# Home > Description

**Key-note lecture**

**Topic: **Networks models of biological structures

**Abstract: **Random biological structures (sets of bacteria, biological tissue, sets of cells etc) can be considered as random two-phase geometric structures described by probabilistic distributions, for instance, by correlation functions. This talk is devoted to a new computationally effective approach for the representative volume element (RVE) based on the so-called e-sums (multidimensional discrete chain convolutions). The e-sums contain geometric statistical information hidden in the considered structures when interactions between particles of various physical phenomena such as viscous, elastic stresses and deformations, diffusion, heat, electric and magnetic fields occur. The general scheme can be briefly described as follows. Let we want to compare two samples which are not statistically distinguishable at the first glance. First, the computer processes pictures in our disposal to obtain the normalized unit cells in digital format. Next, the e-sums for the both samples are computed. If the corresponding e-sums are same within an appropriate precision, we conclude that the structures are statistically equivalent.

The results yields the constructive RVE theory much more effective than vague statistical approaches. We give precise and computationally instant answers to such questions as isotropy of structure and its macroscopic behavior which can be detected as normal or anomalous.

**Key Speaker: ** Vladimir MITYUSHEV (Pedagogical University of Cracow)

Vladimir MITYUSHEV is an Professor at the Pedagogical University in Krakow. He was Professor at the Pedagogical University in Slupsk (1992-2004), Associate Professor at the Belarussian State University in Minsk (1988–1992), Associate Professor at the Belarussian Technological Univeristy in Minsk (1984–1988) and Engineer at the Institute of Geochemistry and Geophysics (1980-1984). He is also a Guest Research Professor/ Senior Researcher at Equipe Milieux Poreux et Fractures, Sisyphe, Universite Paris VI in France since 1998 till present.

He received his PhD in mathematics in 1984 by Belarussian State University in Minsk, and habilitation in technology in 1997 by Poznan University of Technology. He received the title of full professor in mathematics from the President of Poland in 2010.

His research interests are in mathematical modeling and computer simulations, industrial mathematics, boundary value problems and their applications, Riemann-Hilbert problem for multiply connected domains, iterative functional equations and their applications, elliptic PDE, effective properties of composites with deterministic and random structure, fiber composites, RVE, porous media, permeability and diffusion, Navier–Stokes equations in domains with complex geometry, viscous flow in wavy channels, elasticity, thermoelasticity and mechanics of fracture, electroosmotic phenomena, symbolic computations, packing and deterministic and random graphs.

He is a member of the American Mathematical Society and a reviewer of Mathematical Reviews and Zentralblatt für Mathematik.

http://mityu.up.krakow.pl/