Related papers: CTRW Pathways to the Fractional Diffusion Equation
In this paper, we investigate the solutions for a generalized fractional diffusion equation that extends some known diffusion equations by taking a spatial time-dependent diffusion coefficient and an external force into account, which…
The fractional Fokker-Planck equation for subdiffusion in time-dependent force fields is derived from the underlying continuous time random walk. Its limitations are discussed and it is then applied to the study of subdiffusion under the…
Random walk has wide applications in many fields, such as machine learning, biology, physics, and chemistry. Random walk can be discrete or continuous in time and space. Asymmetric random walk could be described by drift-diffusion equation.…
It has been observed in numerous experiments, simulations, and various theoretical treatments that the spreading of particles can be modeled by the continuous-time random walk. We consider two well-known cases, i.e., Gaussian displacements…
We present a physical model to explain the behavior of long-term, time series measurements of chloride, a natural passive tracer, in rainfall and runoff in catchments [Kirchner et al., Nature 403(524), 2000]. A spectral analysis of the data…
We consider a one-dimensional continuous time random walk (CTRW) on a fixed time interval $T$ where at each time step the walker waits a random time $\tau$, before performing a jump drawn from a symmetric continuous probability distribution…
Fractional diffusion equations replace the integer-order derivatives in space and time by their fractional-order analogues. They are used in physics to model anomalous diffusion. This paper develops strong solutions of space-time fractional…
Many important transport phenomena are described by simple mathematical models rooted in the diffusion equation. Geometrical constraints present in such phenomena often have influence of a universal sort and manifest themselves in scaling…
Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a…
We study a symmetric random walk (RW) in one spatial dimension in environment, formed by several zones of finite width, where the probability of transition between two neighboring points and corresponding diffusion coefficient are…
Fractional Brownian motion is a Gaussian stochastic process with stationary, long-time correlated increments and is frequently used to model anomalous diffusion processes. We study numerically fractional Brownian motion confined to a finite…
In this paper we are examining diffusion properties of stationary continuous-time Weierstrass walk (CTWW). We are showing it is a multi-phase representation of the L\'evy walk. The hierarchical spatial-temporal coupling, combined with…
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 walk's…
We formulate a compounded random walk that is physically well defined on both finite and infinite domains, and samples space-dependent forces throughout jumps. The governing evolution equation for the walk limits to a space-fractional…
Anomalous diffusion has recently turned out to be almost ubiquitous in transport problems. When the physical properties of the medium where the transport process takes place are stationary and constant at each spatial location, anomalous…
The Continuous-Time Random Walk (CTRW) formalism can be adapted to encompass stochastic processes with memory. In this article we will show how the random combination of two different unbiased CTRWs can give raise to a process with clear…
Daily, are reported systems in nature that present anomalous diffusion phenomena due to irregularities of medium, traps or reactions process. In this scenario, the diffusion with traps or localised--reactions emerge through various…
The behaviour of the solutions of the time-fractional diffusion equation, based on the Caputo derivative, is studied and its dependence on the fractional exponent is analysed. The time-fractional convection-diffusion equation is also solved…
In this paper, we study both the direct and inverse random source problems associated with the multi-term time-fractional diffusion-wave equation driven by a fractional Brownian motion. Regarding the direct problem, the well-posedness is…
Discrete-time quantum walks (DTQWs) in random artificial electric and gravitational fields are studied analytically and numerically. The analytical computations are carried by a new method which allows a direct exact analytical…