Scaling study of diffusion in dynamic crowded spaces
Harry Bendekgey, Greg Huber, David Yllanes, J. Phys. A: Math. Theor. 57 445207 (2024).
We formulate a scaling theory for the long-time diffusive motion in a space occluded by a high density of moving obstacles in dimensions 1, 2 and 3. Our tracers diffuse anomalously over many decades in time, before reaching a diffusive steady state with an effective diffusion constant Deff, which depends on the obstacle diffusivity and density. The scaling of Deff, above and below a critical regime, is characterized by two independent critical parameters: the conductivity exponent µ, also found in models with frozen obstacles, and an exponent ψ, which quantifies the effect of obstacle diffusivity.
We formulate a scaling theory for the long-time diffusive motion in a space occluded by a high density of moving obstacles in dimensions 1, 2 and 3. Our tracers diffuse anomalously over many decades in time, before reaching a diffusive steady state with an effective diffusion constant Deff, which depends on the obstacle diffusivity and density. The scaling of Deff, above and below a critical regime, is characterized by two independent critical parameters: the conductivity exponent µ, also found in models with frozen obstacles, and an exponent ψ, which quantifies the effect of obstacle diffusivity.