ὅδε οἶκος, ὦ ἑταῖρε, μνημεῖον ἐστιν ζῴων τῶν σοφῶν ἀνδρῶν, καὶ τῶν ἔργων αὐτῶν

Mechanics Colloquim

 

PROGRAM


MATEMATIČKI INSTITUT SANU
ODELJENJE ZA MEHANIKU

PROGRAM ZA APRIL 2007.

Pozivamo Vas da učestvujete u radu sednica Odeljenja i to:

SREDA, 18. april 2007. u 18 sati:


Alfio Grillo, CNISM & DMFCI, University of Catania.
A multiscale approach to modeling transport phenomena in growing living Systems

Biological growth is the variation of mass of a tissue in response to the concurrence of various phenomena which occur both inside the tissue and between the tissue and its surrounding environment, and involve different scales of observation. At the cellular and molecular level, growth is regulated by chemical and cellular processes involving transport mechanisms of chemical species. On the other hand, at the scale at which the tissue is regarded as a macroscopic complex continuum system, growth is modulated by environmental factors, e.g., thermo-mechanical factors. In spite of the separation of scales characterizing these phenomena, transport and thermo-mechanical processes are interconnected. Mixture Theory offers a useful tool for modeling such an interconnection.

We study a growing tissue as an open biphasic mixture with mass-exchange between phases. The solid-phase is identified with a porous matrix, while the fluid-phase is referred to as the ensemble of all chemical substances filling the pore space. We describe the evolution of chemical substances in terms of transport mechanisms determined on the basis of kinematic and constitutive relations, and we propose to consider growth as a process able to influence transport by continuously varying the thermo-mechanics state, material symmetries and inhomogeneities of the tissue. In order to investigate the influence of such a variation on transport, we "Supscale" transport processes (which occur at the pore scale) to the scale at which macroscopic constitutive laws are postulated for the mixture as a whole. By using suitable averaging techniques, we write the macroscopic equation of transport and "Spull them" back to the material form. In the peculiar case of anisotropic growth, we show that such a modulation occurs through a continuous rearrangement of the material symmetries. Finally, by regarding growth as a process characterized by a time scale much slower than that of the transport process of interest, we provide an asymptotic analysis of transport in a growing porous medium based on the adiabatic approximation. In this framework, we provide a formal solution of the transport equation in terms of Green's functions, which shows that the macroscopic concentration of a certain chemical substance is "Smodulated" by anisotropic growth.



Sednice se održavaju u zgradi SANU, Knez Mihailova 35, u sali 2 na prvom spratu.

Sekretar Odeljenja
Bojan Međo
Upravnik Odeljenja
Akademik Teodor Atanacković, s.r.