Dissertation/Thesis Abstract

Exact Thermal Boundary Conditions in 1d Heat Transport
by Mylonakis, Kyle A., Ph.D., University of California, Santa Barbara, 2019, 217; 13899759
Abstract (Summary)

It is well known that 1d atomistic heat transport experiences anomalous phenomenon. Temperature discontinuities and divergence of the conductivity with respect to system size suggest that, at the atomistic scale, Fourier's law does not hold in one dimensional materials. Many different thermostats exist for 1d atomistic systems, however their use is ad-hoc and requires choice of boundary conditions. A dimension reduction technique known as the Mori-Zwanzig procedure applied to infinite harmonic systems produces a type of thermostat whose equations of motion are generalized Langevin equations (GLE's) where the resulting noise term is mean zero Gaussian and stationary, satisfying the fluctuation dissipation theorem.

By using a dimension reduction procedure based on Green's function techniques, it is shown that infinite deterministic baths give rise to GLE thermostats with non-stationary noise. Numerical experiments are then performed to explore the affect of non-stationarity on the temperature profiles in non-equilibrium stationary states (NESS), and on the divergence of the conductivity. Comparisons to other simple models are also reported.

Indexing (document details)
Advisor: Garcia-Cervera, Carlos Javier
Commitee: Ceniceros, Hector, Yang, Xu
School: University of California, Santa Barbara
Department: Mathematics
School Location: United States -- California
Source: DAI-B 81/3(E), Dissertation Abstracts International
Source Type: DISSERTATION
Subjects: Applied Mathematics, Statistical physics
Keywords: Dimension reduction, Generalized Langevin equation, Memory, Mori-Zwanzig, Thermostats
Publication Number: 13899759
ISBN: 9781088312964
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