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.
|Advisor:||Garcia-Cervera, Carlos Javier|
|Commitee:||Ceniceros, Hector, Yang, Xu|
|School:||University of California, Santa Barbara|
|School Location:||United States -- California|
|Source:||DAI-B 81/3(E), Dissertation Abstracts International|
|Subjects:||Applied Mathematics, Statistical physics|
|Keywords:||Dimension reduction, Generalized Langevin equation, Memory, Mori-Zwanzig, Thermostats|
Copyright in each Dissertation and Thesis is retained by the author. All Rights Reserved
The supplemental file or files you are about to download were provided to ProQuest by the author as part of a
dissertation or thesis. The supplemental files are provided "AS IS" without warranty. ProQuest is not responsible for the
content, format or impact on the supplemental file(s) on our system. in some cases, the file type may be unknown or
may be a .exe file. We recommend caution as you open such files.
Copyright of the original materials contained in the supplemental file is retained by the author and your access to the
supplemental files is subject to the ProQuest Terms and Conditions of use.
Depending on the size of the file(s) you are downloading, the system may take some time to download them. Please be