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Seminario - Multiple scale expansions
Venerdì 24 Giugno 2016 ore 12:00
Sala Riunioni terzo piano Dip. di Fisica e Geologia
G. Gubbiotti, Universita' degli Studi Roma Tre ed INFN Sezione Roma Tre
Multiple scale expansions and application to non-equilibrium thermodynamics
The description of physical phenomena often produces equations which are too difficult to treat unless than in some simple case. To avoid these problems during the centuries many ways to find approximated solutions to equations otherwise intractable. Among the various methods developed the multiple scales method is the one which is particularly seful when the underlying system shows different behaviors.
In this talk we review the foundations of this method with an instructive
example and then we present a recent application of this method to a
relevant physical problem [D. Chiuchiu' and G. Gubbiotti J. Stat. Mech. 2016 053110]. We take the equations derived by Cerino et al. [Phys. Rev. E 91,
032128] describing the dynamic evolution of a gas-piston system. We cast
them in a dimensionless form and we derive the asymptotic approximation of
the solution of these equation multiple scales expansion method. The
approximated solutions we obtained encompass all the relevant physical
behaviors of the system and can be used to express in a closed form the
heat exchanged by the gas-piston system with the reservoir for a large
class of relevant non-equilibrium situations. Though approximates such result is good since the non-equilibrium thermodynamics of a gas inside a piston is problem where analytic results are rare.
Prof. Luca Gammaitoni

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