Steady State NEMD Investigation of Heat Conduction of a 1-D Lattice Chain Subjected to a Temperature Gradient and Statement of a Variational Principle for Second Law Compliance of Heat Transfer

Publication Issue: 
Volume 39, Issue 2, 2018
Page No: 
Date Received: 
Wednesday, January 31, 2018
Authors' Name: 
Christopher G. Jesudason
Authors' Affiliation and Address: 
Center for Theoretical Physics and Chemistry Department Science Faculty, University of Malaya, 50603 Kuala Lumpur, Malaysia
Two aspects of conductive heat are reviewed here, (i) its basic definitions and (ii) the results of nonequilibrium molecular dynamics (NEMD) simulation for a 1-D lattice chain for the harmonic and non-harmonic FPU-β standard model potentials subjected to a temperature gradient that results in both thermal energy flow and a distinct temperature profile at the steady state. Ever since the publication of the Rieder-Lebowitz-Lieb (RLL) theory approximately half a century ago, it has been taken as axiomatic by the global Physics community that their rationalization and prediction of a near flat temperature profile along the central region of the harmonic lattice is unique and the only one possible for the ballistic trajectory that ensues for such intermolecular potentials. We note that the RLL theory is replete with assumptions concerning the nature of how the particles interact with the potential field which was mathematically convenient in providing the boundary conditions that allows one to derive exact solutions to the matrix differential equations. Using non-synthetic NEMD algorithms that conserves energy and momentum, we observe that other solutions to the steady state problem exists, where the temperature profile varies sinusoidally, which also obtains for non- harmonic potentials depending on the strength of the potential coefficients for the harmonic part of the potential. This investigation will describe some of the potentials used and the ensuing results. Apart from the obvious theoretical implications of these results, we surmise that systems exhibiting a near harmonic potential could be used for the construction of thermal PN junctions in regulating heat flows in applications.
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