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Heterogeneous continuous-time random walks.

Denis S Grebenkov1,2, Liubov Tupikina1

  • 1Laboratoire de Physique de la Matière Condensée (UMR 7643), CNRS-Ecole Polytechnique, 91128 Palaiseau, France.

Physical Review. E
|February 17, 2018
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Summary
This summary is machine-generated.

We introduce a heterogeneous continuous-time random walk (HCTRW) model for diffusion in complex systems. This model analyzes how medium heterogeneities impact diffusion dynamics and first-passage times.

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Area of Science:

  • Physics
  • Applied Mathematics
  • Complex Systems

Background:

  • Diffusion processes are fundamental in various scientific fields.
  • Modeling diffusion in heterogeneous media presents significant challenges.

Purpose of the Study:

  • Introduce a versatile analytical formalism, the heterogeneous continuous-time random walk (HCTRW) model.
  • Investigate the impact of spatiotemporal heterogeneities on diffusion dynamics.

Main Methods:

  • Derivation of the exact propagator for the HCTRW model.
  • Analysis of spectral properties of the generalized transition matrix.
  • Examination of first-passage time distributions.

Main Results:

  • The HCTRW model provides a unified framework for diffusion studies.
  • Spatiotemporal heterogeneities significantly alter diffusive dynamics.
  • Local and global heterogeneities affect first-passage time distributions.

Conclusions:

  • The HCTRW model offers a powerful tool for understanding diffusion in complex environments.
  • This formalism has broad applications across material science, physics, chemistry, biology, and social sciences.