titolo

Seminario - Multiple scale expansions

target

totem,dipartimento,ppim

inizio

Venerdì 24 Giugno 2016 ore 12:00

luogo

Sala Riunioni terzo piano Dip. di Fisica e Geologia

relatore

G. Gubbiotti, Universita' degli Studi Roma Tre ed INFN Sezione Roma Tre

titoloevento

Multiple scale expansions and application to non-equilibrium thermodynamics

abstract

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.

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.

organizzatori

Prof. Luca Gammaitoni