Lévy walks
Random walk is a fundamental concept with applications ranging from quantum physics to
econometrics. Remarkably, one specific model of random walks appears to be ubiquitous …
econometrics. Remarkably, one specific model of random walks appears to be ubiquitous …
Anomalous diffusion models and their properties: non-stationarity, non-ergodicity, and ageing at the centenary of single particle tracking
Modern microscopic techniques following the stochastic motion of labelled tracer particles
have uncovered significant deviations from the laws of Brownian motion in a variety of …
have uncovered significant deviations from the laws of Brownian motion in a variety of …
The continuous time random walk, still trendy: fifty-year history, state of art and outlook
In this article we demonstrate the very inspiring role of the continuous-time random walk
(CTRW) formalism, the numerous modifications permitted by its flexibility, its various …
(CTRW) formalism, the numerous modifications permitted by its flexibility, its various …
Unravelling the origins of anomalous diffusion: from molecules to migrating storks
Anomalous diffusion or, more generally, anomalous transport, with nonlinear dependence of
the mean-squared displacement on the measurement time, is ubiquitous in nature. It has …
the mean-squared displacement on the measurement time, is ubiquitous in nature. It has …
Single-big-jump principle in physical modeling
The big-jump principle is a well-established mathematical result for sums of independent
and identically distributed random variables extracted from a fat-tailed distribution. It states …
and identically distributed random variables extracted from a fat-tailed distribution. It states …
Diffusion and Fokker-Planck-Smoluchowski equations with generalized memory kernel
We consider anomalous stochastic processes based on the renewal continuous time
random walk model with different forms for the probability density of waiting times between …
random walk model with different forms for the probability density of waiting times between …
[BOOK][B] Modeling anomalous diffusion: from statistics to mathematics
Let us now consider the Fokker-Planck equation, which is a partial differential equation that
describes the time evolution of the PDF of the positions of particles, and was introduced in …
describes the time evolution of the PDF of the positions of particles, and was introduced in …
Transient anomalous diffusion in periodic systems: ergodicity, symmetry breaking and velocity relaxation
We study far from equilibrium transport of a periodically driven inertial Brownian particle
moving in a periodic potential. As detected for a SQUID ratchet dynamics, the mean square …
moving in a periodic potential. As detected for a SQUID ratchet dynamics, the mean square …
Adaptive finite element method for fractional differential equations using hierarchical matrices
A robust and fast solver for the fractional differential equation (FDEs) involving the Riesz
fractional derivative is developed using an adaptive finite element method. It is based on the …
fractional derivative is developed using an adaptive finite element method. It is based on the …
Physics-informed neural network algorithm for solving forward and inverse problems of variable-order space-fractional advection–diffusion equations
S Wang, H Zhang, X Jiang - Neurocomputing, 2023 - Elsevier
A new physics-informed neural network (PINN) algorithm is proposed to solve variable-order
space-fractional partial differential equations (PDEs). For the forward problem, PINN …
space-fractional partial differential equations (PDEs). For the forward problem, PINN …