Relevant bibliographies by topics / Non-equilibrium and Equilibrium Monte Carlo Simulations

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Non-equilibrium and Equilibrium Monte Carlo Simulations'

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Published: 6 September 2023

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Journal articles on the topic "Non-equilibrium and Equilibrium Monte Carlo Simulations"

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MacGillivray, M. C., D. L. Hunter, and Naeem Jan. "“Local” equilibrium Monte Carlo simulations." Physica A: Statistical Mechanics and its Applications 197, no. 1-2 (July 1993): 144–52. http://dx.doi.org/10.1016/0378-4371(93)90463-e.

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Liu, Xiao, John C. Crocker, and Talid Sinno. "Coarse-grained Monte Carlo simulations of non-equilibrium systems." Journal of Chemical Physics 138, no. 24 (June 28, 2013): 244111. http://dx.doi.org/10.1063/1.4811656.

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Kaiser, Waldemar, and Alessio Gagliardi. "Stepping Out of Equilibrium: The Quest for Understanding the Role of Non-Equilibrium (Thermo-)Dynamics in Electronic and Electrochemical Processes." Entropy 22, no. 9 (September 10, 2020): 1013. http://dx.doi.org/10.3390/e22091013.

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This editorial aims to interest researchers and inspire novel research on the topic of non-equilibrium Thermodynamics and Monte Carlo for Electronic and Electrochemical Processes. We present a brief outline on recent progress and challenges in the study of non-equilibrium dynamics and thermodynamics using numerical Monte Carlo simulations. The aim of this special issue is to collect recent advances and novel techniques of Monte Carlo methods to study non-equilibrium electronic and electrochemical processes at the nanoscale.
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Nada, Alessandro, Michele Caselle, and Marco Panero. "The equation of state with non-equilibrium methods." EPJ Web of Conferences 175 (2018): 07028. http://dx.doi.org/10.1051/epjconf/201817507028.

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Jarzynski’s equality provides an elegant and powerful tool to directly compute differences in free energy in Monte Carlo simulations and it can be readily extended to lattice gauge theories to compute a large set of physically interesting observables. In this talk we present a novel technique to determine the thermodynamics of stronglyinteracting matter based on this relation, which allows for a direct and efficient determination of the pressure using out-of-equilibrium Monte Carlo simulations on the lattice. We present results for the equation of state of the SU(3) Yang-Mills theory in the confined and deconfined phases. Finally, we briefly discuss the generalization of this method for theories with fermions, with particular focus on the equation of state of QCD.
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Liu Mingzhe, 刘明哲, 庹先国 Tuo Xianguo, 王磊 Wang Lei, and 李哲 Li Zhe. "Application of Monte Carlo simulations to non-equilibrium dynamic systems." High Power Laser and Particle Beams 25, no. 1 (2013): 263–68. http://dx.doi.org/10.3788/hplpb20132501.0263.

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Prudnikov, V. V., and P. V. Prudnikov. "Ageing and non-equilibrium critical phenomena in Monte Carlo simulations." Journal of Physics: Conference Series 510 (May 15, 2014): 012020. http://dx.doi.org/10.1088/1742-6596/510/1/012020.

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Di Staso, G., H. J. H. Clercx, S. Succi, and F. Toschi. "Lattice Boltzmann accelerated direct simulation Monte Carlo for dilute gas flow simulations." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 374, no. 2080 (November 13, 2016): 20160226. http://dx.doi.org/10.1098/rsta.2016.0226.

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Hybrid particle–continuum computational frameworks permit the simulation of gas flows by locally adjusting the resolution to the degree of non-equilibrium displayed by the flow in different regions of space and time. In this work, we present a new scheme that couples the direct simulation Monte Carlo (DSMC) with the lattice Boltzmann (LB) method in the limit of isothermal flows. The former handles strong non-equilibrium effects, as they typically occur in the vicinity of solid boundaries, whereas the latter is in charge of the bulk flow, where non-equilibrium can be dealt with perturbatively, i.e. according to Navier–Stokes hydrodynamics. The proposed concurrent multiscale method is applied to the dilute gas Couette flow, showing major computational gains when compared with the full DSMC scenarios. In addition, it is shown that the coupling with LB in the bulk flow can speed up the DSMC treatment of the Knudsen layer with respect to the full DSMC case. In other words, LB acts as a DSMC accelerator. This article is part of the themed issue ‘Multiscale modelling at the physics–chemistry–biology interface’.
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Algotsson, Jenny, Torbjörn Åkesson, and Jan Forsman. "Monte Carlo simulations of Donnan equilibrium in cartilage." Magnetic Resonance in Medicine 68, no. 4 (August 13, 2012): 1298–302. http://dx.doi.org/10.1002/mrm.24409.

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Alamatsaz, Arghavan, and Ayyaswamy Venkattraman. "Characterizing deviation from equilibrium in direct simulation Monte Carlo simulations." Physics of Fluids 31, no. 4 (April 2019): 042005. http://dx.doi.org/10.1063/1.5093732.

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Medvedeva, M., and Pavel V. Prudnikov. "Non-Equilibrium Critical Relaxation of Heisenberg Ferromagnets with Long-Range Correlated Defects." Solid State Phenomena 190 (June 2012): 39–42. http://dx.doi.org/10.4028/www.scientific.net/ssp.190.39.

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The dynamic critical behavior of the three-dimensional Heisenberg model with longrangecorrelated disorder was studied by using short-time Monte Carlo simulations at criticality.The static and dynamic critical exponents are determined. The simulation was performed fromordered initial state. The obtained values of the exponents are in a good agreement with resultsof the field-theoretic description of the critical behavior of this model in the two-loopapproximation.
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Dissertations / Theses on the topic "Non-equilibrium and Equilibrium Monte Carlo Simulations"

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De, Joannis Jason. "Equilibrium properties of polymer solutions at surfaces Monte Carlo simulations /." [Florida] : State University System of Florida, 2000. http://etd.fcla.edu/etd/uf/2000/ane5947/dissertation%5Fdone.pdf.

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Thesis (Ph. D.)--University of Florida, 2000.
Title from first page of PDF file. Document formatted into pages; contains ix, 242 p.; also contains graphics. Vita. Includes bibliographical references (p. 232-241).
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Rudzinsky, Michael Steven. "Theoretical and Simulation Studies of a Driven Diffusive System." Diss., Virginia Tech, 2000. http://hdl.handle.net/10919/26162.

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We explore steady-state properties of a driven lattice gas, which is a simple model of interacting many-particle systems, driven far from equilibrium by an external field. First, we study a system on a square lattice with periodic boundary conditions (PBC) along both principal lattice axes, while the drive acts along only one of these axes. For such systems, we analyze the full distribution of structure factors. Next, we investigate the effects of imposing other boundary conditions on the system. In particular, we focus on models with shifted periodic boundary conditions (SPBC) along one axis and open boundary conditions (OBC) along the other axis. The OBC allow us to have a steady flux of particles through the system while the SPBC permits us to drive the system in a range of possibilities. Using Monte Carlo simulation techniques, we discover a rich variety of phenomena, especially at low temperatures. A continuum theory for the densities, based on Langevin equations, is formulated and its predictions compared to simulation data. Many large scale properties are described successfully.
Ph. D.
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Anderson, Mark Jule Jr. "Cooperative Behavior in Driven Lattice Systems with Shifted Periodic Boundary Conditions." Diss., Virginia Tech, 1998. http://hdl.handle.net/10919/30606.

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We explore the nature of driven stochastic lattice systems with non-periodic boundary conditions. The systems consist of particle and holes which move by exchanges of nearest neighbor particle-hole pairs. These exchanges are controlled by the energetics associated with an internal Hamiltonian, an external drive and a stochastic coupling to a heat reservoir. The effect of the drive is to bias particle-hole exchanges along the field in such a way that a particle current can be established. Hard-core volume constraints limit the occupation of only one particle (hole) per lattice site. For certain regimes of the overall particle density and temperature, a system displays a homogeneous disordered phase. We investigate cooperative behavior in this phase by using two-point spatial correlation functions and structure factors. By varying the particle density and the temperature, the system orders into a phase separated state, consisting of particle-rich and particle-poor regions. The temperature and density for the co-existence state depend on the boundary conditions. By using Monte Carlo simulations, we establish co-existence curves for systems with shifted periodic boundary conditions.
Ph. D.
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Korniss, György. "Non-equilibrium Phase Transitions and Steady States in Biased Diffusion of Two Species." Diss., Virginia Tech, 1997. http://hdl.handle.net/10919/30607.

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We investigate the dynamics of a three-state stochastic lattice gas, consisting of holes and two oppositely "charged" species of particles, under the influence of an "electric" field, at zero total charge. Interacting only through an excluded volume constraint, particles can hop to nearest neighbor empty sites, but particle-particle exchange between oppositely charged particles is also allowed on a separate time scale. Controlled by this relative time scale, particle density and drive, the system orders into a charge-segregated state. Using a combination of Monte Carlo simulations and continuum field theory techniques, we study the order of these transitions and map out the steady state phase diagram of the system. On a single sheet of transitions, a line of multicritical points is found, separating the first order and continuous transitions. Furthermore, we study the steady-state structure factors in the disordered phase where homogeneous configurations are stable against small harmonic perturbations. The average structure factors show a discontinuity singularity at the origin which in real space predicts an intricate crossover between power laws of different kinds. We also seek for generic statistical properties of these quantities. The probability distributions of the structure factors are universal asymmetric exponential distributions. This research was supported in part by grants from the National Science Foundation through the Division of Materials Research.
Ph. D.
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Siretskiy, Alexey. "Monte Carlo Simulations of the Equilibrium Properties of Semi-stiff Polymer Chains : Efficient Sampling from Compact to Extended Structures." Doctoral thesis, Uppsala universitet, Fysikalisk kemi, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-151618.

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Polymers is a class of molecules which can have many different structures due to a large number of degrees of freedom. Many biopolymers, e.g. DNA, but also synthetic macromolecules have special structural features due to their backbone stiffness. Since such structural properties are important for e.g. the biological function, a lot of effort has been put into the investigation of the configurational properties of semi-stiff molecules. A theoretical treatment of these systems is often accompanied by computer simulations. The main idea is to compare theoretically derived models with experimental results for real polymers. Using Monte Carlo simulations, I have investigated how this computational technique can build a bridge between theoretical models and experimentally observed phenomena. The effort was mainly directed to develop sampling techniques, for efficiently exploring the configurational space of semi-stiff chains in a wide range of structures. The work was concentrated on compact conformations, since they, as is well known from previous studies, are difficult to sample using conventional methods. In my studies I have shown that the simple and, at a first glance, time consuming method of bead-by-bead regrow as a way of changing the configuration of a semi-stiff chain gave very promising and encouraging results when combined with modern simulation techniques, like Entropic Sampling with the Wang-Landau algorithm. The resulting simulation package was also suitable for parallelization which resulted in a further speed-up of the calculations. In addition to the more elaborate sampling methods, I also investigated external conditions to induce compaction of a semi-stiff polymer. In the case of a polyampholyte the condensing agent could be a multivalent salt, creating effective attraction between the loops of the chain, while for neutral polymers, an external field and the geometry of the confining volume can induce a compaction.
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Patel, Sonal. "Determination of Phase Equilibria and the Critical Point Using Two-Phase Molecular Dynamics Simulations with Monte Carlo Sampling." BYU ScholarsArchive, 2012. https://scholarsarchive.byu.edu/etd/3587.

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The two-phase MD technique employed in this work determines the liquid and vapor phase densities from a histogram of molecular densities within phase clusters in the simulation cell using a new Monte Carlo (MC) sampling method. These equilibrium densities are then fitted in conjunction with known critical-point scaling laws to obtain the critical temperature, and the critical density. This MC post-processing method was found to be more easily implemented in code, and it is efficient and easily applied to complex, structured molecules. This method has been successfully applied and benchmarked for a simple Lennard-Jones (LJ) fluid and a structured molecule, propane. Various degrees of internal flexibility in the propane models showed little effect on the coexisting densities far from critical point, but internal flexibility (angle bending and bond vibrations) seemed to affect the saturated liquid densities in the near-critical region, changing the critical temperature by approximately 20 K. Shorter cutoffs were also found to affect the phase dome and the location of the critical point. The developed MD+MC method was then used to test the efficacy of two all-atom, site-site pair potential models (with and without point charges) developed solely from the energy landscape obtained from high-level ab initio pair interactions for the first time. Both models produced equivalent phase domes and critical loci. The model's critical temperature for methanol is 77 K too high while that for 1-propanol is 80 K too low, but the critical densities are in good agreement. These differences are likely attributable to the lack of multi-body interactions in the true pair potential models used here. Lastly, the transferability of the ab initio potential model was evaluated by applying it to 1-pentanol. An attempt has been made to separate the errors due to transferability of the potential model from errors due to the use of a true-pair potential. The results suggested a good level of transferability for the site-site model. The lack of multi-body effects appears to be dominant weakness in using the generalized ab initio potential model for determination of the phase dome and critical properties of larger alcohols.
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Krometis, Justin. "Lane Preference in a Simple Traffic Model." Thesis, Virginia Tech, 2004. http://hdl.handle.net/10919/42365.

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We examine the effect of lane preference on a quasi one-dimensional three-state driven lattice gas, consisting of holes and positive and negative particles, and periodic boundary conditions in the longitudinal direction. Particles move via particle-hole and, with a lesser rate, particle-particle exchanges; the species are driven in opposite directions along the lattice, each preferring one of the lanes with a given probability, p. The model can be interpreted as traffic flow on a two-lane beltway, with fast cars preferring the left lane and slow cars preferring the right, viewed in a comoving frame. In steady-sate, the system typically exhibits a macroscopic cluster containing a majority of the particles. At very high values of p, a first order transition takes the system to a spatially disordered state. Using Monte Carlo simulations to analyze the system, we find that the size of the cluster increases with lane preference. We also observe a region of negative response, where increasing the lane preference decreases the number of particles in their favored lane, against all expectations. In addition, simulations show an intriguing sequence of density profiles for the two species. We apply mean-field theory, continuity equations, and symmetries to derive relationships between observables to make a number of predictions verified by the Monte Carlo data.
Master of Science
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Li, Linjun. "Systems Driven out of Equilibrium with Energy Input at Interfaces or Boundaries." Diss., Virginia Tech, 2015. http://hdl.handle.net/10919/77884.

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We study the non-equilibrium behavior of systems that are driven out of equilibrium from the interface. In the first part of this thesis, we study a model of a two-dimensional lattice gas that is in contact with two heat baths that are at different temperatures. Performing Monte Carlo simulations, we find that there are three possible types of non-equilibrium steady states, depending on the values of certain system parameters. They include a disordered phase, a fully phase separated state, and an interesting state with striped patterns in the half of the lattice where the temperature is lower. The last one is a novel non-equilibrium steady state that we study systematically by varying the system parameters. To obtain the non-equilibrium finite-size phase diagram, we perform a spectrum analysis to classify not only the three major states, but also the sub-states of the striped phase. In the second part of the thesis, we study magnetic friction that results when two Potts systems move with respect to each other. In this research, we first study a model that consists of two interacting Potts blocks, where one block moves on top of the other. As a result, the system is driven out of equilibrium constantly. In our research we find for weak interfacial couplings that the contacting surfaces behave rather similar to a free surface. If the interfacial coupling is strong, however, anisotropic spin patterns appear on the contacting surfaces. This study is extended to a three-dimensional Potts wedge with a tip sliding along the surface of a Potts block. It is found that the shape of the Potts lattice influences the surface behavior of the system.
Ph. D.
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Binauld, Quentin. "Modélisation et simulation du rayonnement dans les jets de moteurs à propergol solide à haute altitude." Thesis, Université Paris-Saclay (ComUE), 2018. http://www.theses.fr/2018SACLC090/document.

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Le rayonnement dans les jets issus de moteurs à propergol solide constitue un phénomène essentiel à l’estimation des flux aux parois et à la prédiction de la signature radiative des engins. A haute altitude, de l’ordre de 100 km, ces jets sont caractérisés par des écoulements compressibles diphasiques, à fort aspect raréfié dans certaines régions, compos ´es de particules d’alumine et de gaz de combustion. Le transfert radiatif y joue un rôle important dans la mesure où il influence fortement le refroidissement et le changement de phase des particules. Afin de simuler numériquement les jets et leur rayonnement, différents modèles ont été développés. Le rayonnement des gaz a été pris en compte à l’aide de modèles statistiques à bandes étroites. Le phénomène de surfusion qui régit le changement de phase de l’alumine et les champs de température associés aux différentes tailles de particules, a été pris en compte. Enfin, une méthode de splitting des puissances radiatives a été mise en œuvre afin de permettre le couplage entre le rayonnement et l’écoulement dans des milieux en des ‘équilibre thermique gaz/particules. Ces modèles ont été implémentes dans une plateforme de calcul, permettant de coupler un solveur fluide utilisant une approche Navier-Stokes, un solveur eulérien pour traiter la phase dispersée et un solveur radiatif qui utilise une méthode de Monte Carlo. L’outil numérique développe a été partiellement validé en comparant nos résultats aux mesures obtenues dans le cadre de l’expérience BSUV2. Dans les conditions de cette expérience, le rayonnement des particules est prédominant mais la contribution des gaz s’avère non négligeable. Des simulations sous différentes hypothèses ont permis de mettre en évidence le rôle primordial du transfert radiatif, couplé au phénomène de surfusion, dans l’établissement des champs de température des particules. La dernière partie de ces travaux s’est attachée à l’étude du déséquilibre vibrationnel de la phase gazeuse et de son impact sur le rayonnement dans les jets. Il est montré que le gel partiel des niveaux de vibration de la molécule CO2 durant la détente du jet peut augmenter de façon significative son rayonnement
Radiation from solid propellant rocketplumes is important for the prediction of thermalfluxes on vehicle walls and of plume signature. Athigh altitudes, of approximately 100 km, those plumesare characterized by two-phase compressible flows,highly rarefied in some regions, composed of aluminaparticles and exhaust combustion gases. Radiativetransfer plays an important role in the cooling and thephase change of the particles.In order to carry out numerical simulations of rocketplumes and their radiation, several models have beendeveloped. The radiation of the gas phase is takeninto account using statistical narrow bands models.The supercooling phenomenon has been modeled todeal with the phase change of alumina and to obtaincorrect temperature fields for the different size classesof particles. Finally, a splitting method of the radiativepower has been established to enable the couplingbetween radiation and the flow field under gas/particlethermal non-equelibrium. These models have beenimplemented in a calculation platform, enabling tocouple a Navier-Stokes solver for the gas phase, anEulerian solver dealing with the dispersed phase anda radiative solver based on a Monte Carlo method.The developed numerical tool has been partly validatedcomparing our results with the measurementsobtained during the BSUV2 experiment. In the conditionsof this experiment, particle radiation is shownto be predominant but the contribution of the gasphase is found to be non-negligible. Simulations underdifferent hypotheses have put the emphasis onthe importance of radiative transfer, coupled with thesupercooling phenomenon, for an accurate evaluationof particle temperature fields.The last part of this work focuses on the study ofgas vibrational non-equilibrium and its impact on radiationfrom high altitude plumes. It is shown thatthe slow deexcitation of vibrational levels of the CO2molecule during the plume expansion may increasesignificantly its radiation
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Rodrigues, Áttila Leães. "Estudo de transições de fase em sistemas com simetria \"up-down\" e estados absorventes." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-26092014-105955/.

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Neste trabalho estudamos um modelo estocástico com simetria Ising e dois estados absorventes em três dimensões com uma rede cúbica e em duas dimensões através de uma rede triangular. O estudo levou em conta cálculos de aproximação de campo médio e simulações de Monte Carlo. Os resultados mostraram que o modelo tem transição de segunda ordem de uma fase paramagnética para uma fase ferromagnética, uma transição da fase ferromagnética para uma fase absorvente, também de segunda ordem, e ainda uma transição de primeira ordem da fase paramagnética para a fase absorvente. No espaço de parâmetros as três linhas de transição se encontram no diagrama de fases em um ponto onde o modelo se comporta como o modelo do votante.
In this work we studied a stochastic model with ising symmetry and two simmetric absorbing configurations in a three-dimensional cubic lattice and in two dimensions using a triangular lattice. The study took into account simple mean-field approximations and Monte Carlo simulations. The results showed that the model has a second-order transition from a paramagnetic phase to a ferromagnetic phase and second-order transition from ferromagnetic phase to the absorbing one. A first-order phase transition from the paramagnetic phase to the absorbing phase is observed too. In the phase diagram the two second-order transition lines aproaches to the point where the model behaves like the voter model.
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Books on the topic "Non-equilibrium and Equilibrium Monte Carlo Simulations"

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Gallis, Michael A. On the modeling of thermochemical non-equilibrium in particle simulations. London: Imperial College of Science, Technology & Medicine, Dept. of Aeronautics, 1995.

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Institute for Computer Applications in Science and Engineering., ed. Some developments of the equilibrium particle simulation method for the direct simulation of compressible flows. Hampton, VA: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1995.

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Allen, Michael P., and Dominic J. Tildesley. Advanced Monte Carlo methods. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198803195.003.0009.

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This chapter describes the ways in which the Monte Carlo importance sampling method may be adapted to improve the calculation of ensemble averages, particularly those associated with free energy differences. These approaches include umbrella sampling, non-Boltzmann sampling, the Wang–Landau method, and nested sampling. In addition, a range of special techniques have been developed to accelerate the simulation of flexible molecules, such as polymers. These approaches are illustrated with scientific examples and program code. The chapter also explains the analysis of such simulations using techniques such as weighted histograms, and acceptance ratio calculations. Practical advice on selection of methods, parameters, and the direction in which to make comparisons, are given. Monte Carlo methods for modelling phase equilibria and chemical reactions at equilibrium are described.
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Coolen, A. C. C., A. Annibale, and E. S. Roberts. Graphs with hard constraints: further applications and extensions. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198709893.003.0007.

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This chapter looks at further topics pertaining to the effective use of Markov Chain Monte Carlo to sample from hard- and soft-constrained exponential random graph models. The chapter considers the question of how moves can be sampled efficiently without introducing unintended bias. It is shown mathematically and numerically that apparently very similar methods of picking out moves can give rise to significant differences in the average topology of the networks generated by the MCMC process. The general discussion in complemented with pseudocode in the relevant section of the Algorithms chapter, which explicitly sets out some accurate and practical move sampling approaches. The chapter also describes how the MCMC equilibrium probabilities can be purposely deformed to, for example, target desired correlations between degrees of connected nodes. The mathematical exposition is complemented with graphs showing the results of numerical simulations.
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Fox, Raymond. The Use of Self. Oxford University Press, 2011. http://dx.doi.org/10.1093/oso/9780190616144.001.0001.

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This monograph presents recent advances in neural network (NN) approaches and applications to chemical reaction dynamics. Topics covered include: (i) the development of ab initio potential-energy surfaces (PES) for complex multichannel systems using modified novelty sampling and feedforward NNs; (ii) methods for sampling the configuration space of critical importance, such as trajectory and novelty sampling methods and gradient fitting methods; (iii) parametrization of interatomic potential functions using a genetic algorithm accelerated with a NN; (iv) parametrization of analytic interatomic potential functions using NNs; (v) self-starting methods for obtaining analytic PES from ab inito electronic structure calculations using direct dynamics; (vi) development of a novel method, namely, combined function derivative approximation (CFDA) for simultaneous fitting of a PES and its corresponding force fields using feedforward neural networks; (vii) development of generalized PES using many-body expansions, NNs, and moiety energy approximations; (viii) NN methods for data analysis, reaction probabilities, and statistical error reduction in chemical reaction dynamics; (ix) accurate prediction of higher-level electronic structure energies (e.g. MP4 or higher) for large databases using NNs, lower-level (Hartree-Fock) energies, and small subsets of the higher-energy database; and finally (x) illustrative examples of NN applications to chemical reaction dynamics of increasing complexity starting from simple near equilibrium structures (vibrational state studies) to more complex non-adiabatic reactions. The monograph is prepared by an interdisciplinary group of researchers working as a team for nearly two decades at Oklahoma State University, Stillwater, OK with expertise in gas phase reaction dynamics; neural networks; various aspects of MD and Monte Carlo (MC) simulations of nanometric cutting, tribology, and material properties at nanoscale; scaling laws from atomistic to continuum; and neural networks applications to chemical reaction dynamics. It is anticipated that this emerging field of NN in chemical reaction dynamics will play an increasingly important role in MD, MC, and quantum mechanical studies in the years to come.
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Raff, Lionel, Ranga Komanduri, Martin Hagan, and Satish Bukkapatnam. Neural Networks in Chemical Reaction Dynamics. Oxford University Press, 2012. http://dx.doi.org/10.1093/oso/9780199765652.001.0001.

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This monograph presents recent advances in neural network (NN) approaches and applications to chemical reaction dynamics. Topics covered include: (i) the development of ab initio potential-energy surfaces (PES) for complex multichannel systems using modified novelty sampling and feedforward NNs; (ii) methods for sampling the configuration space of critical importance, such as trajectory and novelty sampling methods and gradient fitting methods; (iii) parametrization of interatomic potential functions using a genetic algorithm accelerated with a NN; (iv) parametrization of analytic interatomic potential functions using NNs; (v) self-starting methods for obtaining analytic PES from ab inito electronic structure calculations using direct dynamics; (vi) development of a novel method, namely, combined function derivative approximation (CFDA) for simultaneous fitting of a PES and its corresponding force fields using feedforward neural networks; (vii) development of generalized PES using many-body expansions, NNs, and moiety energy approximations; (viii) NN methods for data analysis, reaction probabilities, and statistical error reduction in chemical reaction dynamics; (ix) accurate prediction of higher-level electronic structure energies (e.g. MP4 or higher) for large databases using NNs, lower-level (Hartree-Fock) energies, and small subsets of the higher-energy database; and finally (x) illustrative examples of NN applications to chemical reaction dynamics of increasing complexity starting from simple near equilibrium structures (vibrational state studies) to more complex non-adiabatic reactions. The monograph is prepared by an interdisciplinary group of researchers working as a team for nearly two decades at Oklahoma State University, Stillwater, OK with expertise in gas phase reaction dynamics; neural networks; various aspects of MD and Monte Carlo (MC) simulations of nanometric cutting, tribology, and material properties at nanoscale; scaling laws from atomistic to continuum; and neural networks applications to chemical reaction dynamics. It is anticipated that this emerging field of NN in chemical reaction dynamics will play an increasingly important role in MD, MC, and quantum mechanical studies in the years to come.
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Book chapters on the topic "Non-equilibrium and Equilibrium Monte Carlo Simulations"

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Kindt, James T. "Grand Canonical Monte Carlo Simulations of Equilibrium Polymers and Networks." In ACS Symposium Series, 298–312. Washington, DC: American Chemical Society, 2003. http://dx.doi.org/10.1021/bk-2003-0861.ch019.

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Nagai, O., Y. Yamada, and Y. Miyatake. "Monte Carlo Simulations of Three-Dimensional Heisenberg and Transverse-Ising Magnets." In Quantum Monte Carlo Methods in Equilibrium and Nonequilibrium Systems, 95–103. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-83154-6_9.

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Marcu, M. "Investigation of One- and Two-Dimensional Quantum Spin Systems by Monte Carlo Simulations." In Quantum Monte Carlo Methods in Equilibrium and Nonequilibrium Systems, 64–74. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-83154-6_6.

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Evans, J. W. "Kinetic Monte Carlo Simulation of Non-Equilibrium Lattice-Gas Models: Basic and Refined Algorithms Applied to Surface Adsorption Processes." In Handbook of Materials Modeling, 1753–67. Dordrecht: Springer Netherlands, 2005. http://dx.doi.org/10.1007/1-4020-3286-2_88.

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Evans, J. W. "Kinetic Monte Carlo Simulation of Non-Equilibrium Lattice-Gas Models: Basic and Refined Algorithms Applied to Surface Adsorption Processes." In Handbook of Materials Modeling, 1753–67. Dordrecht: Springer Netherlands, 2005. http://dx.doi.org/10.1007/978-1-4020-3286-8_88.

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Bruno, D., M. Capitelli, S. Longo, and P. Minelli. "Direct Simulation Monte Carlo Modeling of Non Equilibrium Reacting Flows. Issues for the Inclusion into a ab initio Molecular Processes Simulator." In Computational Science and Its Applications – ICCSA 2004, 383–91. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-24709-8_41.

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Okabe, Y., and M. Kikuchi. "High-Speed Algorithm for Quantum Monte Carlo Simulation." In Quantum Monte Carlo Methods in Equilibrium and Nonequilibrium Systems, 34–40. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-83154-6_3.

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Hirsch, J. E. "Simulation of Magnetic Impurities in Metals." In Quantum Monte Carlo Methods in Equilibrium and Nonequilibrium Systems, 205–15. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-83154-6_20.

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De Raedt, H., A. Lagendijk, and P. de Vries. "Computer Simulation of Polaron and Bipolaron Systems." In Quantum Monte Carlo Methods in Equilibrium and Nonequilibrium Systems, 188–96. Berlin, Heidelberg: Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-83154-6_18.

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Dirks, Andreas, Thomas Pruschke, and Jong E. Han. "Monte-Carlo Approach to Stationary Non-equilibrium of Mesoscopic Systems." In NATO Science for Peace and Security Series B: Physics and Biophysics, 187–97. Dordrecht: Springer Netherlands, 2012. http://dx.doi.org/10.1007/978-94-007-4984-9_12.

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Conference papers on the topic "Non-equilibrium and Equilibrium Monte Carlo Simulations"

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Terao, Takamichi, Ai Kono, and Wataru Takahashi. "Non-equilibrium dynamics of Coulomb glass: Kinetic Monte Carlo simulation." In 4TH INTERNATIONAL SYMPOSIUM ON SLOW DYNAMICS IN COMPLEX SYSTEMS: Keep Going Tohoku. American Institute of Physics, 2013. http://dx.doi.org/10.1063/1.4794591.

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Longo, S. "Monte Carlo Simulation of Charged Species Kinetics in Non Equilibrium Gases." In RAREFIED GAS DYNAMICS: 24th International Symposium on Rarefied Gas Dynamics. AIP, 2005. http://dx.doi.org/10.1063/1.1941681.

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Stefanov, S. K., Michail D. Todorov, and Christo I. Christov. "Direct Simulation Monte Carlo Algorithms for Simulation of Non-equilibrium Gas Flows." In APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: Proceedings of the 2nd International Conference. AIP, 2010. http://dx.doi.org/10.1063/1.3526643.

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Pop, Eric, Sanjiv Sinha, and Kenneth E. Goodson. "Monte Carlo Modeling of Heat Generation in Electronic Nanostructures." In ASME 2002 International Mechanical Engineering Congress and Exposition. ASMEDC, 2002. http://dx.doi.org/10.1115/imece2002-32124.

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This work develops a Monte Carlo (MC) simulation method for calculating the heat generation rate in electronic nanostructures. Electrons accelerated by the electric field scatter strongly with optical phonons, yet heat transport in silicon occurs via the faster acoustic modes. The MC method incorporates the appropriate energy transfer rates from electrons to each phonon branch. This accounts for the non-equilibrium energy exchange between the electrons and phonon branches. Using the MC method with an electron energy-dependent scattering rate intrinsically accounts for the non-locality of the heat transfer near a strongly peaked electric field. This approach provides more information about electronically generated heat at nanoscale dimensions compared to traditional macroscopic field-dependent methods. The method has applications in any region of high spatial or temporal non-equilibrium between electrons and phonons, and particularly facilitates careful microscopic analysis of heating in a nanoscale transistor.
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Hinz, Alexander, Egon P. Hassel, and Johannes Janicka. "NUMERICAL SIMULATION OF TURBULENT NON-EQUILIBRIUM METHANE-AIR JET FLAMES USING MONTE CARLO PDF METHOD." In First Symposium on Turbulence and Shear Flow Phenomena. Connecticut: Begellhouse, 1999. http://dx.doi.org/10.1615/tsfp1.550.

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Kim, Jae Gang, Oh Joon Kwon, and Chul Park. "State-to-State Transition and Non-Equilibrium Chemical Reaction in Direct Simulation Monte Carlo Method." In 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2010. http://dx.doi.org/10.2514/6.2010-989.

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GALLIS, M., and J. HARVEY. "Non-equilibrium thermal radiation from air shock layers modelled with the Direct Simulation Monte Carlo method." In 28th Thermophysics Conference. Reston, Virigina: American Institute of Aeronautics and Astronautics, 1993. http://dx.doi.org/10.2514/6.1993-2805.

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Tsuchiya, Ogawa, Miyoshi, Svizhenko, and Anantram. "Comparison of non-equilibrium Green's function and quantum-corrected Monte Carlo approaches in nano MOS simulation." In Electrical Performance of Electronic Packaging. IEEE, 2004. http://dx.doi.org/10.1109/iwce.2004.1407340.

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Gu, X. J., B. John, G. H. Tang, and D. R. Emerson. "Heat and Mass Transfer of a Rarefied Gas in a Driven Micro-Cavity." In ASME 2009 Second International Conference on Micro/Nanoscale Heat and Mass Transfer. ASMEDC, 2009. http://dx.doi.org/10.1115/mnhmt2009-18236.

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A high-order moment method is employed to construct the transport model for non-equilibrium gas flow in micro-scale geometries. The motion of a gas in a two-dimensional square micro-cavity is solved using the 26 moment equations for low Reynolds and Mach number flows in the early transition regime. The computed velocity and temperature fields are compared with data obtained from the direct simulation Monte Carlo method. It is found that the 26 moment equations are able to capture the non-equilibrium phenomena in a driven micro-cavity, such as counter-gradient heat transfer, which are not embedded in the Navier-Stokes-Fourier equations.
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Beretta, Gian Paolo, and Nicolas G. Hadjiconstantinou. "Steepest Entropy Ascent Models of the Boltzmann Equation: Comparisons With Hard-Sphere Dynamics and Relaxation-Time Models for Homogeneous Relaxation From Highly Non-Equilibrium States." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-64905.

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We present a family of steepest entropy ascent (SEA) models of the Boltzmann equation. The models preserve the usual collision invariants (mass, momentum, energy), as well as the non-negativity of the phase-space distribution, and have a strong built-in thermodynamic consistency, i.e., they entail a general H-theorem valid even very far from equilibrium. This family of models features a molecular-speed-dependent collision frequency; each variant can be shown to approach a corresponding BGK model with the same variable collision frequency in the limit of small deviation from equilibrium. This includes power-law dependence on the molecular speed for which the BGK model is known to have a Prandtl number that can be adjusted via the power-law exponent. We compare numerical solutions of the constant and velocity-dependent collision frequency variants of the SEA model with the standard relaxation-time model and a Monte Carlo simulation of the original Boltzmann collision operator for hard spheres for homogeneous relaxation from near-equilibrium and highly non-equilibrium states. Good agreement is found between all models in the near-equilibrium regime. However, for initial states that are far from equilibrium, large differences are found; this suggests that the maximum entropy production statistical ansatz is not equivalent to Boltzmann collisional dynamics and needs to be modified or augmented via additional constraints or structure.
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