@article{GrebenkovMetzlerOshanin2021,
  author    = {Grebenkov, Denis S. and Metzler, Ralf and Oshanin, Gleb},
  title     = {A molecular relay race: sequential first-passage events to the terminal reaction centre in a cascade of diffusion controlled processes},
  series = {New Journal of Physics (NJP)},
  volume    = {23},
  journal   = {New Journal of Physics (NJP)},
  publisher = {IOP - Institute of Physics Publishing},
  address   = {Bristol},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/ac1e42},
  pages     = {18},
  year      = {2021},
  abstract  = {We consider a sequential cascade of molecular first-reaction events towards a terminal reaction centre in which each reaction step is controlled by diffusive motion of the particles. The model studied here represents a typical reaction setting encountered in diverse molecular biology systems, in which, e.g. a signal transduction proceeds via a series of consecutive 'messengers': the first messenger has to find its respective immobile target site triggering a launch of the second messenger, the second messenger seeks its own target site and provokes a launch of the third messenger and so on, resembling a relay race in human competitions. For such a molecular relay race taking place in infinite one-, two- and three-dimensional systems, we find exact expressions for the probability density function of the time instant of the terminal reaction event, conditioned on preceding successful reaction events on an ordered array of target sites. The obtained expressions pertain to the most general conditions: number of intermediate stages and the corresponding diffusion coefficients, the sizes of the target sites, the distances between them, as well as their reactivities are arbitrary.},
  language  = {en}
}
@misc{GrebenkovMetzlerOshanin2021,
  author    = {Grebenkov, Denis S. and Metzler, Ralf and Oshanin, Gleb},
  title     = {A molecular relay race: sequential first-passage events to the terminal reaction centre in a cascade of diffusion controlled processes},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-52194},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-521942},
  pages     = {20},
  year      = {2021},
  abstract  = {We consider a sequential cascade of molecular first-reaction events towards a terminal reaction centre in which each reaction step is controlled by diffusive motion of the particles. The model studied here represents a typical reaction setting encountered in diverse molecular biology systems, in which, e.g. a signal transduction proceeds via a series of consecutive 'messengers': the first messenger has to find its respective immobile target site triggering a launch of the second messenger, the second messenger seeks its own target site and provokes a launch of the third messenger and so on, resembling a relay race in human competitions. For such a molecular relay race taking place in infinite one-, two- and three-dimensional systems, we find exact expressions for the probability density function of the time instant of the terminal reaction event, conditioned on preceding successful reaction events on an ordered array of target sites. The obtained expressions pertain to the most general conditions: number of intermediate stages and the corresponding diffusion coefficients, the sizes of the target sites, the distances between them, as well as their reactivities are arbitrary.},
  language  = {en}
}
@misc{XuZhouMetzleretal.2022,
  author    = {Xu, Pengbo and Zhou, Tian and Metzler, Ralf and Deng, Weihua},
  title     = {Stochastic harmonic trapping of a L{\´e}vy walk: transport and first-passage dynamics under soft resetting strategies},
  series = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Zweitver{\"o}ffentlichungen der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  publisher = {Universit{\"a}tsverlag Potsdam},
  address   = {Potsdam},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-56040},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-560402},
  pages     = {1 -- 28},
  year      = {2022},
  abstract  = {We introduce and study a L{\´e}vy 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.},
  language  = {en}
}
@article{XuZhouMetzleretal.2022,
  author    = {Xu, Pengbo and Zhou, Tian and Metzler, Ralf and Deng, Weihua},
  title     = {Stochastic harmonic trapping of a L{\´e}vy walk},
  series = {New journal of physics : the open-access journal for physics / Deutsche Physikalische Gesellschaft ; IOP, Institute of Physics},
  volume    = {24},
  journal   = {New journal of physics : the open-access journal for physics / Deutsche Physikalische Gesellschaft ; IOP, Institute of Physics},
  number    = {3},
  publisher = {Deutsche Physikalische Gesellschaft},
  address   = {Bad Honnef},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/ac5282},
  pages     = {1 -- 28},
  year      = {2022},
  abstract  = {We introduce and study a L{\´e}vy 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.},
  language  = {en}
}
@article{DoerriesChechkinMetzler2022,
  author    = {Doerries, Timo J. and Chechkin, Aleksei V. and Metzler, Ralf},
  title     = {Apparent anomalous diffusion and non-Gaussian distributions in a simple mobile-immobile transport model with Poissonian switching},
  series = {Interface : journal of the Royal Society},
  volume    = {19},
  journal   = {Interface : journal of the Royal Society},
  number    = {192},
  publisher = {Royal Society},
  address   = {London},
  issn      = {1742-5689},
  doi       = {10.1098/rsif.2022.0233},
  pages     = {14},
  year      = {2022},
  abstract  = {We analyse mobile-immobile transport of particles that switch between the mobile and immobile phases with finite rates. Despite this seemingly simple assumption of Poissonian switching, we unveil a rich transport dynamics including significant transient anomalous diffusion and non-Gaussian displacement distributions. Our discussion is based on experimental parameters for tau proteins in neuronal cells, but the results obtained here are expected to be of relevance for a broad class of processes in complex systems. Specifically, we obtain that, when the mean binding time is significantly longer than the mean mobile time, transient anomalous diffusion is observed at short and intermediate time scales, with a strong dependence on the fraction of initially mobile and immobile particles. We unveil a Laplace distribution of particle displacements at relevant intermediate time scales. For any initial fraction of mobile particles, the respective mean squared displacement (MSD) displays a plateau. Moreover, we demonstrate a short-time cubic time dependence of the MSD for immobile tracers when initially all particles are immobile.},
  language  = {en}
}
@article{GuggenbergerChechkinMetzler2022,
  author    = {Guggenberger, Tobias and Chechkin, Aleksei and Metzler, Ralf},
  title     = {Absence of stationary states and non-Boltzmann distributions of fractional Brownian motion in shallow external potentials},
  series = {New journal of physics : the open-access journal for physics},
  volume    = {24},
  journal   = {New journal of physics : the open-access journal for physics},
  number    = {7},
  publisher = {Dt. Physikalische Ges.},
  address   = {[Bad Honnef]},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/ac7b3c},
  pages     = {18},
  year      = {2022},
  abstract  = {We study the diffusive motion of a particle in a subharmonic potential of the form U(x) = |x|( c ) (0 < c < 2) driven by long-range correlated, stationary fractional Gaussian noise xi ( alpha )(t) with 0 < alpha <= 2. In the absence of the potential the particle exhibits free fractional Brownian motion with anomalous diffusion exponent alpha. While for an harmonic external potential the dynamics converges to a Gaussian stationary state, from extensive numerical analysis we here demonstrate that stationary states for shallower than harmonic potentials exist only as long as the relation c > 2(1 - 1/alpha) holds. We analyse the motion in terms of the mean squared displacement and (when it exists) the stationary probability density function. Moreover we discuss analogies of non-stationarity of Levy flights in shallow external potentials.},
  language  = {en}
}
@article{VilkAghionNathanetal.2022,
  author    = {Vilk, Ohad and Aghion, Erez and Nathan, Ran and Toledo, Sivan and Metzler, Ralf and Assaf, Michael},
  title     = {Classification of anomalous diffusion in animal movement data using power spectral analysis},
  series = {Journal of physics : A, Mathematical and theoretical},
  volume    = {55},
  journal   = {Journal of physics : A, Mathematical and theoretical},
  number    = {33},
  publisher = {IOP Publishing},
  address   = {Bristol},
  issn      = {1751-8113},
  doi       = {10.1088/1751-8121/ac7e8f},
  pages     = {16},
  year      = {2022},
  abstract  = {The field of movement ecology has seen a rapid increase in high-resolution data in recent years, leading to the development of numerous statistical and numerical methods to analyse relocation trajectories. Data are often collected at the level of the individual and for long periods that may encompass a range of behaviours. Here, we use the power spectral density (PSD) to characterise the random movement patterns of a black-winged kite (Elanus caeruleus) and a white stork (Ciconia ciconia). The tracks are first segmented and clustered into different behaviours (movement modes), and for each mode we measure the PSD and the ageing properties of the process. For the foraging kite we find 1/f noise, previously reported in ecological systems mainly in the context of population dynamics, but not for movement data. We further suggest plausible models for each of the behavioural modes by comparing both the measured PSD exponents and the distribution of the single-trajectory PSD to known theoretical results and simulations.},
  language  = {en}
}
@article{StojkoskiSandevKocarevetal.2022,
  author    = {Stojkoski, Viktor and Sandev, Trifce and Kocarev, Ljupco and Pal, Arnab},
  title     = {Autocorrelation functions and ergodicity in diffusion with stochastic resetting},
  series = {Journal of physics : A, Mathematical and theoretical},
  volume    = {55},
  journal   = {Journal of physics : A, Mathematical and theoretical},
  number    = {10},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1751-8113},
  doi       = {10.1088/1751-8121/ac4ce9},
  pages     = {22},
  year      = {2022},
  abstract  = {Diffusion with stochastic resetting is a paradigm of resetting processes. Standard renewal or master equation approach are typically used to study steady state and other transport properties such as average, mean squared displacement etc. What remains less explored is the two time point correlation functions whose evaluation is often daunting since it requires the implementation of the exact time dependent probability density functions of the resetting processes which are unknown for most of the problems. We adopt a different approach that allows us to write a stochastic solution for a single trajectory undergoing resetting. Moments and the autocorrelation functions between any two times along the trajectory can then be computed directly using the laws of total expectation. Estimation of autocorrelation functions turns out to be pivotal for investigating the ergodic properties of various observables for this canonical model. In particular, we investigate two observables (i) sample mean which is widely used in economics and (ii) time-averaged-mean-squared-displacement (TAMSD) which is of acute interest in physics. We find that both diffusion and drift-diffusion processes with resetting are ergodic at the mean level unlike their reset-free counterparts. In contrast, resetting renders ergodicity breaking in the TAMSD while both the stochastic processes are ergodic when resetting is absent. We quantify these behaviors with detailed analytical study and corroborate with extensive numerical simulations. Our results can be verified in experimental set-ups that can track single particle trajectories and thus have strong implications in understanding the physics of resetting.},
  language  = {en}
}