Related papers: Transition fronts and their universality classes
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 interface separating a liquid from its vapor phase is diffuse: the composition varies continuously from one phase to the other over a finite length. Recent experiments on dynamic jamming fronts in two dimensions [Waitukaitis et al.,…
Many quantum condensed-matter systems, and probably the quantum vacuum of our Universe, are strongly correlated and strongly interacting fermionic systems, which cannot be treated perturbatively. However, physics which emerges in the…
This paper is devoted to the study of spatial propagation dynamics of species in locally spatially inhomogeneous patchy environments or media. For a lattice differential equation with monostable nonlinearity in a discrete homogeneous media,…
We study numerically statistical distributions of sums of chaotic orbit coordinates, viewed as independent random variables, in weakly chaotic regimes of three multi-dimensional Hamiltonian systems: Two Fermi-Pasta-Ulam (FPU-$\beta$)…
We consider both analytical and numerical studies of a steady-state fracture process inside a discrete mass-beam structure, composed of periodically placed masses connected by Euler-Bernoulli beams. A fault inside the structure is assumed…
We show the relevance of the dispersive analogue of the shock waves in the FPU dynamics. In particular we give strict numerical evidences that metastable states emerging from low frequency initial excitations, are indeed constituted by…
Propagation of transition fronts in models of coupled oscillators with non-degenerate on-site potential is usually considered in terms of travelling waves. We show that the system dynamics can be reformulated as an implicit map structure,…
Dynamical phase transitions (DPTs) characterize critical changes in system behavior occurring at finite times, providing a lens to study nonequilibrium phenomena beyond conventional equilibrium physics. While extensively studied in quantum…
Wave front pinning and propagation in damped chains of coupled oscillators are studied. There are two important thresholds for an applied constant stress $F$: for $|F|<F_{cd}$ (dynamic Peierls stress), wave fronts fail to propagate, for…
The investigation of the Hamiltonian dynamical counterpart of phase transitions, combined with the Riemannian geometrization of Hamiltonian dynamics, has led to a preliminary formulation of a differential-topological theory of phase…
We present a simple one dimensional stochastic model with three control parameters and a surprisingly rich zoo of phase transitions. At each (discrete) site $x$ and time $t$, an integer $n(x,t)$ satisfies a linear interface equation with…
We present a class of one-dimensional generic spinless fermion lattice Hamiltonians that express quasi-Fermi liquid physics, manifesting both Luttinger and Fermi liquid features due to solely irrelevant interactions. Using infinite matrix…
In this paper we investigate analytically and numerically the nonlinear Kelvin lattice, namely a chain of masses and nonlinear springs, as in the alpha-Fermi-Pasta-Ulam-Tsingou (FPUT) chain, where, in addition, each mass is connected to a…
We consider infinite FPU-type atomic chains with general convex potentials and study the existence of monotone fronts that are heteroclinic travelling waves connecting constant asymptotic states. Iooss showed that small amplitude fronts…
We study the inhomogeneous kinetic Fermi-Pasta-Ulam (FPU) equation, a nonlinear transport equation describing the evolution of phonon density distributions with four-phonon interactions. The equation combines free transport in physical…
The linear response to temperature variations is well characterised for equilibrium systems but a similar theory is not available, for example, for inertial heat conducting systems, whose paradigm is the Fermi-Pasta-Ulam (FPU) model driven…
In line with Pomeau's conjecture about the relevance of directed percolation (DP) to turbulence onset/decay in wall-bounded flows, we propose a minimal stochastic model dedicated to the interpretation of the spatially intermittent regimes…
The transition from order to chaos has been a major subject of research since the work of Poincare, as it is relevant in areas ranging from the foundations of statistical physics to the stability of the solar system. Along this transition,…
We study various temporal correlation functions of a tagged particle in one-dimensional systems of interacting point particles evolving with Hamiltonian dynamics. Initial conditions of the particles are chosen from the canonical thermal…