@article{DahlenburgChechkinSchumeretal.2021,
  author    = {Dahlenburg, Marcus and Chechkin, Aleksei and Schumer, Rina and Metzler, Ralf},
  title     = {Stochastic resetting by a random amplitude},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {103},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {5},
  publisher = {American Physical Society},
  address   = {Woodbury, NY},
  issn      = {2470-0045},
  doi       = {10.1103/PhysRevE.103.052123},
  pages     = {22},
  year      = {2021},
  abstract  = {Stochastic resetting, a diffusive process whose amplitude is reset to the origin at random times, is a vividly studied strategy to optimize encounter dynamics, e.g., in chemical reactions. Here we generalize the resetting step by introducing a random resetting amplitude such that the diffusing particle may be only partially reset towards the trajectory origin or even overshoot the origin in a resetting step. We introduce different scenarios for the random-amplitude stochastic resetting process and discuss the resulting dynamics. Direct applications are geophysical layering (stratigraphy) and population dynamics or financial markets, as well as generic search processes.},
  language  = {en}
}
@article{DoerriesChechkinSchumeretal.2022,
  author    = {Doerries, Timo J. and Chechkin, Aleksei and Schumer, Rina and Metzler, Ralf},
  title     = {Rate equations, spatial moments, and concentration profiles for mobile-immobile models with power-law and mixed waiting time distributions},
  series = {Physical review : E, Statistical, nonlinear and soft matter physics},
  volume    = {105},
  journal   = {Physical review : E, Statistical, nonlinear and soft matter physics},
  number    = {1},
  publisher = {The American Institute of Physics},
  address   = {Woodbury, NY},
  issn      = {2470-0045},
  doi       = {10.1103/PhysRevE.105.014105},
  pages     = {24},
  year      = {2022},
  abstract  = {We present a framework for systems in which diffusion-advection transport of a tracer substance in a mobile zone is interrupted by trapping in an immobile zone. Our model unifies different model approaches based on distributed-order diffusion equations, exciton diffusion rate models, and random-walk models for multirate mobile-immobile mass transport. We study various forms for the trapping time dynamics and their effects on the tracer mass in the mobile zone. Moreover, we find the associated breakthrough curves, the tracer density at a fixed point in space as a function of time, and the mobile and immobile concentration profiles and the respective moments of the transport. Specifically, we derive explicit forms for the anomalous transport dynamics and an asymptotic power-law decay of the mobile mass for a Mittag-Leffler trapping time distribution. In our analysis we point out that even for exponential trapping time densities, transient anomalous transport is observed. Our results have direct applications in geophysical contexts, but also in biological, soft matter, and solid state systems.},
  language  = {en}
}
@article{VilkAghionAvgaretal.2022,
  author    = {Vilk, Ohad and Aghion, Erez and Avgar, Tal and Beta, Carsten and Nagel, Oliver and Sabri, Adal and Sarfati, Raphael and Schwartz, Daniel K. and Weiß, Matthias and Krapf, Diego and Nathan, Ran and Metzler, Ralf and Assaf, Michael},
  title     = {Unravelling the origins of anomalous diffusion},
  series = {Physical review research / American Physical Society},
  volume    = {4},
  journal   = {Physical review research / American Physical Society},
  number    = {3},
  publisher = {American Physical Society},
  address   = {College Park, MD},
  issn      = {2643-1564},
  doi       = {10.1103/PhysRevResearch.4.033055},
  pages     = {16},
  year      = {2022},
  abstract  = {Anomalous diffusion or, more generally, anomalous transport, with nonlinear dependence of the mean-squared displacement on the measurement time, is ubiquitous in nature. It has been observed in processes ranging from microscopic movement of molecules to macroscopic, large-scale paths of migrating birds. Using data from multiple empirical systems, spanning 12 orders of magnitude in length and 8 orders of magnitude in time, we employ a method to detect the individual underlying origins of anomalous diffusion and transport in the data. This method decomposes anomalous transport into three primary effects: long-range correlations ("Joseph effect"), fat-tailed probability density of increments ("Noah effect"), and nonstationarity ("Moses effect"). We show that such a decomposition of real-life data allows us to infer nontrivial behavioral predictions and to resolve open questions in the fields of single-particle tracking in living cells and movement ecology.},
  language  = {en}
}
@article{ShinCherstvyMetzler2015,
  author    = {Shin, Jaeoh and Cherstvy, Andrey G. and Metzler, Ralf},
  title     = {Self-subdiffusion in solutions of star-shaped crowders: non-monotonic effects of inter-particle interactions},
  series = {New journal of physics : the open-access journal for physics},
  volume    = {17},
  journal   = {New journal of physics : the open-access journal for physics},
  publisher = {IOP Publ. Ltd.},
  address   = {Bristol},
  issn      = {1367-2630},
  doi       = {10.1088/1367-2630/17/11/113028},
  pages     = {12},
  year      = {2015},
  abstract  = {We examine by extensive computer simulations the self-diffusion of anisotropic star-like particles in crowded two-dimensional solutions. We investigate the implications of the area coverage fraction phi of the crowders and the crowder-crowder adhesion properties on the regime of transient anomalous diffusion. We systematically compute the mean squared displacement (MSD) of the particles, their time averaged MSD, and the effective diffusion coefficient. The diffusion is ergodic in the limit of long traces, such that the mean time averaged MSD converges towards the ensemble averaged MSD, and features a small residual amplitude spread of the time averaged MSD from individual trajectories. At intermediate time scales, we quantify the anomalous diffusion in the system. Also, we show that the translational-but not rotational-diffusivity of the particles Dis a nonmonotonic function of the attraction strength between them. Both diffusion coefficients decrease as the power law D(phi) similar to (1 - phi/phi*)(2 ... 2.4) with the area fraction phi occupied by the crowders and the critical value phi*. Our results might be applicable to rationalising the experimental observations of non-Brownian diffusion for a number of standard macromolecular crowders used in vitro to mimic the cytoplasmic conditions of living cells.},
  language  = {en}
}