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Continuous-time random-walk model for anomalous diffusion in expanding media
Expanding media are typical in many different fields, eg, in biology and cosmology. In
general, a medium expansion (contraction) brings about dramatic changes in the behavior …
general, a medium expansion (contraction) brings about dramatic changes in the behavior …
Exact solutions for diffusive transport on heterogeneous growing domains
From the smallest biological systems to the largest cosmological structures, spatial domains
undergo expansion and contraction. Within these growing domains, diffusive transport is a …
undergo expansion and contraction. Within these growing domains, diffusive transport is a …
Diffusion in an expanding medium: Fokker-Planck equation, Green's function, and first-passage properties
We present a classical, mesoscopic derivation of the Fokker-Planck equation for diffusion in
an expanding medium. To this end, we take a conveniently generalized Chapman …
an expanding medium. To this end, we take a conveniently generalized Chapman …
The role of mechanical interactions in EMT
The detachment of cells from the boundary of an epithelial tissue and the subsequent
invasion of these cells into surrounding tissues is important for cancer development and …
invasion of these cells into surrounding tissues is important for cancer development and …
Reaction-diffusion and reaction-subdiffusion equations on arbitrarily evolving domains
Reaction-diffusion equations are widely used as the governing evolution equations for
modeling many physical, chemical, and biological processes. Here we derive reaction …
modeling many physical, chemical, and biological processes. Here we derive reaction …
Standard and fractional Ornstein-Uhlenbeck process on a growing domain
We study normal diffusive and subdiffusive processes in a harmonic potential (Ornstein-
Uhlenbeck process) on a uniformly growing or contracting domain. Our starting point is a …
Uhlenbeck process) on a uniformly growing or contracting domain. Our starting point is a …
Generalized fractional diffusion equations for subdiffusion in arbitrarily growing domains
The ubiquity of subdiffusive transport in physical and biological systems has led to intensive
efforts to provide robust theoretical models for this phenomena. These models often involve …
efforts to provide robust theoretical models for this phenomena. These models often involve …
On Explicit Solutions for Coupled Reaction-Diffusion and Burgers-Type Equations with Variable Coefficients Through a Riccati System
This work is concerned with the study of explicit solutions for generalized coupled reaction-
diffusion and Burgers-type systems with variable coefficients. Including nonlinear models …
diffusion and Burgers-type systems with variable coefficients. Including nonlinear models …
Lévy Walk Dynamics in an External Constant Force Field in Non-Static Media
Based on the recognition of the huge change of the transport properties for diffusion
particles in non-static media, we consider a Lévy walk model subjected to an external …
particles in non-static media, we consider a Lévy walk model subjected to an external …
Exact solutions and critical behaviour for a linear growth-diffusion equation on a time-dependent domain
J Allwright - Proceedings of the Edinburgh Mathematical Society, 2022 - cambridge.org
A linear growth-diffusion equation is studied in a time-dependent interval whose location
and length both vary. We prove conditions on the boundary motion for which the solution …
and length both vary. We prove conditions on the boundary motion for which the solution …