TY  - JOUR
A1  - Xu, Pengbo
A1  - Zhou, Tian
A1  - Metzler, Ralf
A1  - Deng, Weihua
T1  - Stochastic harmonic trapping of a Lévy walk
BT  - transport and first-passage dynamics under soft resetting strategies
JF  - New journal of physics : the open-access journal for physics / Deutsche Physikalische Gesellschaft ; IOP, Institute of Physics
N2  - We introduce and study a Lévy walk (LW) model of particle spreading with a finite propagation speed combined with soft resets, stochastically occurring periods in which an harmonic external potential is switched on and forces the particle towards a specific position. Soft resets avoid instantaneous relocation of particles that in certain physical settings may be considered unphysical. Moreover, soft resets do not have a specific resetting point but lead the particle towards a resetting point by a restoring Hookean force. Depending on the exact choice for the LW waiting time density and the probability density of the periods when the harmonic potential is switched on, we demonstrate a rich emerging response behaviour including ballistic motion and superdiffusion. When the confinement periods of the soft-reset events are dominant, we observe a particle localisation with an associated non-equilibrium steady state. In this case the stationary particle probability density function turns out to acquire multimodal states. Our derivations are based on Markov chain ideas and LWs with multiple internal states, an approach that may be useful and flexible for the investigation of other generalised random walks with soft and hard resets. The spreading efficiency of soft-rest LWs is characterised by the first-passage time statistic.
KW  - diffusion
KW  - anomalous diffusion
KW  - stochastic resetting
KW  - Levy walks
Y1  - 2022
U6  - https://doi.org/10.1088/1367-2630/ac5282
SN  - 1367-2630
VL  - 24
IS  - 3
SP  - 1
EP  - 28
PB  - Deutsche Physikalische Gesellschaft
CY  - Bad Honnef
ER  - 
TY  - JOUR
A1  - Grebenkov, Denis S.
A1  - Metzler, Ralf
A1  - Oshanin, Gleb
T1  - Distribution of first-reaction times with target regions on boundaries of shell-like domains
JF  - New Journal of Physics (NJP)
N2  - We study the probability density function (PDF) of the first-reaction times between a diffusive ligand and a membrane-bound, immobile imperfect target region in a restricted 'onion-shell' geometry bounded by two nested membranes of arbitrary shapes. For such a setting, encountered in diverse molecular signal transduction pathways or in the narrow escape problem with additional steric constraints, we derive an exact spectral form of the PDF, as well as present its approximate form calculated by help of the so-called self-consistent approximation. For a particular case when the nested domains are concentric spheres, we get a fully explicit form of the approximated PDF, assess the accuracy of this approximation, and discuss various facets of the obtained distributions. Our results can be straightforwardly applied to describe the PDF of the terminal reaction event in multi-stage signal transduction processes.
KW  - diffusion
KW  - first-passage time
KW  - first-reaction time
KW  - shell-like geometries
KW  - approximate methods
Y1  - 2021
U6  - https://doi.org/10.1088/1367-2630/ac4282
SN  - 1367-2630
VL  - 2021
SP  - 1
EP  - 23
PB  - IOP Publishing
CY  - London
ET  - 23
ER  -