This paper is devoted to the derivation of a macroscopic diffusion equation (Fourier’s law) describing the transport of energy in an anharmonic chain. More precisely, we study here the so-called FPU-β chain, which is a very simple model for a one-dimensional crystal in which atoms are coupled to their nearest neighbors by a harmonic potential, weakly perturbed by a quartic potential. The starti...

We present some analytic results aiming at explaining the lack of thermalization observed by Fermi Pasta and Ulam in their celebrated numerical experiment. In particular we focus on results which persist as the number N of particles tends to infinity. After recalling the FPU experiment and some classical heuristic ideas that have been used for its explanation, we concentrate on more recent rigo...

In this paper we prove that near the equilibirum position any periodic FPU chain with an odd number of particles admits a Birkhoff normal form up to order 4, and we obtain an explicit formula of the Hessian of its Hamiltonian at the fixed point.

This article presents a numerical model to study wave turbulence in fluids. The equation is derived by incorporating energy conservation (along with the usual fluid equations of compressible flow), and source nonlinearity rise temperature due acoustic wave's high amplitude. nonlinear Schrödinger (NLS) modified (MNLS) have been then solved numerically. A simulation MNLS used for investigating ge...

In [1], the incorrect version of Fig. 18 was published. The following are correct figures. 18. Results Case III; (a) fpu and $V_{pu}^{dc}$; active power (b) ICs (c) DGs.