The motion of self-propelled particles is modeled as a persistent random walk. An analytical framework is developed that allows the derivation of exact expressions for the time evolution of arbitrary moments of the persistent walks displacement. It i
s shown that the interplay of step length and turning angle distributions and self-propulsion produces various signs of anomalous diffusion at short time scales and asymptotically a normal diffusion behavior with a broad range of diffusion coefficients. The crossover from the anomalous short time behavior to the asymptotic diffusion regime is studied and the parameter dependencies of the crossover time are discussed. Higher moments of the displacement distribution are calculated and analytical expressions for the time evolution of the skewness and the kurtosis of the distribution are presented.
A fully parallel version of the contact dynamics (CD) method is presented in this paper. For large enough systems, 100% efficiency has been demonstrated for up to 256 processors using a hierarchical domain decomposition with dynamic load balancing. T
he iterative scheme to calculate the contact forces is left domain-wise sequential, with data exchange after each iteration step, which ensures its stability. The number of additional iterations required for convergence by the partially parallel updates at the domain boundaries becomes negligible with increasing number of particles, which allows for an effective parallelization. Compared to the sequential implementation, we found no influence of the parallelization on simulation results.
