共查询到20条相似文献,搜索用时 15 毫秒
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Christopher G. Jesudason 《Journal of statistical physics》1996,82(3-4):1207-1211
Simple criteria for convergence of Monte Carlo algorithms not necessarily requiring detailed balance for any specified transition probability are derived and it is shown that it is possible to view the algorithm as a superimposition of a Brownian motion on configurational space coupled to the transition probabilities. As such, the error contributions due to a particular Monte Carlo algorithm and the integration limits in configuration space must be distinguished from those due to the nonuniform sampling of the Brownian motion, and criteria related to the number of steps required to distinguish these errors are provided for the simplest cases involving one dimension and symmetrical probability distributions. 相似文献
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A previously described algorithm [T.A. Brunner, T.J. Urbatsch, T.M. Evans, N.A. Gentile, Comparison of four parallel algorithms for domain decomposed implicit Monte Carlo, Journal of Computational Physics 212 (2) (2006) 527–539] for doing domain decomposed particle Monte Carlo calculations in the context of thermal radiation transport has been improved. It has been extended to support cases where the number of particles in a time step are unknown at the beginning of the time step. This situation arises when various physical processes, such as neutron transport, can generate additional particles during the time step, or when particle splitting is used for variance reduction. Additionally, several race conditions that existed in the previous algorithm and could cause code hangs have been fixed. This new algorithm is believed to be robust against all race conditions. The parallel scalability of the new algorithm remains excellent. 相似文献
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A de Lataillade S BlancoY Clergent J.L DufresneM El Hafi R Fournier 《Journal of Quantitative Spectroscopy & Radiative Transfer》2002,75(5):529-538
It is shown that, starting from any existing Monte Carlo algorithm for estimation of a physical quantity A, it is possible to implement a simple additional procedure that simultaneously estimates the sensitivity of A to any problem parameter. The corresponding supplementary cost is very low as no additional random sampling is required. The principle is presented on a formal basis and simple radiative transfer examples are used for illustration. 相似文献
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Tohru Koma 《Journal of statistical physics》1993,71(1-2):269-297
We propose a new Monte Carlo method for calculating eigenvalues of transfer matrices leading to free energies and to correlation lengths of classical and quantum many-body systems. Generally, this method can be applied to the calculation of the maximum eigenvalue of a nonnegative matrix  such that all the matrix elements of Âk are strictly positive for an integerk. This method is based on a new representation of the maximum eigenvalue of the matrix  as the thermal average of a certain observable of a many-body system. Therefore one can easily calculate the maximum eigenvalue of a transfer matrix leading to the free energy in the standard Monte Carlo simulations, such as the Metropolis algorithm. As test cases, we calculate the free energies of the square-lattice Ising model and of the spin-1/2XY Heisenberg chain. We also prove two useful theorems on the ergodicity in quantum Monte Carlo algorithms, or more generally, on the ergodicity of Monte Carlo algorithms using our new representation of the maximum eigenvalue of the matrixÂ. 相似文献
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Frank W. Elliott Jr. Andrew J. Majda David J. Horntrop Richard M. McLaughlin 《Journal of statistical physics》1995,81(3-4):717-736
Two hierarchical Monte Carlo methods for the generation of self-similar fractal random fields are compared and contrasted. The first technique, successive random addition (SRA), is currently popular in the physics community. Despite the intuitive appeal of SRA, rigorous mathematical reasoning reveals that SRA cannot be consistent with any stationary power-law Gaussian random field for any Hurst exponent; furthermore, there is an inherent ratio of largest to smallest putative scaling constant necessarily exceeding a factor of 2 for a wide range of Hurst exponentsH, with 0.30<H<0.85. Thus, SRA is inconsistent with a stationary power-law fractal random field and would not be useful for problems that do not utilize additional spatial averaging of the velocity field. The second hierarchical method for fractal random fields has recently been introduced by two of the authors and relies on a suitable explicit multiwavelet expansion (MWE) with high-moment cancellation. This method is described briefly, including a demonstration that, unlike SRA, MWE is consistent with a stationary power-law random field over many decades of scaling and has low variance. 相似文献
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It is proved that every dynamic Monte Carlo algorithm for the self-avoiding walk based on a finite repertoire of local,N-conserving elementary moves is nonergodic (hereN is the number of bonds in the walk). Indeed, for largeN, each ergodic class forms an exponentially small fraction of the whole space. This invalidates (at least in principle) the use of the Verdier-Stockmayer algorithm and its generalizations for high-precision Monte Carlo studies of the self-avoiding walk. 相似文献
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Maria Serena Causo 《Journal of statistical physics》2002,108(1-2):247-281
We present a dynamic nonlocal hybrid Monte Carlo algorithm consisting of pivot and cut-and-permute moves. The algorithm is suitable for the study of polymers in semiconfined geometries at the ordinary transition, where the pivot algorithm exhibits quasi-ergodic problems. The dynamic properties of the proposed algorithm are studied in d=3. The hybrid dynamics is ergodic and exhibits the same optimal critical behavior as the pivot algorithm in the bulk. 相似文献
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Patrick S. Brantley 《Journal of Quantitative Spectroscopy & Radiative Transfer》2011,112(4):599-618
We numerically investigate the accuracy of two Monte Carlo algorithms originally proposed by Zimmerman [1] and Zimmerman and Adams [2] for particle transport through binary stochastic mixtures. We assess the accuracy of these algorithms using a standard suite of planar geometry incident angular flux benchmark problems and a new suite of interior source benchmark problems. In addition to comparisons of the ensemble-averaged leakage values, we compare the ensemble-averaged material scalar flux distributions. Both Monte Carlo transport algorithms robustly produce physically realistic scalar flux distributions for the benchmark transport problems examined. The base Monte Carlo algorithm reproduces the standard Levermore-Pomraning model [3] and [4] results. The improved Monte Carlo algorithm generally produces significantly more accurate leakage values and also significantly more accurate material scalar flux distributions. We also present deterministic atomic mix solutions of the benchmark problems for comparison with the benchmark and the Monte Carlo solutions. Both Monte Carlo algorithms are generally significantly more accurate than the atomic mix approximation for the benchmark suites examined. 相似文献
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We report virial coefficients up to third order in density for molecular nitrogen, investigating 103 temperatures in the range (15 K, 3000 K). All calculations are based on an ab initio-based potential taken from the literature. Path-integral Monte Carlo (PIMC) is applied to account for nuclear quantum effects, and these results are compared to a more approximate but faster semiclassical treatment. Additionally, we examine a PIMC approach that employs semiclassical beads for the path-integral images, but find that it offers marginal advantage. A recently developed orientation sampling algorithm is used in conjunction with Mayer sampling to compute precise virial coefficients. We find that, within the precision of our calculations of the second-order coefficient (B2), semiclassical methods are adequate for temperatures greater than 250 K, and are needed to correct classical behaviour for temperatures as high as 800 K. For the third-order coefficient (B3), the semiclassical methods are adequate above 150 K, and are required up to the highest temperature examined (3000 K) in order to correct the classical treatment within the precision of the calculations. However, three-body contributions to the potential are much more significant than nuclear quantum effects for the evaluation of B3. 相似文献
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High resolution Monte Carlo simulations are used to examine the finite size behavior of Q-state Potts models in two dimensions. For Q = 3 we find that at the critical point bulk properties are subject to much larger corrections to finite size scaling than were previously realized. For Q = 4 we find that corrections to finite size scaling are subtle and that the multiplicative logarithmic correction is insufficient to correct the dominant terms. 相似文献
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Braden Kelly 《Molecular physics》2019,117(20):2778-2785
ABSTRACTWe describe a new algorithm for the molecular simulation of chemical reaction equilibria, which we call the Reactive Kinetic Monte Carlo (ReKMC) algorithm. It is based on the use of the equilibrium Kinetic Monte Carlo (eKMC) method (Ustinov et al., J. Colloid Interface Sci., 2012, 366, 216–223) to generate configurations in the underlying nonreacting system and to calculate the species chemical potentials at essentially zero marginal computational cost. We consider in detail the typical case of specified temperature, T and pressure, P, but extensions to other thermodynamic constraints are straightforward in principle. In the course of this work, we also demonstrate an alternative method for calculating simulation box volume changes in NPT ensemble simulations to achieve the specified P. We consider two sets of example reacting systems previously considered in the literature, and compare the ReKMC results and computational efficiencies with those of different implementations of the REMC algorithm (Turner et al., Molec. Simulation, 2008, 34, 119–146). 相似文献
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Iwan Cornelius Susanna Guatelli Pauline Fournier Jeffrey C. Crosbie Manuel Sanchez del Rio Elke Bräuer‐Krisch Anatoly Rosenfeld Michael Lerch 《Journal of synchrotron radiation》2014,21(3):518-528
Microbeam radiation therapy (MRT) is a synchrotron‐based radiotherapy modality that uses high‐intensity beams of spatially fractionated radiation to treat tumours. The rapid evolution of MRT towards clinical trials demands accurate treatment planning systems (TPS), as well as independent tools for the verification of TPS calculated dose distributions in order to ensure patient safety and treatment efficacy. Monte Carlo computer simulation represents the most accurate method of dose calculation in patient geometries and is best suited for the purpose of TPS verification. A Monte Carlo model of the ID17 biomedical beamline at the European Synchrotron Radiation Facility has been developed, including recent modifications, using the Geant4 Monte Carlo toolkit interfaced with the SHADOW X‐ray optics and ray‐tracing libraries. The code was benchmarked by simulating dose profiles in water‐equivalent phantoms subject to irradiation by broad‐beam (without spatial fractionation) and microbeam (with spatial fractionation) fields, and comparing against those calculated with a previous model of the beamline developed using the PENELOPE code. Validation against additional experimental dose profiles in water‐equivalent phantoms subject to broad‐beam irradiation was also performed. Good agreement between codes was observed, with the exception of out‐of‐field doses and toward the field edge for larger field sizes. Microbeam results showed good agreement between both codes and experimental results within uncertainties. Results of the experimental validation showed agreement for different beamline configurations. The asymmetry in the out‐of‐field dose profiles due to polarization effects was also investigated, yielding important information for the treatment planning process in MRT. This work represents an important step in the development of a Monte Carlo‐based independent verification tool for treatment planning in MRT. 相似文献
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Masuo Suzuki 《Journal of statistical physics》1986,43(5-6):883-909
A short review is given concerning the quantum statistical Monte Carlo method based on the equivalence theorem(1) thatd-dimensional quantum systems are mapped onto (d+1)-dimensional classical systems. The convergence property of this approximate tansformation is discussed in detail. Some
applications of this geneal appoach to quantum spin systems are reviewed. A new Monte Carlo method, “thermo field Monte Carlo
method,” is presented, which is an extension of the projection Monte Carlo method at zero temperature to that at finite temperatures.
Invited talk presented at “Frontiers of Quantum Monte Carlo,” Los Alamos National Laboratory, September 3–6, 1985. 相似文献
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Faming Liang 《Journal of statistical physics》2006,122(3):511-529
The flat histogram Monte Carlo algorithms have been successfully used in many problems in scientific computing.However, there
is no a rigorous theory for the convergence of the algorithms. In this paper, a modified flat histogram algorithm is presented
and its convergence is studied. The convergence of the multicanonical algorithm and the Wang-Landau algorithm is argued based
on their relations to the modified algorithm. The numerical results show the superiority of the modified algorithm to the
multicanonical and Wang-Landau algorithms.
PACS number: 02.70.Tt, 02.50.Ng 相似文献
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ABSTRACTWe describe a simple method of incorporating the finite mass of the nucleus directly into atomic variational Monte Carlo calculations. To test this algorithm we computed the energy and 20 other properties of 4He. We then compared these values with those obtained from our earlier infinite nuclear mass algorithm. All of our expectation values are in excellent agreement with previous results on this system. 相似文献
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J. Houdayer 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,22(4):479-484
A new Monte Carlo algorithm for 2-dimensional spin glasses is presented. The use of clusters makes possible global updates
and leads to a gain in speed of several orders of magnitude. As an example, we study the 2-dimensional ±J Edwards-Anderson model. The new algorithm allows us to equilibrate systems of size 1002 down to temperature T = 0.1. Our main result is that the correlation length diverges as an exponential ( ξ∼e
2βJ) and not as a power law as T↦T
c = 0.
Received 10 January 2001 and Received in final form 29 May 2001 相似文献
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We propose a bilinear sampling algorithm in the Green's function Monte Carlo for expectation values of operators that do not commute with the Hamiltonian and for differences between eigenvalues of different Hamiltonians. The integral representations of the Schrödinger equations are transformed into two equations whose solution has the form
a(x) t(x, y)b(y), where a and b are the wavefunctions for the two related systems andt(x, y) is a kernel chosen to couplex andy. The Monte Carlo process, with random walkers on the enlarged configuration spacex y, solves these equations by generating densities whose asymptotic form is the above bilinear distribution. With such a distribution, exact Monte Carlo estimators can be obtained for the expectation values of quantum operators and for energy differences. We present results of these methods applied to several test problems, including a model integral equation, and the hydrogen atom. 相似文献