Fractional Fokker-Planck dynamics: Numerical algorithm and simulations
arXiv:cond-mat/0603516 · doi:10.1103/PhysRevE.73.046133
Abstract
Anomalous transport in a tilted periodic potential is investigated numerically within the framework of the fractional Fokker-Planck dynamics via the underlying CTRW. An efficient numerical algorithm is developed which is applicable for an arbitrary potential. This algorithm is then applied to investigate the fractional current and the corresponding nonlinear mobility in different washboard potentials. Normal and fractional diffusion are compared through their time evolution of the probability density in state space. Moreover, we discuss the stationary probability density of the fractional current values.
10 pages, 9 figures
References in corpus (5)
Cited by in corpus (35)
- Single particle tracking in systems showing anomalous diffusion: the role of weak ergodicity breaking
- Relativistic Brownian Motion
- Viscoelastic subdiffusion: from anomalous to normal
- Biased diffusion in confined media: Test of the Fick-Jacobs approximation and validity criteria
- Monte Carlo simulation of uncoupled continuous-time random walks yielding a stochastic solution of the space-time fractional diffusion equation
- Distribution of Time-Averaged Observables for Weak Ergodicity Breaking
- Use and Abuse of a Fractional Fokker-Planck Dynamics for Time-Dependent Driving
- Weakly non-ergodic Statistical Physics
- Continuous Time Random Walks (CTRWs): Simulation of continuous trajectories
- A fractional Feynman-Kac equation for weak ergodicity breaking
- Full characterization of the fractional Poisson process
- Weak ergodicity breaking in an anomalous diffusion process of mixed origins
- Exceptional Laguerre and Jacobi polynomials and the corresponding potentials through Darboux-Crum Transformations
- Continuous-time random-walk model for anomalous diffusion in expanding media
- Universal fluctuations in subdiffusive transport
- Fluctuation-driven directed transport in the presence of Levy flights
- Subdiffusive Brownian ratchets rocked by a periodic force
- Subordinated diffusion and CTRW asymptotics
- Viscoelastic subdiffusion in a random Gaussian environment
- Weak subordination breaking for the quenched trap model
- Fractional Fokker-Planck subdiffusion in alternating fields
- Persistent random walk of cells involving anomalous effects and random death
- Two-time scale subordination in physical processes with long-term memory
- Flashing subdiffusive ratchets in viscoelastic media
- Rocking Subdiffusive Ratchets: Origin, Optimization and Efficiency
- State transition of a non-Ohmic damping system in a corrugated plane
- Transport in periodic potentials induced by fractional Gaussian noise
- Fractional diffusion in periodic potentials
- Directed transport driven by Lévy flights coexisting with subdiffusion
- Numerical algorithm for the space-time fractional Fokker-Planck system with two internal states
- Escape from the potential well: competition between long jumps and long waiting times
- Quantum breaking of ergodicity in semi-classical charge transfer dynamics
- Competition between ac driving-forces and Lévy flights in a nonthermal ratchet
- Variational principle for fractional kinetics and the Lévy Ansatz
- Numerical scheme for the Fokker-Planck equations describing anomalous diffusions with two internal states