Simulation of continuous-time random walks with anharmonicity

Anomalous diffusion processes are best described and analyzed by a continuous-time random walk (CTRW) formalism. The latter is a generalization of a transport model using random walk processes that are not limited to Markovian systems. Using a robust numerical generation of continuous trajectories based on Langevin equations, sample paths from a CTRW system encountering a nonlinear net force were generated and analyzed. The resultant force comprised of a linear repelling term and an anharmonic term, that is, f(x) = -k₁ x + k₂ x³.