We discuss the general link between mode-coupling like equations (which serve as the basis of some recent theories of supercooled liquids) and the dynamical equations governing mean-field spin-glass models, or the dynamics of a particle in a random potential. The physical consequences of this interrelation are underlined. It suggests to extend the mode-coupling approximation to temperatures wel...

In this paper we analyze molecular dynamics simulation results on supercooled water in a MCM-41 pore in order to test the mode coupling theory. A layer analysis must be performed for water in the pore in order to exclude the contribution of water bound to the strongly hydrophilic surface. Upon supercooling a range of temperatures is reached where the liquid follows the mode coupling theory. Fro...

We analyze the glassy dynamics of binary mixtures of hard disks in two dimensions. Predictions of the mode-coupling theory (MCT) are tested with extensive Brownian dynamics simulations. Measuring the collective particle density correlation functions in the vicinity of the glass transition, we verify four predicted mixing effects. For instance, for large size disparities, adding a small amount o...

– We consider a toy model for glassy dynamics of colloidal suspensions: a single Brownian particle diffusing among immobile obstacles. If Gaussian factorization of static density fluctuations is assumed, this model can be solved without factorization approximation for any dynamic correlation function. The solution differs from that obtained from the ideal mode coupling theory (MCT). The latter ...

Studies reported in the last Quarterly Progress Report (1) have been modified and extended. The purpose of these studies is to find a formal basis and justification for Pierce's coupling-of-modes formalism (2) as it applies to uniform slowwave structures containing two or more subsystems that individually propagate slow waves (e.g., traveling-wave tubes). If it can be assumed that the coupling ...

We write equations of motion for density variables that are equivalent to Newtons equations. We then propose a set of trial equations parameterised by two unknown functions to describe the exact equations. These are chosen to best fit the exact Newtonian equations. Following established ideas, we choose to separate these trial functions into a set representing integrable motions of density wave...

A method is provided to compute the exponent parameter λ yielding the dynamic exponents of critical slowing down in mode coupling theory. It is independent from the dynamic approach and based on the formulation of an effective static field theory. Expressions of λ in terms of third order coefficients of the action expansion or, equivalently, in terms of six point cumulants are provided. Applica...

We examine the problem of damage spreading in the off-equilibrium mode coupling equations. This study is conducted for the spherical p-spin model introduced by Crisanti, Horner and Sommers. For p > 2 we show the existence of a temperature transition T0 well above any relevant thermodynamic transition temperature. Above T0 the asymptotic damage decays to zero while below T0 it decays to a finite...

Finite difference equations are given for second-harmonic generation in two-dimensional planar structures for coupling between TE polarizations at two frequencies as well as for TM polarizations at two frequencies, including the effect of birefringence in the latter case. Attention is given to obtaining accurate expressions for the finite difference operators for points close to interfaces, and...

The only available quantitative description of the slowing down of the dynamics upon approaching the glass transition has been, so far, the mode-coupling theory, developed in the 1980s by Götze and collaborators. The standard derivation of this theory does not result from a systematic expansion. We present a field-theoretic formulation that arrives at very similar mode-coupling equation but whi...