TY  - JOUR
A1  - Granado, Felipe Le Vot
A1  - Abad, Enrique
A1  - Metzler, Ralf
A1  - Yuste, Santos B.
T1  - Continuous time random walk in a velocity field
BT  - role of domain growth, Galilei-invariant advection-diffusion, and kinetics of particle mixing
JF  - New Journal of Physics
N2  - We consider the emerging dynamics of a separable continuous time random walk (CTRW) in the case when the random walker is biased by a velocity field in a uniformly growing domain. Concrete examples for such domains include growing biological cells or lipid vesicles, biofilms and tissues, but also macroscopic systems such as expanding aquifers during rainy periods, or the expanding Universe. The CTRW in this study can be subdiffusive, normal diffusive or superdiffusive, including the particular case of a Lévy flight. We first consider the case when the velocity field is absent. In the subdiffusive case, we reveal an interesting time dependence of the kurtosis of the particle probability density function. In particular, for a suitable parameter choice, we find that the propagator, which is fat tailed at short times, may cross over to a Gaussian-like propagator. We subsequently incorporate the effect of the velocity field and derive a bi-fractional diffusion-advection equation encoding the time evolution of the particle distribution. We apply this equation to study the mixing kinetics of two diffusing pulses, whose peaks move towards each other under the action of velocity fields acting in opposite directions. This deterministic motion of the peaks, together with the diffusive spreading of each pulse, tends to increase particle mixing, thereby counteracting the peak separation induced by the domain growth. As a result of this competition, different regimes of mixing arise. In the case of Lévy flights, apart from the non-mixing regime, one has two different mixing regimes in the long-time limit, depending on the exact parameter choice: in one of these regimes, mixing is mainly driven by diffusive spreading, while in the other mixing is controlled by the velocity fields acting on each pulse. Possible implications for encounter–controlled reactions in real systems are discussed.
KW  - diffusion
KW  - expanding medium
KW  - continuous time random walk
Y1  - 2020
U6  - https://doi.org/10.1088/1367-2630/ab9ae2
SN  - 1367-2630
VL  - 22
PB  - Dt. Physikalische Ges.
CY  - Bad Honnef
ER  - 
TY  - GEN
A1  - Granado, Felipe Le Vot
A1  - Abad, Enrique
A1  - Metzler, Ralf
A1  - Yuste, Santos B.
T1  - Continuous time random walk in a velocity field
BT  - role of domain growth, Galilei-invariant advection-diffusion, and kinetics of particle mixing
T2  - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - We consider the emerging dynamics of a separable continuous time random walk (CTRW) in the case when the random walker is biased by a velocity field in a uniformly growing domain. Concrete examples for such domains include growing biological cells or lipid vesicles, biofilms and tissues, but also macroscopic systems such as expanding aquifers during rainy periods, or the expanding Universe. The CTRW in this study can be subdiffusive, normal diffusive or superdiffusive, including the particular case of a Lévy flight. We first consider the case when the velocity field is absent. In the subdiffusive case, we reveal an interesting time dependence of the kurtosis of the particle probability density function. In particular, for a suitable parameter choice, we find that the propagator, which is fat tailed at short times, may cross over to a Gaussian-like propagator. We subsequently incorporate the effect of the velocity field and derive a bi-fractional diffusion-advection equation encoding the time evolution of the particle distribution. We apply this equation to study the mixing kinetics of two diffusing pulses, whose peaks move towards each other under the action of velocity fields acting in opposite directions. This deterministic motion of the peaks, together with the diffusive spreading of each pulse, tends to increase particle mixing, thereby counteracting the peak separation induced by the domain growth. As a result of this competition, different regimes of mixing arise. In the case of Lévy flights, apart from the non-mixing regime, one has two different mixing regimes in the long-time limit, depending on the exact parameter choice: in one of these regimes, mixing is mainly driven by diffusive spreading, while in the other mixing is controlled by the velocity fields acting on each pulse. Possible implications for encounter–controlled reactions in real systems are discussed.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1005 
KW  - diffusion
KW  - expanding medium
KW  - continuous time random walk
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-479997
SN  - 1866-8372
IS  - 1005
SP  - 28
ER  -