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On properties of the Wang-Landau algorithm
Cornell University
,
2018.
No. 1808.09251.
We review recent advances in the analysis of the Wang--Landau algorithm, which is designed for the direct Monte Carlo estimation of the density of states (DOS). In the case of a discrete energy spectrum, we present an approach based on introducing the transition matrix in the energy space (TMES). The TMES fully describes a random walk in the energy space biased with the Wang-Landau probability. Properties of the TMES can explain some features of the Wang-Landau algorithm, for example, the flatness of the histogram. We show that the Wang--Landau probability with the true DOS generates a Markov process in the energy space and the inverse spectral gap of the TMES can estimate the mixing time of this Markov process. We argue that an efficient implementation of the Wang-Landau algorithm consists of two simulation stages: the original Wang-Landau procedure for the first stage and a 1/t modification for the second stage. The mixing time determines the characteristic time for convergence to the true DOS in the second simulation stage. The parameter of the convergence of the estimated DOS to the true DOS is the difference of the largest TMES eigenvalue from unity. The characteristic time of the first stage is the tunneling time, i.e., the time needed for the system to visit all energy levels.
Буравцев В. Н., Макарова Т. И., Полетаев А. И. et al., Вестник Московского университета. Серия 3: Физика и астрономия 2013 Т. 4 С. 34-38
We observe the self-assembling of the dipolar hard sphere particles at low temperature by Monte Carlo simulation. We find different types of stable structures of dipolar particles which appear when the isotropic phase of the system becomes unstable. Specifically, we find an interesting case of parallel cylindrical domains. The value of the total dipole moment ...
Added: November 25, 2013
Arbuzov A., Bardin D., Bondarenko S. et al., JETP Letters 2016 Vol. 103 No. 2 P. 131-136
This article presents new features of the MCSANC v.1.20 program, a Monte Carlo tool for calculation of the next-to-leading order electroweak and QCD corrections to various Standard Model processes. The extensions concern implementation of Drell--Yan-like processes and include a systematic treatment of the photon-induced contribution in proton--proton collisions and electroweak corrections beyond NLO approximation. There ...
Added: June 28, 2018
Barash L. Yu., Weigel M., Shchur L.N. et al., European Physical Journal: Special Topics 2017 Vol. 226 No. 4 P. 595-604
Population annealing is a hybrid of sequential and Markov chain Monte Carlo methods geared towards the efficient parallel simulation of systems with complex free-energy landscapes. Systems with first-order phase transitions are among the problems in computational physics that are difficult to tackle with standard methods such as local-update simulations in the canonical ensemble, for example ...
Added: October 20, 2017
Efremov R., Journal of Chemical Information and Modeling 2019 Vol. 59 No. 6 P. 2765-2775
Atomistic aspects of the structural organization, dynamics, and functioning of hydrated lipid bilayers - model cell membranes - are primarily governed by the fine balance of intermolecular interactions between all constituents of these systems. Besides the hydrophobic effect, which shapes the overall skeleton of lipid membranes, very important contribution to their behavior is made by ...
Added: August 7, 2019
Barash L. Yu., Фадеева М. А., Shchur L. N., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2017 Vol. 96 No. 4 P. 043307-1-043307-7
The Wang-Landau (WL) algorithm has been widely used for simulations in many areas of physics. Our analysis of the WL algorithm explains its properties and shows that the difference of the largest eigenvalue of the transition matrix in the energy space from unity can be used to control the accuracy of estimating the density of ...
Added: October 20, 2017
Russkov A., Chulkevich R., Shchur L., Computer Physics Communications 2021 Vol. 261 P. 107786
The population annealing method is a promising approach for large-scale simulations because it is potentially scalable on any parallel architecture. We present an implementation of the algorithm on a hybrid program architecture combining CUDA and MPI. The problem is to keep all general-purpose graphics processing unit devices as busy as possible by efficiently redistributing replicas. ...
Added: December 28, 2020
Фадеева М. А., Shchur L., Журнал экспериментальной и теоретической физики 2022 Т. 162 № 6 С. 909-916
The critical behavior of the four-component Potts model on a hexagonal lattice is studied numerically. The modified Wang-Landau method with the control of the density of states estimation accuracy is used. A finite-dimensional analysis of the results obtained confirms the presence of a second-order phase transition with critical exponents corresponding to the universality class of ...
Added: September 5, 2022
Burovskiy E., Janke W., Guskova M. et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2019 Vol. 100 No. 6 P. 063303-1-063303-8
We study properties of Markov chain Monte Carlo simulations of classical spin models with local updates. We derive analytic expressions for the mean value of the acceptance rate of single-spin-flip algorithms for the one-dimensional Ising model. We find that for the Metropolis algorithm the average acceptance rate is a linear function of energy. We further provide numerical results ...
Added: November 5, 2019
Bondarenko S., Сапронов А. А., Computer Physics Communications 2013 No. 184 P. 2343-2350
mcsanc is a Monte-Carlo tool based on the SANC (Support for Analytic and Numeric Calculations for experiments at colliders) modules for higher order calculations in hadron collider physics. It allows to evaluate NLO QCD and EW cross sections for Drell-Yan processes (inclusive), associated Higgs and gauge boson production and single-top quark production in s- and ...
Added: June 27, 2018
Blinov V. N., Журнал экспериментальной и теоретической физики 2013 Т. 144 № 2 С. 397-404
Численное моделирование модели Штокмаера проводится методом Монте-Карло для частиц с достаточно большим дипольным моментом (m*<4.2). При концентрациях 0.16<p<0.31 показано наличие колончатой фазы, состоящей из параллельных цилиндрических слоёв, причём в каждом цилиндре частицы образуют кристаллическую структуру, а их дипольи сонаправлены и параллельны оси цилиндра. Направления диполей ближайших цилиндров противоположны. ...
Added: December 24, 2013
Weigel M., Barash L., Shchur L. et al., / Cornell University. Series cond-mat "arxiv.org". 2021. No. 2102.06611.
Population annealing is a recent addition to the arsenal of the practitioner in computer simulations in statistical physics and beyond that is found to deal well with systems with complex free-energy landscapes. Above all else, it promises to deliver unrivaled parallel scaling qualities, being suitable for parallel machines of the biggest caliber. Here we study ...
Added: February 15, 2021
Shchur L., Journal of Physics: Conference Series 2019 Vol. 1252 P. 012010-1-012010-7
We review recent advances in the analysis of the Wang–Landau algorithm, which is designed for the direct Monte Carlo estimation of the density of states (DOS). In the case of a discrete energy spectrum, we present an approach based on introducing the transition matrix in the energy space (TMES). The TMES fully describes a random ...
Added: August 22, 2019
Фадеева М. А., Shchur L., Journal of Physics: Conference Series 2018 Vol. 955 No. 012028 P. 1-4
We present preliminary results of the investigation of the properties of the Markov random walk in the energy space generated by the Wang-Landau probability. We build transition matrix in the energy space (TMES) using the exact density of states for one-dimensional and two-dimensional Ising models. The spectral gap of TMES is inversely proportional to the ...
Added: February 1, 2018
Golo V. L., Blinov V. N., Письма в Журнал экспериментальной и теоретической физики 2012 Т. 96 № 7 С. 523-527
A new method based on the local analysis of the orientational order has been presented for analysis of the phase behavior of the Stockmayer fluid. A quantity has been introduced to quantitatively describe the ordering degree of particles at small distances. It has been used to analyze the phase diagram of the model under consideration. ...
Added: December 24, 2013
Norman G., Saitov I., Sartan R., Contributions to Plasma Physics 2019 Vol. 59 No. 6 P. e201800173
Warm dense hydrogen is studied in the region of fluid–fluid phase transition within
the framework of the density functional theory. We report a procedure of obtaining
metastable states and calculate the equation of state. Metastable states are diagnosed by pair correlation functions and values of conductivity. We obtain a strong
overlapping through the density of metastable and equilibrium ...
Added: October 30, 2019
Буров А.А., Герман А. Д., Косенко И. И., Космические исследования 2014 Т. 52 № 4 С. 307-312
The problem of planar oscillations of a pendulum with variable length suspended on the Moon’s surface is considered. It is assumed that the Earth and Moon (or, in the general case, a planet and its satellite, or an asteroid and a spacecraft) revolve around the common center of mass in unperturbed elliptical Keplerian orbits. We ...
Added: November 8, 2014
Guskova M., Shchur V., Shchur L., Lobachevskii Journal of Mathematics 2020 Vol. 41 No. 6 P. 992-995
We simulate the oscillation of the viscous drop in the viscous liquid. We combine methods of chromodynamics model and Shan-Chen pseudo-potential for the immiscible fluids. We measure the frequency of the first nontrivial eigenmode using the initial ellipsoid form of the drop. Drop oscillates about the equilibrium spherical form of radius $R$. Computed frequency as ...
Added: June 2, 2020
IEEE, 2015
Added: March 16, 2015
Зеленый Л. М., Григоренко Е. Е., Малова Х. В. et al., Письма в Журнал экспериментальной и теоретической физики 2018 Т. 108 № 8 С. 586-599
В статье представлены наблюдения токовых конфигураций с магнитным широм в хвосте магнитосферы Земли спутниковым квартетом Cluster, и в солнечном ветре - спутником Wind. Показано, что в токовых конфигурациях с магнитным широм наблюдаются следующие структурные особенности: 1) утолщение токового слоя; 2) распределение плотности плазмы, асимметричное относительно плоскости слоя; 3) формирование асимметричного профиля плотности тока. Рассмотрены кинетические ...
Added: March 5, 2020
Пенза : ПГУ, 2015
В сборник трудов включены доклады юбилейного ХХ-го Международного симпозиума «Надежность и качество», проходившего с 25 по 31 мая 2015 г. в городе Пензе.
Рассмотрены актуальные проблемы теории и практики повышения надежности и качества; эффективности внедрения инновационных и информационных технологий в фундаментальных научных и прикладных исследованиях, образовательных и коммуникативных системах и средах, экономике и юриспруденции; методов и ...
Added: May 31, 2015
Сапронов А. А., Aad G., Glazov A., Physics Letters B 2016 Vol. 759 P. 601-621
Measurements of the W±→ℓ±ν and Z→ℓ+ℓ− production cross sections (where ℓ±=e±,μ± ) in proton–proton collisions at s=13 TeV are presented using data recorded by the ATLAS experiment at the Large Hadron Collider, corresponding to a total integrated luminosity of 81 pb −1 . The total inclusive W± -boson production cross sections times the single-lepton-flavour branching ratios ...
Added: August 7, 2018
Сапронов А. А., Aaboud M., Journal of High Energy Physics 2017 Vol. 2017 No. 12 P. 1-78
This paper presents a measurement of the triple-differential cross section for the Drell-Yan process Z/γ * → ℓ + ℓ − where ℓ is an electron or a muon. The measurement is performed for invariant masses of the lepton pairs, m ℓℓ , between 46 and 200 GeV using a sample of 20.2 fb−1of pp collisions data at a centre-of-mass energy of s√=8s=8 TeV collected by the ATLAS detector at the LHC ...
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Aaij R., Beteta C. A., Ustyuzhanin A. et al., Physical Review D - Particles, Fields, Gravitation and Cosmology 2020 No. 102 P. 071101
The Ξc0 baryon is unstable and usually decays into charmless final states by the c→sud¯ transition. It can, however, also disintegrate into a π- meson and a Λc+ baryon via s quark decay or via cs→dc weak scattering. The interplay between the latter two processes governs the size of the branching fraction B(Ξc0→π-Λc+), first measured ...
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Burovskiy E., Cheianov V., Gamayun O. et al., Physical Review A: Atomic, Molecular, and Optical physics 2014 Vol. 89 P. 041601
We investigate the time evolution of the momentum of an impurity atom injected into a degenerate Tonks-Girardeau gas. We establish that given an initial momentum p0 the impurity relaxes to a steady state with a nonvanishing momentum p∞. The nature of the steady state is found to depend drastically on whether the masses of the impurity and the host ...
Added: September 7, 2016