Related papers: Multiple Front Propagation into Unstable States
We investigate spreading properties of solutions of a large class of two-component reaction-diffusion systems, including prey-predator systems as a special case. By spreading properties we mean the long time behaviour of solution fronts…
A high degree of control over the structure and dynamics of domain patterns in nonequilibrium systems can be achieved by applying nonuniform external fields near parity breaking front bifurcations. An external field with a linear spatial…
We study the properties of the survival probability of an unstable quantum state described by a Lee Hamiltonian. This theoretical approach resembles closely Quantum Field Theory (QFT): one can introduce in a rather simple framework the…
For scalar reaction-diffusion equations, a traveling wave is a front which transforms a higher energy state to a lower energy state. The same is true for a system of equations with a gradient structure. At the core of this phenomenon, the…
We study the stability and dynamics of traveling-front solutions of a modified Kuramoto--Sivashinsky equation arising in the modeling of nanoscale ripple patterns that form when a nominally flat solid surface is bombarded with a broad ion…
The dynamical steady state behaviour of the random field Ising ferromagnet swept by a propagating magnetic field wave is studied at zero temperature by Monte Carlo simulation in two dimensions. The distribution of the random field is…
Nonequilibrium conditions fundamentally change how systems undergo phase separation. In systems with temperature gradients, attractive particles have been shown to form periodic patterns and steady convective currents, but a clear…
The analysis of the time evolution of unstable states which are linear superposition of other, observable, states can, in principle, be carried out in two distinct, non-equivalent ways. One of the methods, usually employed for the neutral…
These are lecture notes of a course given at the 9th International Summer School on Fundamental Problems in Statistical Mechanics, held in Altenberg, Germany, in August 1997. In these notes, we discuss at an elementary level three themes…
The dynamics of the domains is studied in a two-dimensional model of the microphase separation of diblock copolymers in the vicinity of the transition. A criterion for the validity of the mean field theory is derived. It is shown that at…
The concept of Turing instability, namely that diffusion can destabilize the uniform steady state, is well known either in the context of partial differential equations (PDEs) or in networks of dynamical systems. Recently reaction-diffusion…
This review addresses recent developments in nonequilibrium statistical physics. Focusing on phase transitions from fluctuating phases into absorbing states, the universality class of directed percolation is investigated in detail. The…
We show that propagation speeds in invasion processes modeled by reaction-diffusion systems are determined by marginal spectral stability conditions, as predicted by the marginal stability conjecture. This conjecture was recently settled in…
Domain walls in equilibrium phase transitions propagate in a preferred direction so as to minimize the free energy of the system. As a result, initial spatio-temporal patterns ultimately decay toward uniform states. The absence of a…
We report the first experimental realization of pattern formation in a spatially extended nonlinear system when the system is alternated between two states, neither of which exhibits patterning. Dynamical equations modeling the system are…
We consider a propagation of transition fronts in one-dimensional chains with bi-stable nondegenerate on-site potential. If one adopts linear coupling in the chain and piecewise linear on-site force, then it is possible to develop…
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…
We study the transient dynamics of single species reaction diffusion systems whose reaction terms $f(u)$ vary nonlinearly near $u\approx 0$, specifically as $f(u)\approx u^{2}$ and $f(u)\approx u^{3}$. We consider three cases, calculate…
We quantitatively characterize the metastability in a multi-phase lattice Boltzmann model. The structure factor of density fluctuations is theoretically obtained and numerically verified to a high precision, for all simulated wave-vectors…
Nonlinear instabilities are responsible for spontaneous pattern formation in a vast number of natural and engineered systems ranging from biology to galaxies build-up. We propose a new instability mechanism leading to pattern formation in…