3rd European Congress of Mathematics [610093]

3rd European Congress of Mathematics
Poster sessions
Section 14: Mathematical Physics Poster number 270
Homogenization methods for thermal dispersion problems
Claudia Timofte, Department of Mathematics, Faculty of Physics, University of Bucharest, Romania.
ABSTRACT
In the last decades, many eorts have been made to develop suitable mathematical methods for modeling
thermal diusion phenomena in order to obtain the macroscale behavior and the properties of some
heterogeneous complex thermal systems. These methods include the generalized method of moments,
variational methods, center-manifold techniques, projection-operator techniques and also some probabilistic
methods. In this paper, we shall be especially interested in getting a macrotransport paradigm for a class of
thermal diusion phenomena occuring in some complex periodic adiabatic systems. Our analysis is based on
two alternative methods: the generalized method of moments and a probabilistic method based on a central
limit theorem for Markov processes. The viability of these models can be justied by introducing the notion of
a generic conserved tracer entity, called a "thermion", in the case of internal energy transport. In this manner
we are able to establish a macrotransport paradigm for thermal transport phenomena and to express the
macroscale coecients in terms of the prescribed microscale data and the system geometry. We shall be also
interested in getting the asymptotic behavior of these macroscale coecients as functions of the velocity and
the spatial scale parameters which characterize our transport processes. Specic examples are given to
illustrate the computation of the macroscale coecients as functions of the comparable microscale data.
References
[1] R.N.Bhattacharya, A central limit theorem for diusions with periodic coecients,
Ann.Prob. ,13(1985), 385-396.
[2] H.Brenner, D.A.Edwards, Macrotransport Processes , Butterworth-Heinemann, Boston
(1993).
[3] C.Timofte, Ph.D.Thesis , Institute of Mathematics of the Romanian Academy, Bucharest
(1996) (in Romanian).
[4] C.Timofte, Applications of central limit theorems to thermal dispersion in periodic media,
Proceedings of the Fourth Colloquium France-Romania , Metz, France (1998).
[5] C.Timofte, Asymptotics of thermal dispersion in periodic media, Journal of Theoretical
and Applied Mechanics , 1,37(1999), 95-108.
Keywords: method of moments, central limit theorem, macrotransport equation, macroscale coecients
Mathematics Subject Classication: 60J60, 60F17
Contact Address: [anonimizat]