Langevin picture of anomalous diffusion processes in expanding medium

Abstract

Expanding medium is very common in many different fields, such as biology and cosmology. It brings a nonnegligible influence on particle's diffusion, which is quite different from the effect of an external force field. The dynamic mechanism of particle's motion in expanding medium has only been investigated in the framework of continuous-time random walk. To focus on more diffusion processes and physical observables, we build the Langevin picture of anomalous diffusion in expanding medium, and conduct detailed analyses in the framework of Langevin equation. With the help of a subordinator, both subdiffusion process and superdiffusion process in expanding medium are discussed. We find that the expanding medium with different changing rate (exponential form and power-law form) leads to quite different diffusion phenomena. The particle's intrinsic diffusion behavior also plays an important role. Our detailed theoretical analyses and simulations present a panoramic view of investigating anomalous diffusion in expanding medium under the framework of Langevin equation.

arXiv comment14 pages, 7 figures

References in corpus (46)

• Anomalous transport in the crowded world of biological cells
• Lévy walks
• Random Time-Scale Invariant Diffusion and Transport Coefficients
• Single particle tracking in systems showing anomalous diffusion: the role of weak ergodicity breaking
• Langevin equations for continuous time Lévy flights
• Anomalous diffusion and ergodicity breaking in heterogeneous diffusion processes
• Scaled Brownian motion: a paradoxical process with a time dependent diffusivity for the description of anomalous diffusion
• Inequivalence of time and ensemble averages in ergodic systems: exponential versus power-law relaxation in confinement
• Population splitting, trapping, and non-ergodicity in heterogeneous diffusion processes
• Anomalous diffusion in correlated continuous time random walks
• Anomalous Diffusion of Inertial, Weakly Damped Particles
• Scaled Brownian motion as a mean field model for continuous time random walks
• Joint Probability Distributions for a Class of Non-Markovian Processes
• Time averaged Einstein relation and fluctuating diffusivities for the Lévy walk
• Asymptotic densities of ballistic Lévy walks
• Random time averaged diffusivities for Lévy walks
• Superluminal problem in diffusion of relativistic particles and its phenomenological solution
• Continuous-time random-walk model for anomalous diffusion in expanding media
• On relation between generalized diffusion equations and subordination schemes
• Subordinated Langevin Equations for Anomalous Diffusion in External Potentials - Biasing and Decoupled Forces
• Anomalous processes with general waiting times: functionals and multi-point structure
• A fractional diffusion equation for two-point probability distributions of a continuous-time random walk
• Lévy-walk-like Langevin dynamics
• Diffusion in an expanding medium: Fokker-Planck equation, Green's function and first-passage properties
• Area coverage of radial Levy flights with periodic boundary conditions
• Subdiffusion in an external force field
• Sub-diffusion in External Potential: Anomalous hiding behind Normal
• Tempered fractional Langevin-Brownian motion with inverse $\beta$-stable subordinator
• Scale invariant Green-Kubo relation for time averaged diffusivity
• Feynman-Kac equation for anomalous processes with space- and time-dependent forces
• Continuous time random walks and Fokker-Planck equation in expanding media
• Reaction-diffusion and reaction-subdiffusion equations on arbitrarily evolving domains
• Ergodic property of random diffusivity system with trapping events
• Ergodic property of Langevin systems with superstatistical, uncorrelated or correlated diffusivity
• Langevin formulation of a subdiffusive continuous time random walk in physical time
• Extended Poisson-Kac theory: A unifying framework for stochastic processes with finite propagation velocity
• Continuous Time Random Walk in a velocity field: Role of domain growth, Galilei-invariant advection-diffusion, and kinetics of particle mixing
• Generalised fractional diffusion equations for subdiffusion on arbitrarily growing domains
• Langevin dynamics for Lévy walk with memory
• Langevin picture of Lévy walk in a constant force field
• Lévy-walk-like Langevin dynamics affected by a time-dependent force
• Theory of relaxation dynamics for anomalous diffusion processes in harmonic potential
• Encounter-controlled coalescence and annihilation on a one-dimensional growing domain
• Self-reinforcing directionality generates Lévy walks without the power-law assumption
• Einstein gravity of a diffusing fluid
• Novel anomalous diffusion phenomena of underdamped Langevin equation with random parameters

Cited by in corpus (2)

• Anomalous diffusion of the heavy quarks through the fractional Langevin equation
• Subdiffusion of heavy quark in hot QCD matter by the fractional Langevin equation