Gene F. Mazenko

Diffusive motion in a model for particle hopping

Abstract The diffusive motion of adsorbates on crystal planes is studied by means of a lattice gas model with stochastic dynamics, in the disordered phase and at half coverage. The diffusion coefficient and the time-correlation functions measured in field-emission experiments are calculated. These correlation functions are shown to have the proper hydrodynamic power law decay at long times. It is pointed out that if experiments are done at times before the onset of the hydrodynamic regime the value of the diffusion coefficient obtained will be too small. Our results show also that correlations among the adsorbed particles persist for times longer than predicted by a hydrodynamical approximation.

Defect structures in the growth kinetics of the Swift-Hohenberg model.

The growth of striped order resulting from a quench of the two-dimensional Swift-Hohenberg model is studied in the regime of a small control parameter and quenches to zero temperature. We introduce an algorithm for finding and identifying the disordering defects (dislocations, disclinations, and grain boundaries) at a given time. We can track their trajectories separately. We find that the coarsening of the defects and lowering of the effective free energy in the system are governed by a growth law L(t) approximately t(x) with an exponent x near 1/3. We obtain scaling for the correlations of the nematic order parameter with the same growth law. The scaling for the order parameter structure factor is governed, as found by others, by a growth law with an exponent smaller than x and near to 1/4. By comparing two systems with different sizes, we clarify the finite-size effect. We find that the system has a very low density of disclinations compared to that for dislocations and fraction of points in grain boundaries. We also measure the speed distributions of the defects at different times and find that they all have power-law tails and the average speed decreases as a power law.

Metastable dynamics above the glass transition

The element of metastability is incorporated in the fluctuating nonlinear hydrodynamic description of the mode coupling theory (MCT) of the liquid-glass transition. This is achieved through the introduction of the defect density variable

Nonlinear hydrodynamical approach to granular materials.

n

Fundamental theory of statistical particle dynamics.

into the set of slow variables with the mass density

Response functions in phase-ordering kinetics

\rho

Equations of fluctuating nonlinear hydrodynamics for normal fluids

and the momentum density

Smoluchowski dynamics and the ergodic-nonergodic transition.

{\bf g}

Granular clustering in a hydrodynamic simulation.

. As a first approximation, we consider the case where motions associated with

Density nonlinearities and a field theory for the dynamics of simple fluids

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