D. Stauffer

Crossover in the Cont–Bouchaud percolation model for market fluctuations

Monte Carlo simulations of the Cont–Bouchaud herding model for stock market traders show power-law distributions for short times and exponential truncation for longer time intervals, if they are made at the percolation threshold in two to seven dimensions.

Non-equilibrium and irreversible simulation of competition among languages

The bit-string model of Schulze and Stauffer [Int. J. Mod. Phys. C 16 (2005) 781] is applied to non-equilibrium situations and then gives better agreement with the empirical distribution of language sizes. Here the size is the number of people having this language as mother tongue. In contrast, when equilibrium is combined with irreversible mutations of languages, one language always dominates and is spoken by at least 80% of the population.

Theory of Strain Percolation in Metals: Mean Field and Strong Boundary Universality Class

For the percolation model of strain in a deforming metal proposed earlier, we develop sum rule and mean field approximations which predict a critical point. The numerical work is restricted to the simpler of two cases proposed in the earlier work, in which the cell walls are “strong”, and unzipping of the dislocation entities which lock the walls into the lattice is not permitted. For this case, we find that strain percolation is a new form of correlated percolation, but that it is in the same universality class as standard percolation.

New simulations on old biased diffusion

Recent progress with Sornette, Dhar and Kirsch is reviewed on the old question of how diffusing particles in a fixed external field travel through a random medium (biased ants in a labyrinth). Simulations show log-periodic oscillations in time for strong bias and suggest a phase transition between drift and no drift for intermediate bias. Similar results are known for “topological” bias.

Dynamics of Swendsen-Wang clusters in 2D Ising model

Droplets are found by Monte Carlo simulation at the Curie point to relax towards their equilibrium size distribution with a relaxation time varying roughly logarithmically with cluster size.

Simulation of gelation for gelatin in microemulsions

The Widom microemulsion model is combined with a bond percolation approximation to describe gelatin dissolved in water nanodroplets. Besides the normal oil-water phase separation, we simulate a percolation line for electrical transport and a gelation line for crosslinking of nanodroplets.

Monte Carlo simulation of thin Ising films

Plates of LL × L × W and L × W Ising lattices with W ⪡ L are simulated by Monte Carlo, with up to 108 spins, using free or random boundary conditions below the Curie temperature Tc. The results indicate an extrapolation length diverging at Tc in three dimensions, and long-lived metastable ferromagnetism in two dimensions.

Geometry and dynamics of randomly connected fractal clusters

The dynamics of critical Ising droplets and suitable other clusters is argued to come from growth and decay in small steps, not via aggregation of large clusters. The resulting critical exponent z for Metropolis-Glauber kinetics is related to the exponent for the chain lengths of the cluster branches. Simulations of 609602 and 14093 Ising models confirm roughly the exponent z but throw doubts on the small-step approach when interpreted with the help of the Becker-Doring equation.

Metastability in Monte Carlo simulation of 2D Ising films and in Fe monolayer strips

Effective Curie-temperatures measured in Fe monolayer strips agree reasonably with computer simulations of two-dimensional Ising model strips. The simulations confirm the domain structure seen already by Albano et al. (1989).