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Дифференциальные операторы на сингулярных пространствах, алгебраически интегрируемые системы и квантование
26 марта 2018 г. 18:40, г. Москва, Главное здание МГУ им. М. В. Ломоносова, аудитория 13-24

How heterogeneity influences random walks on graphs

Л. В. Тупикина

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Аннотация: We introduce a heterogeneous continuous time random walk (HCTRW) [1] model as a versatile analytical formalism for studying and modeling diffusion processes in heterogeneous structures [2,3]. We derive the exact form of the propagator and investigate the effects of spatio-temporal heterogeneities onto the diffusive dynamics via the spectral properties of the generalized transition matrix. Since in our HCTRW approach, the space and time characteristics of individual jumps on a graph are coupled that requires developing new theoretical tools. In particular, we show how the distribution of first passage times changes due to local and global heterogeneities of the medium in comparison to the well known CTRW model. The HCTRW formalism offers a unified mathematical language to address various diffusion-reaction problems, with numerous applications in material sciences, physics, chemistry, biology, and social sciences. This framework can be used in order to describe porous media [4], another aspect, we discuss, is connection of HCTRW model with the theory of barrier models [5].
[1] D. Grebenkov, L.Tupikina, "Heterogeneous continuous time random walks", 97 012148 PRE (2018). [2] R. Friedrich, J. Peinke, M. Sahimi, M. R. R. Tabar, “Approaching complexity by stochastic methods: From biological systems to turbulence”, Phys. Rep. 506, 87-162 (2011). [3] H. Scher and M. Lax, “Stochastic Transport in a disordered solid. I. Theory”, Phys. Rev. B 7, 4491 (1973). [4] P. Levitz, V. Tariel, M. Stampanoni, and E. Gallucci, “Topology of evolving pore networks”, Eur. Phys. J. Appl. Phys. 60, 24202 (2012). [5] J.Klafter, I.Sokolov, “First steps in random walks“, Oxford University Press (2011).

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