TY  - JOUR
A1  - Xu, Pengbo
A1  - Deng, Weihua
A1  - Sandev, Trifce
T1  - Levy walk with parameter dependent velocity
BT  - hermite polynomial approach and numerical simulation
JF  - Journal of physics : A, Mathematical and theoretical
N2  - To analyze stochastic processes, one often uses integral transform (Fourier and Laplace) methods. However, for the time-space coupled cases, e.g. the Levy walk, sometimes the integral transform method may fail. Here we provide a Hermite polynomial expansion approach, being complementary to the integral transform method, to the Levy walk. Two approaches are compared for some already known results. We also consider the generalized Levy walk with parameter dependent velocity. Namely, we consider the Levy walk with velocity which depends on the walking length or on the duration of each step. Some interesting features of the generalized Levy walk are observed, including the special shapes of the probability density function, the first passage time distributions, and various diffusive behaviors of the mean squared displacement.
KW  - Hermite polynomial expansion
KW  - Levy walk
KW  - anomalous diffusion
KW  - parameter
KW  - dependent velocity
Y1  - 2020
U6  - https://doi.org/10.1088/1751-8121/ab7420
SN  - 1751-8113
SN  - 1751-8121
VL  - 53
IS  - 11
PB  - IOP Publ. Ltd.
CY  - Bristol
ER  - 
TY  - JOUR
A1  - Xu, Pengbo
A1  - Zhou, Tian
A1  - Metzler, Ralf
A1  - Deng, Weihua
T1  - Lévy walk dynamics in an external harmonic potential
JF  - Physical review : E, Statistical, nonlinear, and soft matter physics
N2  - Levy walks (LWs) are spatiotemporally coupled random-walk processes describing superdiffusive heat conduction in solids, propagation of light in disordered optical materials, motion of molecular motors in living cells, or motion of animals, humans, robots, and viruses. We here investigate a key feature of LWs-their response to an external harmonic potential. In this generic setting for confined motion we demonstrate that LWs equilibrate exponentially and may assume a bimodal stationary distribution. We also show that the stationary distribution has a horizontal slope next to a reflecting boundary placed at the origin, in contrast to correlated superdiffusive processes. Our results generalize LWs to confining forces and settle some longstanding puzzles around LWs.
Y1  - 2020
U6  - https://doi.org/10.1103/PhysRevE.101.062127
SN  - 2470-0045
SN  - 2470-0053
SN  - 1550-2376
SN  - 1063-651X
SN  - 1539-3755
VL  - 101
IS  - 6
PB  - American Physical Society
CY  - College Park
ER  -