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Fractional Dynamics In Comb-like Structures (Hardcover)
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Fractional Dynamics In Comb-like Structures (Hardcover)
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Random walks often provide the underlying mesoscopic mechanism for
transport phenomena in physics, chemistry and biology. In
particular, anomalous transport in branched structures has
attracted considerable attention. Combs are simple caricatures of
various types of natural branched structures that belong to the
category of loopless graphs. The comb model was introduced to
understand anomalous transport in percolation clusters. Comb-like
models have been widely adopted to describe kinetic processes in
various experimental applications in medical physics and
biophysics, chemistry of polymers, semiconductors, and many other
interdisciplinary applications.The authors present a random walk
description of the transport in specific comb geometries, ranging
from simple random walks on comb structures, which provide a
geometrical explanation of anomalous diffusion, to more complex
types of random walks, such as non-Markovian continuous-time random
walks. The simplicity of comb models allows to perform a rigorous
analysis and to obtain exact analytical results for various types
of random walks and reaction-transport processes.
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