@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}
}