|Ph.D Student||Zolotarevskiy Vadim|
|Subject||Heat Transport in Low-Dimensional Models: Effects|
of Disorder and Dimensionality
|Department||Department of Mechanical Engineering||Supervisors||Professor Oleg Gendelman|
|Professor Yuli Starosvetsky|
|Full Thesis text|
This thesis is devoted to a problem of microscopic foundations for Fourier's law of heat conduction. Motivated by the long-time need for rigorous first principles description of the heat conduction phenomenon and by increasing progress in the micro and nano industry, we investigate heat transport in classical lattices with realistic features pertinent to various problems in physics, chemistry and engineering. The primary goal of this work is the analysis and interpretation of the mechanisms of energy diffusion leading to normal heat conductivity.
In the first part of the study we describe numerical investigation of nonhomogeneous one-dimensional lattices with a hard-point as well as Lennard-Jones and periodic interatomic interactions. The lattices consist of particles with two different masses. We introduce a correlation parameter, which defines the probability of two neighboring particles to have identical mass. Consequently, this parameter controls the chain structure. We examine the effect of the correlated disorder on the heat conductivity. It is found that the disorder mainly affects the magnitude of the heat conduction coefficient, rather than the nature of its convergence.
The second part of the study is dedicated to the heat transfer in a chain comprised of linearly elastic disks with rigid cores. A repulsive interaction between disks is considered. The simulations were performed for one-dimensional and quasi-one-dimensional models. The parameters like chain dimensions and packing, modeling temperature etc. have been examined. We observe convergence of heat conductivity in the presented models. In addition, we investigate modeling parameters at which the model exhibits a transition from effectively one-dimensional to two-dimensional behavior.
The final part of the study considers heat conductivity of two-dimensional lattices subjected to substrate potentials e.g. sinh-Gordon and discrete sine-Gordon, as well as periodic potential with normal heat conductivity. In particular, we revisit recently published results claiming that the convergence behavior of heat conductivity in 1D models breaks down with an increase in dimensionality. Our work shows that such a conclusion was based on erroneous interpretation of analysis caused by insufficient sizes of models.