TY - JOUR
A1 - Sposini, Vittoria
A1 - Grebenkov, Denis S
A1 - Metzler, Ralf
A1 - Oshanin, Gleb
A1 - Seno, Flavio
T1 - Universal spectral features of different classes of random-diffusivity processes
JF - New Journal of Physics
N2 - Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments and the displacement probability density function. Here we develop the complementary power spectral description for a broad class of random-diffusivity processes. In our approach we cater for typical single particle tracking data in which a small number of trajectories with finite duration are garnered. Apart from the diffusing-diffusivity model we study a range of previously unconsidered random-diffusivity processes, for which we obtain exact forms of the probability density function. These new processes are different versions of jump processes as well as functionals of Brownian motion. The resulting behaviour subtly depends on the specific model details. Thus, the central part of the probability density function may be Gaussian or non-Gaussian, and the tails may assume Gaussian, exponential, log-normal, or even power-law forms. For all these models we derive analytically the moment-generating function for the single-trajectory power spectral density. We establish the generic 1/f²-scaling of the power spectral density as function of frequency in all cases. Moreover, we establish the probability density for the amplitudes of the random power spectral density of individual trajectories. The latter functions reflect the very specific properties of the different random-diffusivity models considered here. Our exact results are in excellent agreement with extensive numerical simulations.
KW - diffusion
KW - power spectrum
KW - random diffusivity
KW - single trajectories
Y1 - 2020
U6 - https://doi.org/10.1088/1367-2630/ab9200
SN - 1367-2630
VL - 22
IS - 6
PB - Dt. Physikalische Ges.
CY - Bad Honnef
ER -
TY - GEN
A1 - Sposini, Vittoria
A1 - Grebenkov, Denis S
A1 - Metzler, Ralf
A1 - Oshanin, Gleb
A1 - Seno, Flavio
T1 - Universal spectral features of different classes of random-diffusivity processes
T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2 - Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments and the displacement probability density function. Here we develop the complementary power spectral description for a broad class of random-diffusivity processes. In our approach we cater for typical single particle tracking data in which a small number of trajectories with finite duration are garnered. Apart from the diffusing-diffusivity model we study a range of previously unconsidered random-diffusivity processes, for which we obtain exact forms of the probability density function. These new processes are different versions of jump processes as well as functionals of Brownian motion. The resulting behaviour subtly depends on the specific model details. Thus, the central part of the probability density function may be Gaussian or non-Gaussian, and the tails may assume Gaussian, exponential, log-normal, or even power-law forms. For all these models we derive analytically the moment-generating function for the single-trajectory power spectral density. We establish the generic 1/f²-scaling of the power spectral density as function of frequency in all cases. Moreover, we establish the probability density for the amplitudes of the random power spectral density of individual trajectories. The latter functions reflect the very specific properties of the different random-diffusivity models considered here. Our exact results are in excellent agreement with extensive numerical simulations.
T3 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 999
KW - diffusion
KW - power spectrum
KW - random diffusivity
KW - single trajectories
Y1 - 2020
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-476960
SN - 1866-8372
IS - 999
ER -
TY - JOUR
A1 - Grebenkov, Denis S
A1 - Metzler, Ralf
A1 - Oshanin, Gleb
T1 - From single-particle stochastic kinetics to macroscopic reaction rates
BT - fastest first-passage time of N random walkers
JF - New Journal of Physics
N2 - We consider the first-passage problem for N identical independent particles that are initially released uniformly in a finite domain Ω and then diffuse toward a reactive area Γ, which can be part of the outer boundary of Ω or a reaction centre in the interior of Ω. For both cases of perfect and partial reactions, we obtain the explicit formulas for the first two moments of the fastest first-passage time (fFPT), i.e., the time when the first out of the N particles reacts with Γ. Moreover, we investigate the full probability density of the fFPT. We discuss a significant role of the initial condition in the scaling of the average fFPT with the particle number N, namely, a much stronger dependence (1/N and 1/N² for partially and perfectly reactive targets, respectively), in contrast to the well known inverse-logarithmic behaviour found when all particles are released from the same fixed point. We combine analytic solutions with scaling arguments and stochastic simulations to rationalise our results, which open new perspectives for studying the relevance of multiple searchers in various situations of molecular reactions, in particular, in living cells.
KW - diffusion
KW - first-passage
KW - fastest first-passage time of N walkers
Y1 - 2020
U6 - https://doi.org/10.1088/1367-2630/abb1de
SN - 1367-2630
VL - 22
PB - Dt. Physikalische Ges.
CY - Bad Honnef
ER -
TY - GEN
A1 - Grebenkov, Denis S
A1 - Metzler, Ralf
A1 - Oshanin, Gleb
T1 - From single-particle stochastic kinetics to macroscopic reaction rates
BT - fastest first-passage time of N random walkers
T2 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2 - We consider the first-passage problem for N identical independent particles that are initially released uniformly in a finite domain Ω and then diffuse toward a reactive area Γ, which can be part of the outer boundary of Ω or a reaction centre in the interior of Ω. For both cases of perfect and partial reactions, we obtain the explicit formulas for the first two moments of the fastest first-passage time (fFPT), i.e., the time when the first out of the N particles reacts with Γ. Moreover, we investigate the full probability density of the fFPT. We discuss a significant role of the initial condition in the scaling of the average fFPT with the particle number N, namely, a much stronger dependence (1/N and 1/N² for partially and perfectly reactive targets, respectively), in contrast to the well known inverse-logarithmic behaviour found when all particles are released from the same fixed point. We combine analytic solutions with scaling arguments and stochastic simulations to rationalise our results, which open new perspectives for studying the relevance of multiple searchers in various situations of molecular reactions, in particular, in living cells.
T3 - Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1018
KW - diffusion
KW - first-passage
KW - fastest first-passage time of N walkers
Y1 - 2020
U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-484059
SN - 1866-8372
IS - 1018
ER -