arXiv subjects

Christophe Josserand

Publications and source records attributed to Christophe Josserand.

60 records · Page 4Linked to original sources

arXiv2004

Stationary shear flows of dense granular materials : a tentative continuum modelling

We propose a simple continuum model to interpret the shearing motion of dense, dry and cohesion-less granular media. Compressibility, dilatancy and Coulomb-like friction are the three basic ingredients. The granular stress is split into a rate-dependent part representing the rebound-less impacts between grains and a rate-independent part associated with long-lived contacts. Because we consider stationary flows only, the grain compaction and the grain velocity are the two main variables. The predicted velocity and compaction profiles are in apparent agreement with the experimental or numerical results concerning free-surface shear flows as well as confined shear flows

cond-mat.mtrl-sci↗

arXiv2004

Wave turbulence and Bose-Einstein condensates

Asymptotic behavior of a class of nonlinear Schrödinger equations are studied. Particular cases of 1D weakly focusing and Bose-Einstein condensates are considered. A statistical approach is presented to describe the stationary probability density of a discretized finite system. Using a maximum entropy argument, the theory predicts that the statistical equilibrium is described by energy equivalued fluctuation modes around the coherent structure minimizing the Hamiltonian of the system. Good quantitative agreement is found with numerical simulations. In particular, the particle number spectral density follows an effective $1/k^2$ law for the asymptotic large time averaged solutions. Transient dynamics from a given initial condition to the statistically steady regime shows rapid oscillation of the condensate.

cond-mat↗

arXiv2001

Non-linear growth of periodic patterns

We study the growth of a periodic pattern in one dimension for a model of spinodal decomposition, the Cahn-Hilliard equation. We particularly focus on the intermediate region, where the non-linearity cannot be negected anymore, and before the coalescence dominates. The dynamics is captured through the standard technique of a solubility condition performed over a particular family of quasi-static solutions. The main result is that the dynamics along this particular class of solutions can be expressed in terms of a simple ordinary differential equation. The density profile of the stationary regime found at the end of the non-linear growth is also well characterized. Numerical simulations correspond satisfactorily to the analytical results through three different methods and asymptotic dynamics are well recovered, even far from the region where the approximations hold.

cond-mat.stat-mech↗

arXiv2000

Memory Effects in Granular Material

We present a combined experimental and theoretical study of memory effects in vibration-induced compaction of granular materials. In particular, the response of the system to an abrupt change in shaking intensity is measured. At short times after the perturbation a granular analog of aging in glasses is observed. Using a simple two-state model, we are able to explain this short-time response. We also discuss the possibility for the system to obey an approximate pseudo-fluctuation-dissipation theorem relationship and relate our work to earlier experimental and theoretical studies of the problem.

cond-mat.mtrl-sci↗

arXiv1999

Self-organization in nonlinear wave turbulence

We present a statistical equilibrium model of self-organization in a class of focusing, nonintegrable nonlinear Schrodinger (NLS) equations. The theory predicts that the asymptotic-time behavior of the NLS system is characterized by the formation and persistence ofa large-scale coherent solitary wave, which minimizes the Hamiltonian given the conserved particle number,coupled with small-scale random fluctuations, or radiation. The fluctuations account for the difference between the conserved value of the Hamiltonian and the Hamiltonian of the coherent state. The predictions of the statistical theory are tested against the results of direct numerical simulations of NLS, and excellent qualitative and quantitative agreement is demonstrated. In addition, a careful inspection of the numerical simulations reveals interesting features of the transitory dynamics leading up to the to the long-time statistical equilibrium state starting from a given initial condition. As time increases, the system investigates smaller and smaller scales, and it appears that at a given intermediate time after the coalescense of the soliton structures has ended, the system is nearly in statistical equilibrium over the modes that it has investigated up to that time.

chao-dyn↗

arXiv1998

Cavitation induced by explosion in a model of ideal fluid

We discuss the problem of an explosion in the cubic-quintic superfluid model, in relation to some experimental observations. We show numerically that an explosion in such a model might induce a cavitation bubble for large enough energy. This gives a consistent view for rebound bubbles in superfluid and we indentify the loss of energy between the successive rebounds as radiated waves. We compute self-similar solution of the explosion for the early stage, when no bubbles have been nucleated. The solution also gives the wave number of the excitations emitted through the shock wave.

cond-mat↗