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Obviating the bin width effect of the 1/t algorithm for multidimensional numerical integration

APPLIED NUMERICAL MATHEMATICS 2016年 104卷 133-140页

作者： Atisattapong, Wanyok Maruphanton, Pasin Thammasat Univ Fac Sci & Technol Dept Math & Stat Pathum Thani 12120 Thailand

In this work we improve the accuracy and the convergence of the 1/t algorithm for multidimensional numerical integration. The proposed strategy is to introduce a new approximation method which obviates the bin width effect of the conventional 1/t algorithm by using the average of y values, which varies as the number of Monte Carlo trials changes, instead of the fixed value of y. The non-convergence of the 1/t algorithm and the convergence of the new method are proved by theoretical analysis. The potential of the method is illustrated by the evaluation of one-, two- and multi- dimensional integrals up to six dimensions. Our results show that the numerical estimates from our method converge to their exact values without either error saturation or the bin with effect, in contrast with the conventional 1/t algorithm. (C) 2015 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： Monte Carlo integration wang-landau algorithm

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Thermodynamic, critical properties and phase transitions of the Ising model on a square lattice with competing interactions

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SOLID STATE COMMUNICATIONS 2016年 233卷 35-40页

作者： Ramazanov, M. K. Murtazaev, A. K. Magomedov, M. A. RAS Inst Phys Dagestan Sci Ctr Makhachkala 367003 Russia Dagestan State Univ Makhachkala 367000 Russia

The thermodynamic and critical properties, and phase transitions of two-dimensional Ising model on a square lattice with competing interactions are investigated by the Monte Carlo method. Estimations are made for the magnitude relations of the next-nearest-neighbor and nearest-neighbor exchange interactions r=J(2)/J(1) in the value ranges of 0.1 <= r <= 1.0. The anomalies of thermodynamic observables are shown to be present in this model on the interval 0.45 <= r <= 0.5. The phase diagram for the dependence of the critical temperature on a value of next-nearest neighbor interaction is plotted. A phase transition for all values in the interval 0.45 <= r <= 0.5 is shown to be a second order. Our data show that the temperature of the heat capacity maximum at r=0.5 tends to a finite value. The static critical exponents of the heat capacity a, susceptibility gamma, order parameter beta, correlation length nu, and the Fisher exponent eta are calculated by means of the finite-size scaling theory. It is found that the change in next-nearest neighbor interaction value in the range 0.7 <= r <= 1.0 leads to nonuniversal critical behavior. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Frustration Monte Carlo method wang-landau algorithm Ising model Phase transitions

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Evaluation of the grand-canonical partition function using expanded wang-landau simulations. V. Impact of an electric field on the thermodynamic properties and ideality contours of water

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JOURNAL OF CHEMICAL PHYSICS 2016年第18期145卷 184504-184504页

作者： Desgranges, Caroline Delhommelle, Jerome Univ North Dakota Dept Chem 151 Cornell St Stop 9024 Grand Forks ND 58202 USA

Using molecular simulation, we assess the impact of an electric field on the properties of water, modeled with the SPC/E potential, over a wide range of states and conditions. Electric fields of the order of 0.1 V/angstrom and beyond are found to have a significant impact on the grand-canonical partition function of water, resulting in shifts in the chemical potential at the vapor-liquid coexistence of up to 20%. This, in turn, leads to an increase in the critical temperatures by close to 7% for a field of 0.2 V/angstrom, to lower vapor pressures, and to much larger entropies of vaporization (by up to 35%). We interpret these results in terms of the greater density change at the transition and of the increased structural order resulting from the applied field. The thermodynamics of compressed liquids and of supercritical water are also analyzed over a wide range of pressures, leading to the determination of the Zeno line and of the curve of ideal enthalpy that span the supercritical region of the phase diagram. Rescaling the phase diagrams obtained for the different field strengths by their respective critical properties allows us to draw a correspondence between these systems for fields of up to 0.2 V/angstrom. Published by AIP Publishing.

关键词： CANONICAL partition function wang-landau algorithm ELECTRIC fields THERMAL properties of water MOLECULAR simulation methods VAPOR-liquid equilibrium

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Control globular structure formation of a copolymer chain through inverse design

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JOURNAL OF CHEMICAL PHYSICS 2016年第22期144卷 224902-224902页

作者： Yang, Xi Lu, Zhong-Yuan Jilin Univ Inst Theoret Chem State Key Lab Supramol Struct & Mat Changchun 130021 Peoples R China Jilin Univ Inst Theoret Chem State Key Lab Supramol Struct & Mat Int Joint Res Lab Nanomicro Architecture Chem Changchun 130021 Peoples R China

A copolymer chain in dilute solution can exhibit various globular structures with characteristic morphologies, which makes it a potentially useful candidate for artificial materials design. However, the chain has a huge conformation space and may not naturally form the globular structure we desire. An ideal way to control globular structure formation should be inverse design, i.e., starting from the target structure and finding out what kind of polymers can effectively generate it. To accomplish this, we propose an inverse design procedure, which is combined with wang-landau Monte Carlo to fully and precisely explore the huge conformation space of the chain. Starting from a desired target structure, all the geometrically possible sequences are exactly enumerated. Interestingly, reasonable interaction strengths are obtained and found to be not specified for only one sequence. Instead, they can be combined with many other sequences and also achieve a relatively high yield for target structure, although these sequences may be rather different. These results confirm the possibility of controlling globular structure formation of a copolymer chain through inverse design and pave the way for targeted materials design. Published by AIP Publishing.

关键词： GLOBULAR proteins COPOLYMERS wang-landau algorithm MONTE Carlo method MORPHOLOGY

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Scaling Laws and Critical Properties for fcc and hcp Metals

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JOURNAL OF PHYSICAL CHEMISTRY B 2016年第23期120卷 5255-5261页

作者： Desgranges, Caroline Widhalm, Leanna Delhommelle, Jerome Univ N Dakota Dept Chem Grand Forks ND 58202 USA

The determination of the critical parameters of metals has remained particularly challenging both experimentally, because of the very large temperatures involved, and theoretically, because of the many-body interactions that take place in metals. Moreover, experiments have shown that these systems exhibit an unusually strong asymmetry of their binodal. Recent theoretical work has led to new similarity laws, based on the calculation of the Zeno line and of the underlying Boyle parameters, which provided results for the critical properties of atomic and molecular systems in excellent agreement with experiments. Using the recently developed expanded wang landau (EWL) simulation method, we evaluate the grand-canonical partition function, over a wide range of conditions, for 11 fcc and hcp metals (Ag, Al, Au, Be, Cu, Ir, Ni, Pb, Pd, Pt, and Rh), modeled with a many-body interaction potential. This allows us to calculate the binodal, Zeno line, and Boyle parameters and, in turn, obtain the critical properties for these systems. We also propose two scaling laws for the enthalpy and entropy of vaporization, and identify critical exponents of 0.4 and 1.22 for these two laws, respectively.

关键词： SCALING laws (Nuclear physics) wang-landau algorithm PARTITION functions ENTHALPY ENTROPY VAPORIZATION

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Density-functional Monte-Carlo simulation of CuZn order-disorder transition

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Physical Review B 2016年第2期93卷 024203-024203页

作者： S. N. Khan Markus Eisenbach Materials Science and Technology Division Oak Ridge National Laboratory Oak Ridge Tennessee 37831-6114 USA

We perform a wang-landau Monte-Carlo simulation of a Cu0.5Zn0.5 order-disorder transition using 250 atoms and pairwise atom swaps inside a 5×5×5 body-centered-cubic supercell. Each time step uses energies calculated from density-functional theory via the all-electron Korringa-Kohn-Rostoker method and self-consistent potentials. Here we find that CuZn undergoes a transition from a disordered A2 to an ordered B2 structure, as observed in experiment. Our calculated transition temperature is near 870 K, comparing favorably to the known experimental peak at 750 K. We also plot the entropy, temperature, specific heat, and short-range order as a function of internal energy.

关键词： COPPER compounds DENSITY functional theory MONTE Carlo method wang-landau algorithm BODY centered cubic structure SPECIFIC heat

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THE GIBBS-PLAID BICLUSTERING MODEL

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ANNALS OF APPLIED STATISTICS 2015年第3期9卷 1643-1670页

作者： Chekouo, Thierry Murua, Alejandro Raffelsberger, Wolfgang Univ Texas MD Anderson Canc Ctr Dept Biostat Houston TX 77030 USA Univ Montreal Dept Math & Stat Montreal PQ H3C 3J7 Canada Univ Strasbourg INSERM CNRS ICubeLBGI F-67085 Strasbourg France Univ Strasbourg INSERM CNRS IGBMC F-67404 Illkirch Graffenstaden France

We propose and develop a Bayesian plaid model for biclustering that accounts for the prior dependency between genes (and/or conditions) through a stochastic relational graph. This work is motivated by the need for improved understanding of the molecular mechanisms of human diseases for which effective drugs are lacking, and based on the extensive raw data available through gene expression profiling. We model the prior dependency information from biological knowledge gathered from gene ontologies. Our model, the Gibbs-plaid model, assumes that the relational graph is governed by a Gibbs random field. To estimate the posterior distribution of the bicluster membership labels, we develop a stochastic algorithm that is partly based on the wang-landau flat-histogram algorithm. We apply our method to a gene expression database created from the study of retinal detachment, with the aim of confirming known or finding novel subnetworks of proteins associated with this disorder.

关键词： Clustering relational graph autologistic model wang-landau algorithm plaid model gene expression gene ontology retinal detachment

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First-order phase transition and tricritical scaling behavior of the Blume-Capel model: A wang-landau sampling approach

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Physical Review E 2015年第2期92卷 022134-022134页

作者： Wooseop Kwak Joohyeok Jeong Juhee Lee Dong-Hee Kim Department of Physics Chosun University Gwangju 61452 Korea Department of Physics and Photon Science School of Physics and Chemistry Gwangju Institute of Science and Technology Gwangju 61005 Korea

We investigate the tricritical scaling behavior of the two-dimensional spin-1 Blume-Capel model by using the wang-landau method of measuring the joint density of states for lattice sizes up to 48×48 sites. We find that the specific heat deep in the first-order area of the phase diagram exhibits a double-peak structure of the Schottky-like anomaly appearing with the transition peak. The first-order transition curve is systematically determined by employing the method of field mixing in conjunction with finite-size scaling, showing a significant deviation from the previous data points. At the tricritical point, we characterize the tricritical exponents through finite-size-scaling analysis including the phenomenological finite-size scaling with thermodynamic variables. Our estimation of the tricritical eigenvalue exponents, yt=1.804(5), yg=0.80(1), and yh=1.925(3), provides the first wang-landau verification of the conjectured exact values, demonstrating the effectiveness of the density-of-states-based approach in finite-size scaling study of multicritical phenomena.

关键词： FIRST-order phase transitions PHASE transformations (Physics) wang-landau algorithm MONTE Carlo method FINITE size scaling (Statistical physics)

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Sequence Determines Degree of Knottedness in a Coarse-Grained Protein Model

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Physical Review Letters 2015年第2期114卷 028102-028102页

作者： Thomas Wüst Daniel Reith Peter Virnau Scientific IT Services ETH Zürich 8092 Zürich Switzerland Institut für Physik Johannes Gutenberg-Universität Mainz Staudinger Weg 9 55128 Mainz Germany

Knots are abundant in globular homopolymers but rare in globular proteins. To shed new light on this long-standing conundrum, we study the influence of sequence on the formation of knots in proteins under native conditions within the framework of the hydrophobic-polar lattice protein model. By employing large-scale wang-landau simulations combined with suitable Monte Carlo trial moves we show that even though knots are still abundant on average, sequence introduces large variability in the degree of self-entanglements. Moreover, we are able to design sequences which are either almost always or almost never knotted. Our findings serve as proof of concept that the introduction of just one additional degree of freedom per monomer (in our case sequence) facilitates evolution towards a protein universe in which knots are rare.

关键词： KNOT theory RESEARCH GLOBULAR proteins wang-landau algorithm HYDROPHOBIC interactions MONOMERS

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Dynamical traps in wang-landau sampling of continuous systems: Mechanism and solution

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Physical Review E 2015年第2期92卷 023306-023306页

作者： Yang Wei Koh Adelene Y. L. Sim Hwee Kuan Lee []Bioinformatics Institute 30 Biopolis Street No. 07-01 Matrix Singapore 138671

We study the mechanism behind dynamical trappings experienced during wang-landau sampling of continuous systems reported by several authors. Trapping is caused by the random walker coming close to a local energy extremum, although the mechanism is different from that of the critical slowing-down encountered in conventional molecular dynamics or Monte Carlo simulations. When trapped, the random walker misses the entire or even several stages of wang-landau modification factor reduction, leading to inadequate sampling of the configuration space and a rough density of states, even though the modification factor has been reduced to very small values. Trapping is dependent on specific systems, the choice of energy bins, and the Monte Carlo step size, making it highly unpredictable. A general, simple, and effective solution is proposed where the configurations of multiple parallel wang-landau trajectories are interswapped to prevent trapping. We also explain why swapping frees the random walker from such traps. The efficacy of the proposed algorithm is demonstrated.

关键词： DENSITY of states wang-landau algorithm METALS -- Electron theory CLASSICAL mechanics MECHANICAL movements

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