טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentKachman Tal
SubjectNon Stationary Heat Conduction in Disordered lattices
DepartmentDepartment of Mechanical Engineering
Supervisor Professor Oleg Gendelman
Full Thesis textFull thesis text - English Version


Abstract

Understanding transport phenomena on the micro scale is of interest from both  fundamental theoretical point of view and practical one. We aim to investigate heat transfer in microscopic one dimensional chains. The main focus of our work will be on transport of kinetic energy through periodic (linear and nonlinear ) chains and the effect of disorder on the transport mechanism.

An example of a linear integrable system is the harmonic lattice. In this system we have shown using molecular dynamics methods, that the system's linear nature leads to lack of a mixing mechanism for the normal modes, This lack of mixing is manifested by the fact that there is no relaxation towards equipartition and furthermore the lack of relaxation is irrespective of the initial wavelength. The above stated facts were also derived in an analytical fashion For which it was shown that equipartition will only be realized in the limit of infinite time processes.

A well-known example of an integrable system that is nonlinear is the Toda lattice. In this system we have shown that the nonlinear nature of the potential provides a mixing mechanism this in turn leads to a temperature relaxation for which in the end there is a uniform temperature profile and the characteristic relaxation times depend on the initial wavelength. Due to integrability, the decay of initial fluctuations in the temperature is not exponential, as in the harmonic chain.

For disordered systems we have studied integrable linear and nonlinear systems as well as non-integrable nonlinear systems. The disorder that was introduced was a mass disorder i.e random masses who's values obey a Gaussian distribution. the disorder causes various phenomena to arise due to the disorder . The most prominent  are localization and locking.

the system evolve in time by manifesting localized modes that lock and do not relax to equilibrium or even the manner in which the relaxation occur when locking breaks.

For the case of Nonlinear non-integrable We chose  two types of systems the  Fermi Pasta Ulam (FPU) potential and a Chain of rotators

(CR) potentials .When disorder is introduced into those systems it is shown that the disorder effects the manner in which the solitary solutions manifests. For the case of the chain of rotators this gives rise to exponentially long relaxation and localization, where for the Fermi Past Ulam the relaxation times are slower but not as in the CR model.