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- B I Henry, T A M Langlands, S L Wearne
- Physical review. E, Statistical, nonlinear, and…
- 2006

We have revisited the problem of anomalously diffusing species, modeled at the mesoscopic level using continuous time random walks, to include linear reaction dynamics. If a constant proportion of walkers are added or removed instantaneously at the start of each step then the long time asymptotic limit yields a fractional reaction-diffusion equation with a… (More)

- T A M Langlands, B I Henry, S L Wearne
- Journal of mathematical biology
- 2009

We introduce fractional Nernst-Planck equations and derive fractional cable equations as macroscopic models for electrodiffusion of ions in nerve cells when molecular diffusion is anomalous subdiffusion due to binding, crowding or trapping. The anomalous subdiffusion is modelled by replacing diffusion constants with time dependent operators parameterized by… (More)

- B I Henry, T A M Langlands, P Straka
- Physical review letters
- 2010

We derive a fractional Fokker-Planck equation for subdiffusion in a general space- and time-dependent force field from power law waiting time continuous time random walks biased by Boltzmann weights. The governing equation is derived from a generalized master equation and is shown to be equivalent to a subordinated stochastic Langevin equation.

- T A M Langlands, B I Henry
- Physical review. E, Statistical, nonlinear, and…
- 2010

We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modeling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macromolecular crowding. The mesoscopic models are formulated using continuous time random walk equations and the… (More)

- B I Henry, T A M Langlands, S L Wearne
- Physical review letters
- 2008

Cable equations with fractional order temporal operators are introduced to model electrotonic properties of spiny neuronal dendrites. These equations are derived from Nernst-Planck equations with fractional order operators to model the anomalous subdiffusion that arises from trapping properties of dendritic spines. The fractional cable models predict that… (More)

- B I Henry, T A M Langlands, S L Wearne
- Physical review. E, Statistical, nonlinear, and…
- 2005

Activator-inhibitor systems of reaction-diffusion equations have been used to describe pattern formation in numerous applications in biology, chemistry, and physics. The rate of diffusion in these applications is manifest in the single parameter of the diffusion constant, and stationary Turing patterns occur above a critical value of d representing the… (More)

- Alain Le Mehauté, J. A. Tenreiro Machado, +20 authors Mikael Enelund
- 2005

- T. A. M. Langlands, Bruce Ian Henry, Susan L. Wearne
- SIAM Journal of Applied Mathematics
- 2011

In recent work we introduced fractional Nernst–Planck equations and related fractional cable equations to model electrodiffusion of ions in nerve cells with anomalous subdiffusion along and across the nerve cells. This work was motivated by many computational and experimental studies showing that anomalous diffusion is ubiquitous in biological systems with… (More)

- T A M Langlands, B I Henry
- 2007

We have investigated Turing pattern formation through linear stability analysis and numerical simulations in a two-species reaction–diffusion system in which a fractional order temporal derivative operates on both species, and on both the diffusion term and the reaction term. The order of the fractional derivative affects the time onset of patterning in… (More)

- Christopher Angstmann, Isaac C. Donnelly, Bruce Ian Henry, B. A. Jacobs, T. A. M. Langlands, J. A. Nichols
- J. Comput. Physics
- 2016