Universe Models with a Variable Cosmological "Constant" and a "Big Bounce"

We present a rich class of exact solutions which contains radiation-dominated and matter-dominated models for the early and late universe. They include a variable cosmological ``constant'' which is derived from a higher dimension and manifests itself in spacetime as an energy density for the vacuum. This is in agreement with observational data and is compatible with extensions of general relativity to string and membrane theory. Our solutions are also typified by a non-singular ``big bounce'' (as opposed to a singular big bang), where matter is created as in inflationary cosmology.Comment: 17 pages, 2 figures, AASTEX. To appear in Ap

A Quasi-Spherical Gravitational Wave Solution in Kaluza-Klein Theory

An exact solution of the source-free Kaluza-Klein field equations is presented. It is a 5D generalization of the Robinson-Trautman quasi-spherical gravitational wave with a cosmological constant. The properties of the 5D solution are briefly described.Comment: 10 pages Latex, Revtex, submitted to GR

Stability and Kinetics of Step Motion on Crystal Surfaces

The kinetics of monoatomic steps in diffusion-controlled crystal growth and evaporation processes are investigated analytically using a Green's function approach. Integro-differential equations of motion for the steps are derived; and a systematic linear stability analysis is carried out treating simultaneously perturbations both along and perpendicular to the steps. Morphological fluctuations of steadily moving steps in response to ambient thermodynamic noises are also studied within a general Langevin formalism. Finally, a phase field model is developed to investigate the time-dependent, collective motion of steps. An application of the model to a finite step train recovers a variety of kinetic behaviors such as the bunching and spreading of steps.Comment: 42 pages in Tex, 10 figures (not included), NSF-ITP-93-13

Phase-field modeling droplet dynamics with soluble surfactants

Using lattice Boltzmann approach, a phase-field model is proposed for simulating droplet motion with soluble surfactants. The model can recover the Langmuir and Frumkin adsorption isotherms in equilibrium. From the equilibrium equation of state, we can determine the interfacial tension lowering scale according to the interface surfactant concentration. The model is able to capture short-time and long-time adsorption dynamics of surfactants. We apply the model to examine the effect of soluble surfactants on droplet deformation, breakup and coalescence. The increase of surfactant concentration and attractive lateral interaction can enhance droplet deformation, promote droplet breakup, and inhibit droplet coalescence. We also demonstrate that the Marangoni stresses can reduce the interface mobility and slow down the film drainage process, thus acting as an additional repulsive force to prevent the droplet coalescence