2018/10/04 by Gorka Muñoz-Gil, Miguel Ángel García-March, Miguel Angel García-March +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Physics and Astronomy · #Biological system #Biology #Boundary (topology) #Computer science #Constant (computer programming) #Diffusion #Diffusion and Search Dynamics #Fractional Differential Equations Solutions #Geology #Mathematical analysis #Mathematics #Mesoscale meteorology #Meteorology #Microscale chemistry #Optics #Particle (ecology) #Physics #Random walk #Statistical physics #Statistics #Thermodynamics #Transmittance #cond-mat.soft #cond-mat.stat-mech #physics.bio-ph #stochastic dynamics and bifurcation
paper · pdf · doi:10.3389/fphy.2019.00031
5 pages, 2 figures
arxiv created 2018/10/04 · openalex created_date 2018/10/12 · arxiv updated 2019/03/12 · openalex publication_date 2019/03/18 · openalex updated_date 2026/08/05
We study the random walk of a particle in a compartmentalized environment, as realized in biological samples or solid state compounds. Each compartment is characterized by its length L and the boundaries transmittance T. We identify two relevant spatio-temporal scales that provide alternative descriptions of the dynamics: i) the microscale, in which the particle position is monitored at constant time intervals; and ii) the mesoscale, in which it is monitored only when the particle crosses a boundary between compartments. Both descriptions provide --by construction-- the same long time behavior. The analytical description obtained at the proposed mesoscale allows for a complete characterization of the complex movement at the microscale, thus representing a fruitful approach for this kind of systems. We show that the presence of disorder in the transmittance is a necessary condition to induce anomalous diffusion, whereas the spatial heterogeneity reduces the degree of subdiffusion and, in some cases, can even compensate for the disorder induced by the stochastic transmittance.