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Survival and confinement under quenched disorder
Tomás Aquino1, G John Lapeyre, Marco Dentz
1Spanish National Research Council (IDAEA-CSIC), 08034 Barcelona, Spain. tomas.decamposaquino@univ-rennes1.fr.
Physical Chemistry Chemical Physics : PCCP
|October 18, 2019
Summary
Random walkers in disordered environments exhibit prolonged survival and confinement due to spatial variations. Their survival probability follows a power law, unlike the typical exponential decay, indicating altered dynamics.
Area of Science:
- Statistical Physics
- Complex Systems
- Mathematical Modeling
Background:
- Random walkers are fundamental models for transport phenomena.
- Quenched disorder introduces spatial heterogeneity in system parameters.
- Understanding survival and confinement is crucial in various physical and biological systems.
Purpose of the Study:
- To investigate the survival and confinement dynamics of random walkers in disordered media.
- To analyze the impact of spatially varying waiting times and decay rates on walker behavior.
- To contrast the observed dynamics with classical models under homogeneous conditions.
Main Methods:
- Theoretical analysis of random walker models with quenched disorder.
- Incorporation of spatially heterogeneous waiting times and decay rates.
- Mathematical derivation of survival probability and mean squared displacement.
Main Results:
- Spatial heterogeneity and segregation induce dynamic coupling between transport and reaction.
- Survival probability exhibits power-law decay, deviating from exponential decay in homogeneous systems.
- Mean squared displacement shows dimension-dependent subdiffusion and subsequent localization, with enhanced confinement in higher dimensions.
Conclusions:
- Disordered environments significantly alter random walker dynamics, leading to history-dependent behavior.
- Power-law survival and localization are key signatures of random walkers in heterogeneous media.
- The dimensionality of the system plays a critical role in the degree of confinement.
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