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Computation of the solid-liquid interfacial free energy in hard spheres by means of thermodynamic integration

Physical Review E 2020年第4期102卷 042123-042123页

作者： M. Bültmann T. Schilling Physikalisches Institut Albert-Ludwigs-Universitt 79104 Freiburg Germany

We used a thermodynamic integration scheme, which is specifically designed for disordered systems, to compute the interfacial free energy of the solid-liquid interface in the hard-sphere model. We separated the bulk contribution to the total free energy from the interface contribution, performed a finite-size scaling analysis, and obtained for the (100)-interface γ=0.591(11)kBTσ−2.

关键词： Interface & surface thermodynamics Thermal properties Liquid-solid interfaces Finite-size scaling metropolis algorithm

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Aging following a zero-temperature quench in the d=3 Ising model

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Physical Review E 2024年第4期109卷 044148-044148页

作者： Denis Gessert Henrik Christiansen Wolfhard Janke Institut für Theoretische Physik Universität Leipzig IPF 231101 04081 Leipzig Germany Centre for Fluid and Complex Systems Coventry University Coventry CV1 5FB United Kingdom

Aging in phase-ordering kinetics of the d=3 Ising model following a quench from infinite to zero temperature is studied by means of Monte Carlo simulations. In this model the two-time spin-spin autocorrelator Cag is expected to obey dynamical scaling and to follow asymptotically a power-law decay with the autocorrelation exponent λ. Previous work indicated that the lower Fisher-Huse bound of λ≥d/2=1.5 is violated in this model. Using much larger systems than previously studied, the instantaneous exponent for λ we obtain at late times does not disagree with this bound. By conducting systematic fits to the data of Cag using different Ansätze for the leading correction term, we find λ=1.58(14), with most of the error attributed to the systematic uncertainty regarding the Ansätze. This result is in contrast to the recent report that below the roughening transition universality might be violated.

关键词： Aging Dynamical phase transitions Nonequilibrium statistical mechanics Nonequilibrium lattice models Nonequilibrium systems Heatbath algorithm Ising model metropolis algorithm Monte Carlo methods Spin lattice models

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Low-temperature ordering of the dimer phase of a two-dimensional model of core-softened particles

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Physical Review E 2021年第4期104卷 044602-044602页

作者： F. Mambretti M. Martinelli F. Civillini M. Bertoletti S. Riva N. Manini D. E. Galli D. Pini Università degli Studi di Milano Dipartimento di Fisica “Aldo Pontremoli” via Celoria 16 20133 Milan Italy Università degli Studi di Padova Dipartimento di Fisica e Astronomia via Marzolo 8 35131 Padua Italy

Purely pairwise interactions of the core-softened type, i.e., featuring a soft repulsion followed by a hard-core interaction at shorter distance, give rise to nontrivial equilibrium structures entirely different from the standard close packing of spheres. In particular, in a suitable low-temperature region of their phase diagram, such interactions are well known to favor a transition from a fluid to a cluster crystal. The residual mutual interaction between individual clusters can lead to the formation of patterns of their reciprocal orientations. In this work, we investigate two examples of such models in two dimensions, at the density most appropriate to the dimer phase, whereby clusters consist of just two particles, studying them with optimization techniques and Monte Carlo simulations. We focus on the dimer crystal, and unveil a second phase transition at extremely low temperature. This transition leads from a triangular dimer lattice with randomly disordered dimer orientations at high temperature to a reduced-symmetry ground state with nematic orientational order and a slightly distorted structure characterized by a centered-rectangular lattice at low temperature.

关键词： Crystal defects Distortions & defects Nematic order Quasicrystalline structure 2-dimensional systems Soft colloids Density functional theory metropolis algorithm Monte Carlo methods

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Ab initio path integral Monte Carlo simulations of hydrogen snapshots at warm dense matter conditions

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Physical Review E 2023年第1期107卷 015206-015206页

作者： Maximilian Böhme Zhandos A. Moldabekov Jan Vorberger Tobias Dornheim Center for Advanced Systems Understanding (CASUS) D-02826 Görlitz Germany Helmholtz-Zentrum Dresden-Rossendorf (HZDR) Institute of Radiation Physics D-01328 Dresden Germany Technische Universität Dresden Institute of Theoretical Physics D-01062 Dresden Germany

We combine ab initio path integral Monte Carlo (PIMC) simulations with fixed ion configurations from density functional theory molecular dynamics (DFT-MD) simulations to solve the electronic problem for hydrogen under warm dense matter conditions [Böhme et al., Phys. Rev. Lett. 129, 066402 (2022)]. The problem of path collapse due to the Coulomb attraction is avoided by utilizing the pair approximation, which is compared against the simpler Kelbg pair potential. We find very favorable convergence behavior towards the former. Since we do not impose any nodal restrictions, our PIMC simulations are afflicted with the notorious fermion sign problem, which we analyze in detail. While computationally demanding, our results constitute an exact benchmark for other methods and approximations within DFT. Our setup gives us the unique capability to study important properties of warm dense hydrogen such as the electronic static density response and exchange-correlation kernel without any model assumptions, which will be very valuable for a variety of applications such as the interpretation of experiments and the development of new XC functionals.

关键词： Warm-dense matter metropolis algorithm Path-integral Monte Carlo

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Exact Calculation of the Probabilities of Rare Events in Cluster-Cluster Aggregation

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Physical Review Letters 2024年第9期133卷 097101页

作者： R. Rajesh V. Subashri Oleg Zaboronski C.I.T. Campus Taramani Chennai 600113 India Training School Complex Anushakti Nagar Mumbai 400094 India Mathematics Institute

We develop an action formalism to calculate probabilities of rare events in cluster-cluster aggregation for arbitrary collision kernels and establish a pathwise large deviation principle with total mass being the rate. As an application, the rate function for the number of surviving particles as well as the optimal evolution trajectory are calculated exactly for the constant, sum, and product kernels. For the product kernel, we argue that the second derivative of the rate function has a discontinuity. The theoretical results agree with simulations tailored to the calculation of rare events.

关键词： Growth processes Irreversible processes Nonequilibrium statistical mechanics Phase transitions Polymers Exact solutions for many-body systems Large deviation & rare event statistics Master equation metropolis algorithm Monte Carlo methods Path-integral methods Scaling methods

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Static and dynamic properties of the nonframework cations in Na-mordenites zeolite

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MOLECULAR SIMULATION 2004年第9期30卷 587-592页

作者： Maurin, G Bell, RG Senet, P Devautour-Vinot, S Univ Aix Marseille 1 Ctr St Jerome UMR 6121 CNRS Lab Madirel F-13397 Marseille 20 France UCL Royal Inst Great Britain Davy Faraday Res Lab London W1S 4BS England Univ Bourgogne Fac Sci Mirande UMR 5027 CNRS Phys Lab F-21078 Dijon France Univ Montpellier 2 Lab Physicochim Mat Condensee UMR 5617 CNRS F-34095 Montpellier France

This work consists of exploring the effect of Si/Al ratio and water content on both the static and dynamic properties of the extra-framework cations in a typical zeolite system Na(+)-Mordenites. Atomistic simulations based on interatomic potentials and minimisation techniques have been used to determine the location of the cations as a function of the Si/Al ratio and the hydration level. Our calculations showed two different cation behaviours depending on the type of channels that they occupy, the positions of the cations in the main channels being substantially perturbed upon the sorption of water molecules whereas those of the cations located in the small side channels being only slightly shifted. By contrast, the populations of the cation sites have almost the same trend when the Si/Al ratio varies. We have then developed a Monte Carlo technique specialised for the simulation of rare events to study the activated cations motions in this zeolite. Mean activation barriers are obtained from minimum energy paths (MEP) calculated for lattices with various Si/Al ratio, by using a metropolis algorithm. Finally, Molecular Dynamics (MD) simulations allowed us to compare the mobility of the cations in hydrated and dehydrated states and confirmed the results expected from the previous static calculations. This modelling has been successfully compared with experimental data obtained by dielectric relaxation spectroscopy (DRS) and provided a microscopic description of the static and dynamic properties of the extra-framework cations.

关键词： Na-mordenites Si/Al ratio Monte Carlo technique metropolis algorithm

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Nonequilibrium Ising model on a two-dimensional additive small-world network

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Physical Review E 2023年第4期107卷 044115-044115页

作者： R. A. Dumer M. Godoy Instituto de Física Universidade Federal de Mato Grosso 78060-900 Cuiabá MT Brazil

In this work, we have studied the Ising model with one- and two-spin flip competing dynamics on a two-dimensional additive small-world network (A-SWN). The system model consists of an L×L square lattice where each site of the lattice is occupied by a spin variable that interacts with the nearest-neighbor spins and it has a certain probability p of being additionally connected at random to one of its farther neighbors. The dynamics present in the system can be defined by the probability q of being in contact with a heat bath at a given temperature T and, at the same time, with a probability of (1−q) the system is subjected to an external flux of energy into the system. The contact with the heat bath is simulated by one-spin flip according to the metropolis prescription, while the input of energy is mimicked by the two-spin flip process, involving a simultaneous flipping of a pair of neighboring spins. We have employed Monte Carlo simulations to obtain the thermodynamic quantities of the system, such as the total mLF and staggered mLAF magnetizations per spin, the susceptibility χL, and the reduced fourth-order Binder cumulant UL. We have built the phase diagram for the stationary states of the model in the plane T versus q, showing the existence of two continuous transition lines for each value of p: one line between the ferromagnetic F and paramagnetic P phases and the other line between the P and antiferromagnetic AF phases. Therefore, we have shown that the phase diagram topology changes when p increases. Using the finite-size scaling analysis, we also obtained the critical exponents for the system, where, varying the parameter p, we have observed a different universality class from the Ising model in the regular square lattice to the A-SWN.

关键词： Critical phenomena Dynamical phase transitions Order parameters Phase diagrams Phase transitions Self-organized systems Finite-size scaling metropolis algorithm

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Comparison of integral equation theories of the liquid state

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Physical Review E 2024年第4期110卷 044608页

作者： Ilian Pihlajamaa Liesbeth M. C. Janssen Soft Matter &amp Biological Physics Department of Applied Physics <a href="https://***/02c2kyt77">Eindhoven University of Technology</a> P.O. Box 513 5600MB Eindhoven The Netherlands.

The Ornstein-Zernike equation is a powerful tool in liquid state theory for predicting structural and thermodynamic properties of fluids. Combined with a suitable closure, it has been shown to reproduce, e.g., the static structure factor, pressure, and compressibility of liquids to a great degree of accuracy. However, out of the multitude of closures that exist for the Ornstein-Zernike equation, it is hard to predict a priori which closure will give the most accurate predictions for the system at hand. To alleviate this problem, we compare the predictive power of many closures on a curated set of representative benchmark systems, including those with hard-sphere, inverse power-law, Gaussian core, and Lennard-Jones particles, in three and two dimensions. For example, we find that the well-known and highly used Percus-Yevick closure gives significantly worse predictions than lesser-known closures of equal complexity in all cases studied. We anticipate that the trends observed in our results will aid in making more informed decisions regarding closure choices. To facilitate the adoption of more modern closure theories, we also have packaged, documented, and distributed the code necessary to numerically solve the equations for a given closure and pair interaction potential.

关键词： Classical statistical mechanics Thermodynamics Classical fluids Liquids Approximation methods for many-body systems metropolis algorithm Monte Carlo methods Virial theorem

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Probabilistic back analysis of unsaturated soil seepage parameters based on Markov chain Monte Carlo method

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ROCK AND SOIL MECHANICS 2013年第8期34卷 2393-2400页

作者： Zuo Zi-bo Zhang Lu-lu Cheng Yan Wang Jian-hua He Ye Shanghai Jiao Tong Univ Sch Naval Architecture Ocean & Civil Engn Shanghai 200240 Peoples R China Shanghai Jiao Tong Univ State Key Lab Ocean Engn Shanghai 200240 Peoples R China

Based on the Bayesian theory, a probabilistic back analysis method using time-varying measurement data is established. The back calculated posterior distributions are determined using the Markov chain Monte Carlo method (MCMC) with the differential evolution adaptive metropolis algorithm. In this paper, a case study of a well instrumented natural terrain is presented. The deterministic model for pore-water pressure evaluation is an analytical model. Field measurements of pore-water pressure are used to calibrate the unsaturated parameters of the deterministic model. Statistical properties of the posterior distributions are presented and discussed. It is found that the posterior standard deviations of the six parameters are all greatly reduced. The predicted and measured pore-water pressures during the calibration period and the validation period are compared. The coverage of the 95% total uncertainty bounds is estimated to be 0.964 for the calibration period, during which the field measured pore pressures are used to back analyze the input parameters. For periods 2 to 4 of the validation period, the coverage by the 95% total uncertainty bounds are 0.52, 0.79 and 0.79, respectively. These results indicate an overall good performance by the calibrated model.

关键词： unsaturated soil seepage Monte Carlo method metropolis algorithm back analysis

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Bayesian Parameter Estimation on Three Models of Influenza

Bayesian Parameter Estimation on Three Models of Influenza

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作者： Torrence, Robert Billington Virginia Tech | University

Mathematical models of viral infections have been informing virology research for years. Estimating parameter values for these models can lead to understanding of biological values. This has been successful in HIV modeling for the estimation of values such as the lifetime of infected CD8 T-Cells. However, estimating these values is notoriously difficult, especially for highly complex models. We use Bayesian inference and Monte Carlo Markov Chain methods to estimate the underlying densities of the parameters (assumed to be continuous random variables) for three models of influenza. We discuss the advantages and limitations of parameter estimation using these methods. The data and influenza models used for this project are from the lab of Dr. Amber Smith in Memphis, Tennessee.

关键词： Influenza Bayesian Inference Parameter Estimation Mathematical Biology MCMC Methods metropolis algorithm Thesis

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