Related papers: Energy transfer between modes in a nonlinear beam …
We consider the links between nonlinear dynamics and thermodynamics in the framework of a simple nonlinear model for DNA. Two analyses of the phase transition, either with the transfer integral approach or by considering the instability of…
We calculate the net energy per unit time exchanged between two sets of modes in a generic system governed by a three-wave kinetic equation. Our calculation is based on the property of detailed energy conservation of the triadic resonant…
Non-equilibrium steady states are subject to intense investigations but still poorly understood. For instance, the derivation of Fourier law in Hamiltonian systems is a problem that still poses several obstacles. In order to investigate…
We investigate the structure and the nonlinear dynamics of two rigid polar rotors coupled through the dipole-dipole interaction in an external homogeneous electric field. In the field-free stable head-tail configuration, an excess energy is…
This paper is devoted to the study of some nonlinear parabolic equations with discontinuous diffusion intensities. Such problems appear naturally in physical and biological models. Our analysis is based on variational techniques and in…
We consider a beam and a wave equations coupled on an elastic beam through transmission conditions. The damping which is locally distributed acts through one of the two equations only; its effect is transmitted to the other equation through…
Fully describing light propagation in a rotating, anisotropic medium with thermal nonlinearity requires modeling the interplay between nonlinear refraction, birefringence, and the nonlinear group index. Incorporating these factors into a…
We shall deal with the periodic problem for nonlinear perturbations of abstract hyperbolic evolution equations generating an evolution system of contractions. We prove an averaging principle for the translation along trajectories operator…
This paper is concerned with the theory of generic non-normal nonlinear evolutionary equations, with potential applications in Fluid Dynamics and Optics. Two theoretical models are presented. The first is a model two-level non-normal…
Nonlinear evolution of one-dimensional planar perturbations in an optically thin radiatively cooling medium in the long-wavelength limit is studied numerically. The accepted cooling function generates in thermal equilibrium a bistable…
The stability of the one-mode nonlinear solutions of the Fermi-Pasta-Ulam - $\beta$ system is numerically investigated. No external perturbation is considered for the one-mode exact analytical solutions, the only perturbation being that…
We demonstrate two periodic or quasi-periodic generalizations of the Chaplygin gas (CG) type models to explain the origins of dark energy as well as dark matter by using the Weierstrass $\wp(t)$, $\sigma(t)$ and $\zeta(t)$ functions with…
A finite (periodic) FPU chain is chosen as a convenient point for investigating the energy exchange phenomenon in nonlinear oscillatory systems. As we have recently shown, this phenomenon may occur as a consequence of the resonant…
While ubiquitous, energy redistribution remains a poorly understood facet of the nonequilibrium thermodynamics of biomolecules. At the molecular level, finite-size effects, pronounced nonlinearities, and ballistic processes produce behavior…
In this paper we investigate, through numerical studies, the dynamical evolutions encoded in a linear one-dimensional nonlocal equation arising in peridynamcs. The different propagation regimes ranging from the hyperbolic to the dispersive,…
The dynamics of transitional flows are governed by an interplay between the non-normal linear dynamics and quadratic nonlinearity in the incompressible Navier-Stokes equations. In this work, we propose a framework for nonlinear stability…
In recent years, Winter's nonlinear model has been adopted in theoretical physics as the prototype for the study of quantum resonances and the dynamics of observables in the context of nonlinear Schr\"odinger equations. However, its…
The numerical solutions of nonlocal and local Boltzmann kinetic equations for the simulation of peripheral and central heavy ion reactions are compared. The experimental finding of enhancement of mid-rapidity matter shows the necessity to…
We consider linear, time-dependent and skew-adjoint perturbations of periodic transport equations on the one-dimensional torus. We describe the long-time behavior of solutions for all non-degenerate perturbations in resonant regime, proving…
The nonlinear interaction, due to quantum electrodynamical (QED) effects, between photons is investigated using a wave-kinetic description. Starting from a coherent wave description, we use the Wigner transform technique to obtain a set of…