate the dynamical stability of the holographic system with two order parameters, which exhibits competition and coexistence of condensations. In the linear regime, we have developed the gauge dependent formalism to calculate the…
Mechanisms of pattern formation---of which the Turing instability is an archetype---constitute an important class of dynamical processes occurring in biological, ecological and chemical systems. Recently, it has been shown that the Turing…
A wide variety of stationary or moving spatially localized structures is present in evolution problems on unbounded domains, governed by higher-than-second-order reversible spatial interactions. This work provides a generic unfolding in one…
We investigate the spatio-temporal dynamics of coupled chaotic systems with nonlocal interactions, where each element is coupled to its nearest neighbors within a finite range. Depending upon the coupling strength and coupling radius, we…
The conserved Swift-Hohenberg equation with cubic nonlinearity provides the simplest microscopic description of the thermodynamic transition from a fluid state to a crystalline state. The resulting phase field crystal model describes a…
In relation to spatiotemporal intermittency, as it can be observed in coupled map lattices, we study the stability of different wavelengths in competition. Introducing a two dimensional map, we compare its dynamics with the one of the whole…
We theoretically investigate the full time evolution of a nonequilibrium double quantum dot structure from initial conditions corresponding to different product states (no entanglement between dot and lead) to a nonequilibrium steady state.…
We present a general approach to prove the existence, both locally and globally in amplitude, of fully localised multi-dimensional patterns in partial differential equations containing a compact spatial heterogeneity. While one-dimensional…
This paper investigates the conditions for the stability and emergence of patterns in a new three-component reaction-diffusion system. The system describes the coexistence and interaction of water reservoirs, vegetation, and bushfire…
Interaction quenches in strongly correlated electron systems provide a powerful route to probe nonequilibrium many-body dynamics. For the Hubbard model, nonequilibrium dynamical mean-field theory has revealed coherent post-quench…
Hyperbolic reaction-diffusion equations have recently attracted attention both for their application to a variety of biological and chemical phenomena, and for their distinct features in terms of propagation speed and novel instabilities…
Turing patterns are a central paradigm for describing spatial patterns in nature. The corresponding theory of reaction-diffusion dynamics combines ideal diffusion with nonlinear reactions, resulting in patterns when species diffuse at…
We study an analytically tractable model with long-range interactions for which an out-of-equilibrium very long-lived coherent structure spontaneously appears. The dynamics of this model is indeed very peculiar: a bicluster forms at low…
Nature is intrinsically heterogeneous, and remarkable phenomena can only be observed in the presence of intrinsically nonlinear heterogeneities. Spontaneous pattern formation in nature has fascinated humankind for centuries, and the…