Related papers: Gaussian density fluctuations and Mode Coupling Th…
We consider a general class of nonlinear diffusive models with bulk dissipation and boundary driving, and derive its hydrodynamic description in the large size limit. Both the average macroscopic behavior and the fluctuating properties of…
A high order morphing continuum theory (MCT) is introduced to model highly compressible turbulence. The theory is formulated under the rigorous framework of rational continuum mechanics. A set of linear constitutive equations and balance…
In this set of lecture notes we review the mode-coupling theory of the glass transition from several perspectives. First, we derive mode-coupling equations for the description of density fluctuations from microscopic considerations with the…
The equations of fluid motions are considered in the case of internal energy depending on mass density, volume entropy and their spatial derivatives. The model corresponds to domains with large density gradients in which the temperature is…
We derive a mode-coupling theory for the slow dynamics of fluids confined in disordered porous media represented by spherical particles randomly placed in space. Its equations display the usual nonlinear structure met in this theoretical…
Motivated by a number of recent experimental and computational studies of the dynamics of fluids plunged in quenched-disordered external fields, we report on a theoretical investigation of this topic within the framework of the…
We discuss the density fluctuations of a fluid due to zero point motion. These can be regarded as density fluctuations in the phonon vacuum state. We assume a linear dispersion relation with a fixed speed of sound and calculate the density…
Using the initial-value formulation, a dynamic theory for systems evolving according to a Generalized Langevin Equation is developed, providing more restrictive conditions on the existence of equilibrium behavior and its…
The predictions of the mode-coupling theory of the glass transition (MCT) for the tagged-particle density-correlation functions and the mean-squared displacement curves are compared quantitatively and in detail to results from Newtonian-…
We investigated the validity of fluctuation-dissipation relations in the nonequilibrium stationary state of fluidized granular media under gravity by two independent approaches, based on theory and numerical simulations. A phenomenological…
The mode-coupling theory of the glass transition treats the dynamics of supercooled liquids in terms of two-point density correlation functions. Here we consider a generalized, hierarchical formulation of schematic mode-coupling equations…
We consider the Mode Coupling Theory (MCT) of Glass transition for a Binary fluid. The Equations of Nonlinear Fluctuating Hydrodynamics are obtained with a proper choice of the slow variables corresponding to the conservation laws. The…
We study the dynamics of a one-component liquid constrained on a spherical substrate, a 2-sphere, and investigate how the mode-coupling theory (MCT) can describe the new features brought by the presence of curvature. To this end we have…
The driving force of the dynamical system can be decomposed into the gradient of a potential landscape and curl flux (current). The fluctuation-dissipation theorem (FDT) is often applied to near equilibrium systems with detailed balance.…
We address the dynamics of damped collective modes in terms of first and second moments. The modes are introduced in a self-consistent fashion with the help of a suitable application of linear response theory. Quantum effects in the…
Dynamical random walk of classical particle in thermodynamically equilibrium fluctuating medium, - Gaussian random potential field, - is considered in the framework of explicit stochastic representation of deterministic interactions. We…
We give a brief introduction to the mode-coupling theory of the glass transition, a theory which was proposed a while ago to describe the dynamics of supercooled liquids. After presenting the basic equations of the theory, we review some of…
Mean-field theories of the glass transition predict a phase transition to a dynamically arrested state, yet no such transition is observed in experiments or simulations of finite-dimensional systems. We resolve this long-standing…
A molecular dynamics simulation is performed for a supercooled liquid of rigid diatomic molecules. The time-dependent self and collective density correlators of the molecular centers of mass are determined and compared with the predictions…
We present a detailed derivation of a microscopic theory for the glass transition of a liquid enclosed between two parallel walls relying on a mode-coupling approximation. This geometry lacks translational invariance perpendicular to the…