Shankar P. Das

Heterogeneities in supercooled liquids: a density-functional study.

A metastable state, characterized by a low degree of mass localization, is identified using density-functional theory (DFT). This free energy minimum, located through the proper evaluation of competing terms in the free energy functional, is independent of the specific form of the DFT used. Computer simulation results on particle motion indicate that this heterogeneous state corresponds to the deeply supercooled state.

Kinetic theory of transport in a hard sphere crystal

The revised Enskog kinetic theory (RET) is used to describe transport in a hard sphere crystal. The connection between the RET and the exact density functional theory (DFT) description of the solid state is established. The RET is used to derive the dissipative linear equations of elasticity. The elastic moduli in these equations are identical to those obtained from equilibrium like DFT. The expressions for the solid state transport coefficients (determining sound absorption and heat conduction in the hard sphere crystal) are new. As for the analogous calculation in the liquid state, the transport coefficients are determined by the (solid state) equilibrium two‐particle distribution function at contact.

Nature of the entropy versus self-diffusivity plot for simple liquids

The empirical relation (D(*))(alpha) = a exp[S] between the self-diffusion coefficient D(*) and the excess entropy S of a liquid is studied here in the context of theoretical model calculation. The coefficient alpha is dependent on the interaction potential and shows a crossover at an intermediate density, where cooperative dynamics become more important. Around this density a departure from the Stokes-Einstein relation is also observed. The above relation between entropy and diffusion is also tested for the scaled total diffusion coefficient in a binary mixture.

Thermal cellular automata fluids

The concepts of local temperature and local thermal equilibrium are introduced in the context of lattice gas cellular automata (LGGAs) whose dynamics conserves energy. Green-Kubo expressions for thermal transport coefficients, in particular for the heat conductivity, are derived in a form, equivalent to those for continuous fluids. All thermal transport coefficients are evaluated in Boltzmann approximation as thermal averages of matrix elements of the inverse Boltzmann collision operator, fully analogous to the results for continuous systems, and fully model-independent. The collision operator is expressed in terms of transition probabilities between in- and out-states. Staggered diffusivities arising from spuriously conserved quantities in LGCAs are also calculated. Examples of models with either cubic or hexagonal symmetries are discussed, where particles may or may not have internal energies.

Model for glass transition in a binary fluid from a mode coupling approach.

We consider the mode coupling theory (MCT) of glass transition for a binary fluid. The equations of nonlinear fluctuating hydrodynamics for the compressible fluid are obtained with a proper choice of slow variables which correspond to the conservation laws in the system. The resulting model equations are used to obtain a coupled set of nonlinear integro-differential equations for the various correlations of partial density fluctuations. These equations are then solved self consistently in the long-time limit to locate the dynamic transition in the system. The transition point from our model is at considerably higher density than predicted in the other existing MCT models for binary systems.

Fragility and Boson peak formation in a supercooled liquid

Abstract 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.

Fluctuating nonlinear hydrodynamics does not support an ergodic-nonergodic transition.

Despite its appeal, real and simulated glass forming systems do not undergo an ergodic-nonergodic (ENE) transition. We reconsider whether the fluctuating nonlinear hydrodynamics (FNH) model for this system, introduced by us in 1986, supports an ENE transition. Using nonperturbative arguments, with no reference to the hydrodynamic regime, we show that the FNH model does not support an ENE transition. Our results support the findings in the original paper. Assertions in the literature questioning the validity of the original work are shown to be in error.

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

Exact equations of motion for the microscopically defined collective density ρ(x,t) and the momentum density ĝ(x,t) of a fluid have been obtained in the past starting 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 Deans 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 with noise. Our analysis demonstrates that on thermal averaging the dependence of the exact equations on the bare interaction potential is converted to dependence on the corresponding thermodynamic direct correlation functions in the coarse-grained equations.

Dynamic Transition in a Binary Liquid and Its Dependence on the Mass-Ratio: Results from a Self Consistent Mode Coupling Model

We use the self-consistent mode coupling model for binary mixtures to investigate the influence of the mass-ratio (m2/m1) of constituent particles, where subscripts 1 and 2, respectively, denote the smaller and bigger size particles, on the dynamic transition. For the higher values of the ratio, m2/m1≥2, we find that there is no significant change in the transition point. This is in qualitative agreement with the simulation studies on the binary mixtures. However, for the case of bigger particle mass, m2, being much smaller than that of the smaller particle mass, m1, a significant change in the transition point is observed. The dependence of the non-ergodicity parameters on the mass-ratio is also predicted for different wave numbers. We also estimate the range in the vicinity of the dynamic transition point where the square root cusp behavior of the non-ergodicity parameter (NEP) dominates.

Scaling behavior near glass instability in mode‐coupling model for dense fluids

The scaling relations close to the ideal glass transition point in a self‐consistent mode coupling model with realistic structural properties are studied. The behavior of the long time limit of the density autocorrelation function or the nonergodicity parameter over a reasonable density range around the transition point follows a scaling relation with an exponent that is q dependent. Next the solution of the model equations for decay of density correlation over the so‐called β‐relaxation regime is studied. The results for different wave vectors indicate a substantial q dependence in the exponents of the power law relaxations.