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Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
Published on: September 26, 2016
Relation between generalized diffusion equations and subordination schemes
1Institute of Physics and Astronomy, Potsdam University, Karl-Liebknecht-Strasse 24/25, 14476 Potsdam-Golm, Germany and Akhiezer Institute for Theoretical Physics, Akademicheskaya Strasse 1, 61108 Kharkow, Ukraine.
Abstract:
Generalized (non-Markovian) diffusion equations with different memory kernels and subordination schemes based on random time change in the Brownian diffusion process are popular mathematical tools for description of a variety of non-Fickian diffusion processes in physics, biology, and earth sciences. Some of such processes (notably, the fluid limits of continuous time random walks) allow for either kind of description, but other ones do not. In the present work we discuss the conditions under which a generalized diffusion equation does correspond to a subordination scheme, and the conditions under which a subordination scheme does possess the corresponding generalized diffusion equation. Moreover, we discuss examples of random processes for which only one, or both kinds of description are applicable.
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