Coarse-grained forms for equations describing the microscopic motion of particles in a fluid

Equations of motion for the microscopic number density $\hat{\rho}({\bf x},t)$ and the momentum density $\hat{\bf g}({\bf x},t)$ of a fluid have been obtained in the past from the corresponding Langevin equations representing the dynamics of the fluid particles. In the present work we average these exact equations of microscopic dynamics over the local equilibrium distribution to obtain stochastic partial differential equations for the coarse grained densities with smooth spatial and temporal dependence. In particular, we consider Dean's exact balance equation for the microscopic density of a system of interacting Brownian particles to obtain the basic equation of the dynamic density functional theory. In the thermally averaged equation for the coarse grained density ${\rho}({\bf x},t)$, the related dependence on the bare interaction potential in Dean's equation is converted to that on the corresponding direct correlation functions of the density functional theory.Comment: 10 page

Transport coefficients at Metastable Densities from models of Generalized Hydrodynamics

In the present work we compute the enhancement in the long time transport coefficients due to correlated motion of fluid particles at high density. The fully wave vecor dependent extended mode coupling model is studied with the inclusion of an additional slow variable of the defect density for the amorphous system. We use the extremely slow relaxation of the density correlation function observed in the light scattering experiments on colloids to estimate the input parameters for the model The ratio of long time to short time diffusion coefficient is studied around the the peak of the structure factor.Comment: 17 pages, 8 figure

Temperature dependence of the Power law exponent of relaxation in a supercooled Liquid

The dynamics of Lennard-Jones fluid is studied through extended mode coupling theory (MCT) with the inclusion of the slow mode of defect density. Inclusion of defect density facilitates the liquid like state for temperatures much lower than predicted from ideal MCT. From the present model the temperature dependence of the power law exponent is obtained at a {\em constant pressure}. We have also computed the wave number dependence of the power law exponent.Comment: 10 pages, 6 figure

The contact angle in inviscid fluid mechanics

We show that in general, the specification of a contact angle condition at the contact line in inviscid fluid motions is incompatible with the classical field equations and boundary conditions generally applicable to them. The limited conditions under which such a specification is permissible are derived; however, these include cases where the static meniscus is not flat. In view of this situation, the status of the many `solutions' in the literature which prescribe a contact angle in potential flows comes into question. We suggest that these solutions which attempt to incorporate a phenomenological, but incompatible, condition are in some, imprecise sense `weak-type solutions'; they satisfy or are likely to satisfy, at least in the limit, the governing equations and boundary conditions everywhere except in the neighbourhood of the contact line. We discuss the implications of the result for the analysis of inviscid flows with free surfaces.Comment: 13 pages, no figures, no table

Fragility and Boson Peak formation in a Supercooled Liquid

We analyze results for the Boson Peak from the neutron time of flight spectroscopy data on Ge-As-Se, and Raman spectra data on m-TCP and OTP, using a recent mode coupling model that takes into account the coupling of density fluctuations with vibrational modes in presence of defects in the supercooled state. From the experimental results for different materials we observe that for more fragile systems characterized by increasing fragility parameter m, a slower relaxation of the defect-density correlation is needed to give rise to the observed peak in the spectra.Comment: 6 pages, 5 figure