相关论文: Critical behaviour for scalar nonlinear waves

The theory of continuous phase transitions predicts the universal collective properties of a physical system near a critical point, which for instance manifest in characteristic power-law behaviours of physical observables. The…

We study the blowup behavior of a class of strongly perturbed wave equations with a focusing supercritical power nonlinearity in three spatial dimensions. We show that the ODE blowup profile of the unperturbed equation still describes the…

Dispersive shock waves dominate wave-breaking phenomena in Hamiltonian systems. In the absence of loss, these highly irregular and disordered waves are potentially reversible. However, no experimental evidence has been given about the…

We study numerically and experimentally the impact of temporal randomness on the formation of analogue optical blast-waves in nonlinear fiber optics. The principle-of-operation is based on a two-components nonlinear interaction occurring…

This article discusses the numerical result predicted by the quantum Langevin equation of the generalized diffusion function of a Brownian particle immersed in an Ohmic quantum bath of harmonic oscillators. The time dependence of the…

We study motion of a phase transition front at a constant temperature between stable and metastable states in fluids with the universal Van der Waals equation of state (which is valid sufficiently close to the fluid's critical point). We…

Critical behaviour of two systems, subjected to the turbulent mixing, is studied by means of the field theoretic renormalization group. The first system, described by the equilibrium model A, corresponds to relaxational dynamics of a…

With extensive variational simulations, dissipative quantum phase transitions in the sub-Ohmic spin-boson model are numerically studied in a dense limit of environmental modes. By employing a generalized trial wave function composed of…

Phase transitions of reaction-diffusion systems with site occupation restriction and with particle creation that requires n>1 parents and where explicit diffusion of single particles (A) exists are reviewed. Arguments based on mean-field…

All complex fluid motions, such as transition and turbulence, obeying the Navier-Stokes equations are non-linear phenomena. Some aspects of the non-linear terms of these equations are not well understood and are, in fact, misunderstood. The…

An asymptotic description of the formation of dispersive shock waves in solutions to the generalized Kadomtsev--Petviashvili (KP) equation is conjectured. The asymptotic description based on a multiscales expansion is given in terms of a…

A universal law for the supercritical bifurcation shape of transverse one-dimensional (1D) systems in presence of additive noise is given. The stochastic Langevin equation of such systems is solved by using a Fokker-Planck equation leading…

Dissipative phase transitions are strongly shaped by the symmetries of the Liouvillian, yet the quantitative impact of weak and strong symmetries on critical behavior has remained unclear. We study a squeezed-photon model with single- and…

In this paper, we study the global conservative weak solutions for a class of nonlinear dispersive wave equations after wave breaking. We first transform the equations into an equivalent semi-linear system by introducing new variables. We…

In this paper we revisit the Brownian motion on the basis of {the fractional Langevin equation which turns out to be a particular case of the generalized Langevin equation introduced by Kubo in 1966. The importance of our approach is to…

Spreading of bacteria in a highly advective, disordered environment is examined. Predictions of super-diffusive spreading for a simplified reaction-diffusion equation are tested. Concentration profiles display anomalous growth and…

We classify all bifurcations from traveling waves to non-trivial time-periodic solutions of the Benjamin-Ono equation that are predicted by linearization. We use a spectrally accurate numerical continuation method to study several paths of…

All solids, whether crystalline or disordered, support elastic wave propagation with a linear dispersion relation in the long-wavelength limit. These waves, corresponding to low-frequency phonons, feature a vibrational density of states…

We provide a both qualitative and quantitative comparison among different approaches aimed to solve the problem of non-linear diffusive acceleration of particles at shocks. In particular, we show that state-of-the-art models (numerical,…

We consider a general reaction--nonlinear-diffusion equation with a region of negative diffusivity, and show how a nonlinear regularisation selects a shock position. Negative diffusivity can model population aggregation, but leads to…