Anomalous diffusion with linear reaction dynamics: From continuous time random walks to fractional reaction-diffusion equations
نویسندگان
چکیده
منابع مشابه
Anomalous diffusion with linear reaction dynamics: from continuous time random walks to fractional reaction-diffusion equations.
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 fractional order temporal derivative o...
متن کاملContinuous-time random walks with internal dynamics and subdiffusive reaction-diffusion equations.
We formulate the generalized master equation for a class of continuous-time random walks in the presence of a prescribed deterministic evolution between successive transitions. This formulation is exemplified by means of an advection-diffusion and a jump-diffusion scheme. Based on this master equation, we also derive reaction-diffusion equations for subdiffusive chemical species, using a mean-f...
متن کاملFractional Reaction-transport Equations Arising from Evanescent Continuous Time Random Walks
Continuous time random walks (CTRWs) describe a particular class of renewal processes used to model a wide variety of phenomena such as the motion of charge carriers in disordered systems, the dynamics of financial markets, the motion of diffusing particles in crowded environments, and certain anomalous relaxation phenomena in dielectric systems. It is well known that, on long time scales, a CT...
متن کامل2 00 6 Fractional Reaction - Diffusion Equations
In a series of papers, Saxena, Mathai, and Haubold (2002, 2004a, 2004b) derived solutions of a number of fractional kinetic equations in terms of generalized Mittag-Leffler functions which provide the extension of the work of Haubold and Mathai (1995, 2000). The subject of the present paper is to investigate the solution of a fractional reaction-diffusion equation. The results derived are of ge...
متن کاملNumerical solutions for fractional reaction-diffusion equations
Fractional diffusion equations are useful for applications where a cloud of particles spreads faster than the classical equation predicts. In a fractional diffusion equation, the second derivative in the spatial variable is replaced by a fractional derivative of order less than two. The resulting solutions spread faster than the classical solutions and may exhibit asymmetry, depending on the fr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physical Review E
سال: 2006
ISSN: 1539-3755,1550-2376
DOI: 10.1103/physreve.74.031116