טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentDana Levanony
SubjectCorrelations and Heat Transfer in a Sthochastic
Model out of Equilibrium
DepartmentDepartment of Physics
Supervisor Full Professor Levine Dov


Abstract

In this work we extend a simple mean field stochastic model which is out of equilibrium, and which can be exactly solved in the mean field regime. Our extension is to give the model spatial structure; we solve the model exactly in the regimes where the spatial structure disappears (i.e., no correlations) and where the dissipation is maximal.


We are interested in the correlations of the system and find them to disappear in the equilibrium regime. We calculate exactly the spatial dependence of these correlations; we find the correlation length to diverge as the system goes to equilibrium, though the correlation strength vanish.


Another property that we calculate is the response of the system. Since this system is out of equilibrium, we define two kinds of response functions; both are local changes of the heat flow into the system through the parameters which control it. We find, in the spirit of fluctuation-dissipation relation. That the spatial behavior of the correlations is the same as the different response functions.


A modification of this model is proposed in order to understand the heat flow in such a model. The granular temperature is calculated exactly and it is found to obey fourier law with a sink term; it is also found to agree with numerical simulations of two dimensional granular gases. The solution of the energy equation is found to merge with the solution of the diffusion equation only in the limit of non-dissipative systems.