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metropolis algorithm for simulating hysteresis in ferromagnetic nanoparticles

PHYSICA B-CONDENSED MATTER 2006年第1-2期372卷 345-349页

作者： De Biasi, E Ramos, CA Zysler, RD Fiorani, D Ctr Atom Bariloche RA-8400 San Carlos De Bariloche Rio Negro Argentina CNR ISM Area Ric Roma I-00016 Rome Italy

We report of Monte Carlo simulations by metropolis algorithm of the magnetization cycles of similar to 3 nm non-interacting ferromagnetic amorphous nanoparticles. Simulations based on a core-shell model, describing the nanoparticles as consisting of a ferromagnetically ordered core and a disordered surface shell, reproduce satisfactorily the significant features observed in experimental magnetization measurement and hysteresis cycles, i.e. H-C(T) and M-r(T) curves. The results provide a clear evidence of the major role played at low temperature by the surface anisotropy and surface-core exchange interaction in determining some anomalies of the hysteresis cycles and the large increase of the effective particle anisotropy at low temperature. (c) 2005 Elsevier B.V. All rights reserved.

关键词： ferromagnetic nanoparticles surface effects Monte Carlo simulation metropolis algorithm

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The metropolis algorithm for on-shell four-momentum phase space

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COMPUTER PHYSICS COMMUNICATIONS 2000年第2-3期127卷 242-260页

作者： Kharraziha, H Moretti, S Univ Hamburg Inst Theoret Phys D-22761 Hamburg Germany Rutherford Appleton Lab Didcot OX11 0QX Oxon England Univ Uppsala Dept Radiat Sci S-75121 Uppsala Sweden

Pie present several implementations of the metropolis method, an adaptive Monte Carlo algorithm, which allow for the calculation of multi-dimensional integrals over arbitrary on-shell four-momentum phase space. The metropolis technique reveals itself very suitable for the treatment of high energy processes in particle physics, particularly when the number of final state objects and of kinematic constraints on the latter gets larger. We compare the performances of the metropolis algorithm with those of other programs widely used in numerical simulations. (C) 2000 Elsevier Science B.V. All rights reserved.

关键词： metropolis algorithm quantum field theory Monte Carlo

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Effect of increasing the energy gap between the two lowest energy states on the mixing time of the metropolis algorithm

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INFORMATION PROCESSING LETTERS 2012年第23期112卷 922-927页

作者： Nakade, Apurv Biswas, Somenath IIT Kanpur Dept Comp Sci & Engn Kanpur 208016 Uttar Pradesh India Chennai Math Inst Kelambakkam 603103 Siruseri India

In order to understand what makes natural proteins fold rapidly. Sali, Shakhnovich and Karplus (1994) [6,7] had used the metropolis algorithm to search for the minimum energy conformations of chains of beads in the lattice model of protein folding. Based on their computational experiments, they concluded that the metropolis algorithm would find the minimum energy conformation of a chain of beads within an acceptable time scale if and only if there is a large gap between the energies of the minimum energy conformation and that of the second minimum. Clote (1999) [1] attempted to support this conclusion by a proof that the mixing time of the underlying Markov chain would decrease as the gap in energies of the minimum energy conformation and that of the second minimum increased. He was able to show that an upper bound on the mixing time does indeed decrease as the energy gap increases. We show in this paper that the mixing time itself, however, is a non-decreasing function of the value of the energy gap. Therefore, our result contradicts what Clote had attempted to prove. (C) 2012 Elsevier B.V. All rights reserved.

关键词： metropolis algorithm Markov chain mixing time Protein folding Randomized algorithms

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Simple Monte Carlo and the metropolis algorithm

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JOURNAL OF COMPLEXITY 2007年第4-6期23卷 673-696页

作者： Mathe, Peter Novak, Erich Univ Jena Math Inst D-07743 Jena Germany Weierstrass Inst Appl Anal & Stochast D-10117 Berlin Germany

We study the integration of functions with respect to an unknown density. Information is available as oracle calls to the integrand and to the non-normalized density function. We are interested in analyzing the integration error of optimal algorithms (or the complexity of the problem) with emphasis on the variability of the weight function. For a corresponding large class of problem instances we show that the complexity grows linearly in the variability, and the simple Monte Carlo method provides an almost optimal algorithm. Under additional geometric restrictions (mainly log-concavity) for the density functions, we establish that a suitable adaptive local metropolis algorithm is almost optimal and outperforms any non-adaptive algorithm. (c) 2007 Elsevier Inc. All rights reserved.

关键词： Monte Carlo methods metropolis algorithm log-concave density rapidly mixing Markov chains optimal algorithms adaptivity complexity

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Efficacy of the metropolis algorithm for the Minimum-Weight Codeword Problem Using Codeword and Generator Search Spaces

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IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION 2020年第4期24卷 664-678页

作者： Ajitha Shenoy, K. B. Biswas, Somenath Kurur, Piyush P. Manipal Acad Higher Educ Dept Informat & Commun Technol Manipal Inst Technol Manipal 576104 India Indian Inst Technol Goa Sch Math & Comp Sci Ponda 403401 India Indian Inst Technol Palakkad Dept Comp Sci & Engn Palakkad 678557 India

This article studies the efficacy of the metropolis algorithm for the minimum-weight codeword problem. The input is a linear code C given by its generator matrix and our task is to compute a nonzero codeword in the code C of least weight. In particular, we study the metropolis algorithm on two possible search spaces for the problem: 1) the codeword space and 2) the generator space. The former is the space of all codewords of the input code and is the most natural one to use and hence has been used in previous work on this problem. The latter is the space of all generator matrices of the input code and is studied for the first time in this article. In this article, we show that for an appropriately chosen temperature parameter the metropolis algorithm mixes rapidly when either of the search spaces mentioned above are used. Experimentally, we demonstrate that the metropolis algorithm performs favorably when compared to previous attempts. When using the generator space, the metropolis algorithm is able to outperform the previous algorithms in most of the cases. We have also provided both theoretical and experimental justification to show why the generator space is a worthwhile search space to use for this problem.

关键词： Combinatorial optimization Markov chain metropolis algorithm minimum-weight codeword mixing time analysis randomized local search heuristics

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Guaranteeing total balance in metropolis algorithm Monte Carlo simulations

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2013年第24期392卷 6288-6299页

作者： Potter, Christopher C. J. Swendsen, Robert H. Carnegie Mellon Univ Pittsburgh PA 15213 USA

The condition of detailed balance has long been used as a proxy for the more difficult-to-prove condition of total balance, which along with ergodicity is required to guarantee convergence of a Markov Chain Monte Carlo (MCMC) simulation to the correct probability distribution. However, some simple-to-program update schemes such as the sequential and checkerboard metropolis algorithms are known not to satisfy detailed balance for such common systems as the Ising model. It has been an open question whether these update schemes satisfy the weaker condition of total balance. In this work, we show that under fairly broad conditions, a large class of update schemes for the metropolis algorithm, including the sequential and checkerboard schemes, do indeed satisfy total balance for important distributions. We also show that detailed balance itself can be satisfied by straightforward modifications to these schemes. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Monte Carlo metropolis algorithm Total balance

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Discrete modelling of continuous dynamic recrystallisation by modified metropolis algorithm

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COMPUTATIONAL MATERIALS SCIENCE 2024年 234卷

作者： Zhu, Siying Borodin, Elijah Jivkov, Andrey P. Univ Manchester Sch Engn Dept Solids & Struct Manchester M13 9PL England

Continuous dynamic recrystallisation (CDRX) is often the primary mechanism for microstructure evolution during severe plastic deformation (SPD) of polycrystalline metals. Its physically realistic simulation remains challenging for the existing modelling approaches based on continuum mathematics because they do not capture important local interactions between microstructure elements and spatial inhomogeneities in plastic strain. An effective discrete method for simulating CDRX is developed in this work. It employs algebraic topology, graph theory and statistical physics tools to represent an evolution of grain boundary networks as a sequence of conversions between low-angle grain boundaries (LAGBs) and high -angle grain boundaries (HAGBs) governed by the principle of minimal energy increase, similar to the well-known Ising model. The energy is minimised by a modified metropolis algorithm. The model is used to predict the equilibrium fractions of HAGBs in several SPD-processed copper alloys. The analysis captures non-equilibrium features of the transitions from sub-grain structures to new HAGB-dominated grain structures and provides estimations of critical values for HAGB fractions and accumulated strain at these transitions.

关键词： Copper alloys Equal-channel angular pressing High-pressure torsion Severe plastic deformation metropolis algorithm Continuous dynamic recrystallisation Grain boundaries Algebraic topology

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On a Generalization of the Preconditioned Crank-Nicolson metropolis algorithm

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FOUNDATIONS OF COMPUTATIONAL MATHEMATICS 2018年第2期18卷 309-343页

作者： Rudolf, Daniel Sprungk, Bjoern Univ Gottingen Inst Math Stochast Goldschmidtstr 7 D-37077 Gottingen Germany Tech Univ Chemnitz Reichenhainer Str 41 D-09107 Chemnitz Germany

metropolis algorithms for approximate sampling of probability measures on infinite dimensional Hilbert spaces are considered, and a generalization of the preconditioned Crank-Nicolson (pCN) proposal is introduced. The new proposal is able to incorporate information on the measure of interest. A numerical simulation of a Bayesian inverse problem indicates that a metropolis algorithm with such a proposal performs independently of the state-space dimension and the variance of the observational noise. Moreover, a qualitative convergence result is provided by a comparison argument for spectral gaps. In particular, it is shown that the generalization inherits geometric convergence from the metropolis algorithm with pCN proposal.

关键词： Markov chain Monte Carlo metropolis algorithm Spectral gap Conductance Bayesian inverse problem

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Robust adaptive metropolis algorithm with coerced acceptance rate

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STATISTICS AND COMPUTING 2012年第5期22卷 997-1008页

作者： Vihola, Matti Univ Jyvaskyla Dept Math & Stat Jyvaskyla 40014 Finland

The adaptive metropolis (AM) algorithm of Haario, Saksman and Tamminen (Bernoulli 7(2):223-242, 2001) uses the estimated covariance of the target distribution in the proposal distribution. This paper introduces a new robust adaptive metropolis algorithm estimating the shape of the target distribution and simultaneously coercing the acceptance rate. The adaptation rule is computationally simple adding no extra cost compared with the AM algorithm. The adaptation strategy can be seen as a multidimensional extension of the previously proposed method adapting the scale of the proposal distribution in order to attain a given acceptance rate. The empirical results show promising behaviour of the new algorithm in an example with Student target distribution having no finite second moment, where the AM covariance estimate is unstable. In the examples with finite second moments, the performance of the new approach seems to be competitive with the AM algorithm combined with scale adaptation.

关键词： Acceptance rate Adaptive Markov chain Monte Carlo Ergodicity metropolis algorithm Robustness

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Performance of metropolis algorithm for the Minimum Weight Code Word Problem 14

Performance of Metropolis Algorithm for the Minimum Weight C...

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16th Genetic and Evolutionary Computation Conference (GECCO)

作者： Shenoy, Ajitha K. B. Biswas, Somenath Kurur, Piyush P. Indian Inst Technol Dept Comp Sci & Engn Kanpur 208016 Uttar Pradesh India

ISBN: (纸本)9781450326629

We study the performance of the metropolis algorithm for the problem of finding a code word of weight less than or equal to M, given a generator matrix of an [n, k]-binary linear code. The algorithm uses the set Sk of all k x k invertible matrices as its search space where two elements are considered adjacent if one can be obtained from the other via an elementary row operation (i.e by adding one row to another or by swapping two rows.) We prove that the Markov chains associated with the metropolis algorithm mix rapidly for suitable choices of the temperature parameter T. We ran the metropolis algorithm for a number of codes and found that the algorithm performed very well in comparison to previously known experimental results.

关键词： Theory algorithms metropolis algorithm Minimum weight code word search space conductance rapid mixing of Markov chain

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