# Application of Hybrid Monte Carlo Algorithm in Heat Transfer

01 Aug 2017-Journal of Heat Transfer-transactions of The Asme (American Society of Mechanical Engineers Digital Collection)-Vol. 139, Iss: 8, pp 082004

About: This article is published in Journal of Heat Transfer-transactions of The Asme.The article was published on 2017-08-01. It has received 1 citations till now. The article focuses on the topics: Hybrid Monte Carlo & Monte Carlo molecular modeling.

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TL;DR: In this article , two-dimensional analytical solutions of heat conduction in nano-films under ultra-fast laser are obtained using the integral transformation method, and the results show that there is a thermal wave phenomenon inside the film, which becomes increasingly evident as the elapse of the lag time of the temperature gradient.

Abstract: The ultra-fast laser heating process of nano-films is characterized by an ultra-short duration and ultra-small space size, in which the classical Fourier law based on the hypothesis of local equilibrium is no longer applicable. Based on the Cattaneo–Vernotte (CV) model and the dual-phase-lag (DPL) model, the two-dimensional analytical solutions of heat conduction in nano-films under ultra-fast laser are obtained using the integral transformation method. The results show that there is a thermal wave phenomenon inside the film, which becomes increasingly evident as the elapse of the lag time of the temperature gradient. Moreover, the wave amplitude in the vertical direction is much larger than that in the horizontal direction of the nano-film. By comparing the numerical result of the two models, it is found that the temperature distribution inside the nano-film based on the DPL model is gentler than that of the CV model. Additionally, the temperature distribution in the two-dimensional solution is lower than that in the one-dimensional solution under the same Knudsen number. In the comparison results of the CV model, the maximum peak difference in the thermal wave reaches 75.08 K when the Knudsen number is 1.0. This demonstrates that the horizontal energy carried by the laser source significantly impacts the temperature distribution within the film.

##### References

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TL;DR: In this article, a modified Monte Carlo integration over configuration space is used to investigate the properties of a two-dimensional rigid-sphere system with a set of interacting individual molecules, and the results are compared to free volume equations of state and a four-term virial coefficient expansion.

Abstract: A general method, suitable for fast computing machines, for investigating such properties as equations of state for substances consisting of interacting individual molecules is described. The method consists of a modified Monte Carlo integration over configuration space. Results for the two‐dimensional rigid‐sphere system have been obtained on the Los Alamos MANIAC and are presented here. These results are compared to the free volume equation of state and to a four‐term virial coefficient expansion.

35,161 citations

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TL;DR: In this article, a hybrid (molecular dynamics/Langevin) algorithm is used to guide a Monte Carlo simulation of lattice field theory, which is especially efficient for quantum chromodynamics which contain fermionic degrees of freedom.

3,377 citations

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TL;DR: In this paper, the authors investigated the feasibility of the Hybrid Monte Carlo method to solve higher-dimensional Bayesian model updating problems and proposed a new formulae for Markov chain convergence assessment.

Abstract: In recent years, Bayesian model updating techniques based on measured data have been applied to system identification of structures and to structural health monitoring. A fully probabilistic Bayesian model updating approach provides a robust and rigorous framework for these applications due to its ability to characterize modeling uncertainties associated with the underlying structural system and to its exclusive foundation on the probability axioms. The plausibility of each structural model within a set of possible models, given the measured data, is quantified by the joint posterior probability density function of the model parameters. This Bayesian approach requires the evaluation of multidimensional integrals, and this usually cannot be done analytically. Recently, some Markov chain Monte Carlo simulation methods have been developed to solve the Bayesian model updating problem. However, in general, the efficiency of these proposed approaches is adversely affected by the dimension of the model parameter space. In this paper, the Hybrid Monte Carlo method is investigated (also known as Hamiltonian Markov chain method), and we show how it can be used to solve higher-dimensional Bayesian model updating problems. Practical issues for the feasibility of the Hybrid Monte Carlo method to such problems are addressed, and improvements are proposed to make it more effective and efficient for solving such model updating problems. New formulae for Markov chain convergence assessment are derived. The effectiveness of the proposed approach for Bayesian model updating of structural dynamic models with many uncertain parameters is illustrated with a simulated data example involving a ten-story building that has 31 model parameters to be updated.

263 citations

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TL;DR: The basic ideas of MCMC and software BUGS (Bayesian inference using Gibbs sampling) are introduced, stressing that a simple and satisfactory intuition for MCMC does not require extraordinary mathemat- ical sophistication.

Abstract: Markov chain Monte Carlo (MCMC) is a statistical innovation that allows researchers to fit far more com- plex models to data than is feasible using conventional methods. Despite its widespread use in a variety of scien- tific fields, MCMC appears to be underutilized in wildlife applications. This may be due to a misconception that MCMC requires the adoption of a subjective Bayesian analysis, or perhaps simply to its lack of familiarity among wildlife researchers. We introduce the basic ideas of MCMC and software BUGS (Bayesian inference using Gibbs sampling), stressing that a simple and satisfactory intuition for MCMC does not require extraordinary mathemat- ical sophistication. We illustrate the use of MCMC with an analysis of the association between latent factors gov- erning individual heterogeneity in breeding and survival rates of kittiwakes (Rissa tridactyla). We conclude with a discussion of the importance of individual heterogeneity for understanding population dynamics and designing management plans.

225 citations

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SLAC National Accelerator Laboratory

^{1}, Istituto Nazionale di Fisica Nucleare^{2}, Paris Diderot University^{3}, University of Trieste^{4}, Rice University^{5}, University of Padua^{6}, University of Perugia^{7}, Goddard Space Flight Center^{8}, École Polytechnique^{9}, Institut de Ciències de l'Espai^{10}, INAF^{11}, United States Naval Research Laboratory^{12}, Agenzia Spaziale Italiana^{13}, Instituto Politécnico Nacional^{14}, University of Tokyo^{15}, University of Southampton^{16}, University of Bordeaux^{17}, University of Toulouse^{18}, Centre national de la recherche scientifique^{19}, Stockholm University^{20}, Hiroshima University^{21}, University of Montpellier^{22}, Max Planck Society^{23}, Santa Cruz Institute for Particle Physics^{24}, Catalan Institution for Research and Advanced Studies^{25}, North-West University^{26}, University of Rome Tor Vergata^{27}, Ohio State University^{28}TL;DR: In this paper, the authors argue that the change in pulsed γ-ray emission is due to a change in emission beaming and speculate that it is precipitated by a shift in the magnetic field structure, leading to either effective magnetic inclination or effective current.

Abstract: Long-term monitoring of PSR J2021+4026 in the heart of the Cygnus region with the Fermi Large Area Telescope unveiled a sudden decrease in flux above 100 MeV over a timescale shorter than a week. The "jump" was near MJD 55850 (2011 October 16), with the flux decreasing from (8.33 ± 0.08) × 10-10 erg cm-2 s-1 to (6.86 ± 0.13) × 10-10 erg cm-2 s-1. Simultaneously, the frequency spindown rate increased from (7.8 ± 0.1) × 10-13 Hz s-1 to (8.1 ± 0.1) × 10-13 Hz s-1. Significant (>5σ) changes in the pulse profile and marginal (<3σ) changes in the emission spectrum occurred at the same time. There is also evidence for a small, steady flux increase over the 3 yr preceding MJD 55850. This is the first observation at γ-ray energies of mode changes and intermittent behavior, observed at radio wavelengths for other pulsars. We argue that the change in pulsed γ-ray emission is due to a change in emission beaming and we speculate that it is precipitated by a shift in the magnetic field structure, leading to a change of either effective magnetic inclination or effective current.

107 citations