Related papers: Transversal interface dynamics of a front connecti…
The properties of interfaces are key to understand the physics of matter. However, the study of quantum interface dynamics has remained an outstanding challenge. Here, we use large-scale Tree Tensor Network simulations to identify the…
We study the influence of boundary conditions on stationary, periodic patterns in one-dimensional systems. We show how a conceptual understanding of the structure of equilibria in large domains can be based on the characterization of…
We consider the dynamics and kinetic roughening of interfaces embedded in uniformly random media near percolation treshold. In particular, we study simple discrete ``forest fire'' lattice models through Monte Carlo simulations in two and…
We study numerically the roughening properties of an interface in a two-dimensional Ising model with either random bonds or random fields, which are representative of universality classes where disorder acts only on the interface or also…
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…
In this work we investigate the development of stable dynamical structures along interfaces separating domains belonging to enemy partnerships, in the context of cyclic predator-prey models with an even number of species $N \ge 8$. We use…
The viscous regularization of an ill-posed diffusion equation with bistable nonlinearity predicts a hysteretic behavior of dynamical phase transitions but a complete mathematical \mbox{understanding} of the intricate multiscale evolution is…
We study numerically the cubic-quintic-septic Swift-Hohenberg (SH357) equation on bounded one-dimensional domains. Under appropriate conditions stripes with wave number $k\approx 1$ bifurcate supercritically from the zero state and form…
We propose a statistical mechanics approach to a coevolving spin system with an adaptive network of interactions. The dynamics of node states and network connections is driven by both spin configuration and network topology. We consider a…
In this paper, we investigate signatures of topological phase transitions in interacting systems. We show that the key signature is the existence of a topologically protected level crossing, which is robust and sharply defines the…
We study the mass-conserved reaction-diffusion system known as the wave-pinning model, which serves as a minimal framework for describing cell polarity. In this model, the interplay between reaction kinetics and slow diffusion forms a sharp…
We study numerically a stochastic differential equation describing an interface driven along the hard direction of an anisotropic random medium. The interface is subject to a homogeneous driving force, random pinning forces and the surface…
We present a numerical study of a model of pattern formation following a convective instability in a non-Boussinesq fluid. It is shown that many of the features observed in convection experiments conducted on $CO_{2}$ gas can be reproduced…
We investigate the evolution of a single unbounded interface between ordered phases in two-dimensional Ising ferromagnets that are endowed with single-spin-flip zero-temperature Glauber dynamics. We examine specifically the cases where the…
In many complex systems, states and interaction structure coevolve towards a dynamic equilibrium. For the adaptive contact process, we obtain approximate expressions for the degree distributions that characterize the interaction network in…
The flow in a Hele-Shaw cell with a time-increasing gap poses a unique shrinking interface problem. When the upper plate of the cell is lifted perpendicularly at a prescribed speed, the exterior less viscous fluid penetrates the interior…
Stationary periodic patterns are widespread in natural sciences, ranging from nano-scale electrochemical and amphiphilic systems to mesoscale fluid, chemical and biological media and to macro-scale vegetation and cloud patterns. Their…
The coarsening process in a class of driven systems exhibiting striped structures is studied. The dynamics is governed by the motion of the driven interfaces between the stripes. When two interfaces meet they coalesce thus giving rise to a…
We consider a kinetic model of two species of particles interacting with a reservoir at fixed temperature, described by two coupled Vlasov-Fokker-Plank equations. We prove that in the diffusive limit the evolution is described by a…
We study the interfaces' time evolution in one-dimensional bistable extended dynamical systems with discrete time. The dynamics is governed by the competition between a local piece-wise affine bistable mapping and any couplings given by the…