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Immunophysics

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Publications Immunophysics Division

2008

Microscopic approach to random walks

Vasily Zaburdaev

Journal of Statistical Physics 133 (1) 159-167 (2008) | Journal

In the present paper the microscopic approach to random walk models is introduced. For any particular model it provides a rigorous way to derive the transport equations for the macroscopic density of walking particles. Although it is not more complicated than the standard random walk framework it has virtually no limitations with respect to the initial distribution of particles. As a consequence, the transport equations derived with this method almost automatically give answers to such important problems as aging and two point probability distribution.

Random walks with random velocities

Vasily Zaburdaev, Michael Schmiedeberg, Holger Stark

Physical Review E 78 (1) 011119 (2008) | Journal

We consider a random walk model that takes into account the velocity distribution of random walkers. Random motion with alternating velocities is inherent to various physical and biological systems. Moreover, the velocity distribution is often the first characteristic that is experimentally accessible. Here, we derive transport equations describing the dispersal process in the model and solve them analytically. The asymptotic properties of solutions are presented in the form of a phase diagram that shows all possible scaling regimes, including superdiffusive, ballistic, and superballistic motion. The theoretical results of this work are in excellent agreement with accompanying numerical simulations.

Stochastic transport through complex comb structures

Vasily Zaburdaev, P. V. Popov, A. S. Romanov, K. V. Chukbar

Journal of Experimental and Theoretical Physics - JETP 106 (5) 999-1005 (2008) | Journal

A unified rigorous approach is used to derive fractional differential equations describing subdiffusive transport through comb structures of various geometrical complexity. A general nontrivial effect of the initial particle distribution on the subsequent evolution is exposed. Solutions having qualitative features of practical importance are given for joined structures with widely different fractional exponents.

Contact

Immunophysics Division
Prof. Vasily Zaburdaev
Principal Investigator

Max-Planck-Zentrum für Physik und Medizin
Kussmaulallee 2
Room 02.116
91054 Erlangen, Germany
+49 9131 8284 102

vasily.zaburdaev@mpzpm.mpg.de

Silke Besold

Secretary

Friedrich-Alexander-Universität Erlangen-Nürnberg
Chair of Mathematics in Life Sciences
Kussmaulallee 2
Room 02.122
91054 Erlangen, Germany
+49 9131 8284 104

silke.besold@fau.de

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