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Thermal Conductivity Calculation with the Molecular Dynamics Direct Method II: Improving the Computational Efficiency

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The molecular dynamics non-equilibrium direct method is a well-established way of predicting thermal conductivity κ, but in good thermal conductors such as crystalline semi-conductors it can yield unacceptably large statistical uncertainties in the extrapolation to a bulk system, κ . We show how to extract more information from the simulation data in order to reliably calculate tight confidence intervals for κ . We prove that the measurement error in κ for a single simulation of size L i and duration D i is proportional to (D i L i 3)−1/2, so that using very large simulations reduces the error more efficiently than using very long durations, as we confirm explicitly with molecular dynamics data. By considering the error propagation we derive an algorithm to determine the optimal set of {L i , D i } which minimizes the probable measurement error in κ for given total computational effort. Overall, these improvements reduce by an order of magnitude the computational effort required to calculate κ with a given statistical uncertainty.


Document Type: Research Article


Publication date: October 1, 2011

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  • Journal of Computational and Theoretical Nanoscience is an international peer-reviewed journal with a wide-ranging coverage, consolidates research activities in all aspects of computational and theoretical nanoscience into a single reference source. This journal offers scientists and engineers peer-reviewed research papers in all aspects of computational and theoretical nanoscience and nanotechnology in chemistry, physics, materials science, engineering and biology to publish original full papers and timely state-of-the-art reviews and short communications encompassing the fundamental and applied research.
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