Bernd Rinn

Phase separation in confined geometries: Solving the Cahn-Hilliard equation with generic boundary conditions

Abstract We apply implicit numerical methods to solve the Cahn–Hilliard equation for confined systems. Generic boundary conditions for hard walls are considered, as they are derived from physical principles. Based on a detailed stability analysis an automatic time step control could be implemented, which makes it possible to explore the demixing kinetics of two thermodynamically stable phases over many orders in time with good space resolution. The power of the method is demonstrated by investigating spinodal decomposition in two-dimensional systems. At early times of the decomposition process the numerical results are in excellent agreement with analytical predictions based on the linearized equations. Due to the efficiency of the variable time step procedure it is possible to monitor the process until a stable equilibrium is reached.

Equilibrium and non-equilibrium dynamics in random-energy landscapes

Abstract Thermally activated transport in rugged energy landscapes is discussed with respect to dispersive transport properties and non-equilibrium ageing phenomena. The disperse transport features are treated by a particular effective-medium approximation that allows one to handle asymmetric hopping rates. This approximation is shown to provide a good account for the approximate scaling properties of conductivity spectra observed in ionic glasses. For the ageing phenomena we find that the characteristic correlation times can depend on the waiting time in various ways, including normal ageing and subageing behaviour, as well as other laws. The possible occurrence of multiple-scaling regimes is demonstrated explicitly.

Hopping dynamics in random energy landscapes: An effective medium approach

An effective medium approximation is given for single-particle hopping in lattices with site energy disorder. Based on this approximation the frequency dependent diffusion coefficient is calculated for a uniform distribution of site energies and the results compared with Monte Carlo simulations. Although the approximation gives a fairly good account of the overall frequency dependence, generally it fails to reproduce the correct zero-frequency limit of the diffusion coefficient. This failure may be resolved by a proper rescaling of the temperature in the effective medium. Possible extensions of the theory are pointed out.