Mathematical Physics
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Research Volchenkov

Renormalization group and instantons in stochastic nonlinear dynamics

We study the stochastic counterparts of nonlinear dynamical problems such as fully developed turbulence, transport  through porous media, theory of whirlpools, waterspouts and tsunami waves, stochastic magneto-hydrodynamics, turbulent  transport in crossed fields, self-organized criticality, dynamics of accelerated wrinkled flame fronts advancing in a wide canal.

D. Volchenkov , “Renormalization group and instantons in stochastic nonlinear dynamics: From self-organized criticality to thermonuclear reactors.” The European Physical Journal - Special Topics 1951-6355 (Print) 1951-6401 (Online) Volume 170(1), pp.1-142 DOI: 10.1140/epjst/e2009-01001-3 © Springer Berlin / Heidelberg (2009).

Urbanization and Urban Spatial Networks

Many neighborhoods are cut off from other parts of the city by poor transport links and haphazard urban planning, which can often lead to social ills. Urban planners have often failed to take such isolation into account when shaping the city landscape, not least because isolation is difficult to quantify in the complex fabric of a major city. Random walks on spatial city graphs spot hidden areas of geographical isolation in the urban landscape.

Ph. Blanchard, D. Volchenkov,  Mathematical Analysis of Urban Spatial Networks,  © Springer Series Understanding Complex Systems, Berlin / Heidelberg (2008).

Communication through Language, Music, and Dance

Interactions between humans via speech, music, and body language  (dance) constitute the unifying theme of research in modern communication technologies. Music, language, and dance, even though highly flexible and versatile, nonetheless might be modular in nature, being comprised of individual stereotypical building blocks programs that cannot be intentionally stopped before their completion. The profound link between action and perception in communication through language, music, and dance might be attested on the ground of mathematical communication theory, studying the problems of signal transmission, reception, and processing.

D. Volchenkov,  Ph. Blanchard, J.-R. Dawin, “Markov Chains or the Game of Structure and Chance. From Complex Networks, to Language Evolution, to Musical Compositions”, The European Physical Journal - Special Topics  184, 1-82 © Springer Berlin / Heidelberg (2010).


Please also see the contact page and the publications page of Dimitry Volchenkov.

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