Showing papers on "Dynamic Monte Carlo method published in 1967"
TL;DR: In this paper, an extension of the Monte Carlo method of Metropolis et al. is described which permits both isochoric and isothermal extrapolations of Monte Carlo data.
Abstract: Extensions of the Monte Carlo method of Metropolis et al. are described which permit both isochoric and isothermal extrapolations of Monte Carlo data. Thermodynamic properties are calculated for liquid argon from Lennard-Jones parameters for a wide V, T-range. The agreement between calculated and experimental values is, on the whole, satisfactory.
152 citations
TL;DR: The use of the Monte Carlo method for the study of deep penetration of radiation into and through shields entails the use of sophisticated methods of variance reduction to make such calculations ec... as mentioned in this paper,.
Abstract: The use of the Monte Carlo method for the study of deep penetration of radiation into and through shields entails the use of sophisticated methods of variance reduction to make such calculations ec...
85 citations
84 citations
TL;DR: In this article, the problem of choosing among point estimators on the basis of their small sample properties is discussed from the sampling point of view, and the indeterminacy of most Monte Carlo studies is analysed and resolved within the framework of statistical decision theory.
Abstract: In this paper the problem of choosing among point estimators on the basis of their small sample properties is discussed from the sampling point of view. The indeterminacy of most Monte Carlo studies is analysed and resolved within the framework of statistical decision theory. A first order autoregressive model is worked through in detail both for its own sake and to illustrate how a complete Monte Carlo study might be done.
51 citations
01 Apr 1967
TL;DR: In this paper, the critical percolation probabilities of a number of two-and three-dimensional lattices were obtained based on Monte Carlo studies of the way in which cluster-size distributions vary as the number of occupied sites in a lattice is progressively increased.
Abstract: In this paper we present results for the critical percolation probabilities of a number of two- and three-dimensional lattices. These results are based upon Monte Carlo studies of the way in which cluster-size distributions vary as the number of occupied sites in a lattice is progressively increased; the principle of the method has been described in some detail in an earlier publication (Dean (1)) in which the results of studies carried out on the ACE computer were reported. The use of a KDF 9 computer with a 32K word high-speed store has now enabled us to obtain results of a very high accuracy indeed; in those cases where our values for critical probabilities can be checked against exactly known values, they differ by no more than 0·1%.
49 citations
TL;DR: In this paper, the evaporation formalism of the compound-statistical theory of nuclear reactions is presented in a form containing the explicit dependence of the emission probability on angular momentum and suitable for computation of excitation functions by the Monte Carlo technique.
36 citations
TL;DR: In this paper, a model for the simulation of the process of mixing ideal particles in an end-loaded barrel mixer is presented, where the only mechanism operating in such a mixer is micromixing by diffusion, which can be considered as a random walk process.
34 citations
TL;DR: This paper discusses a twodimensional unstructured cluster problem, i.e. one in which there is no underlying lattice structure as there is in the structured case, and a Monte Carlo solution is used.
Abstract: In recent years, many papers have appeared describing Monte Carlo techniques which have been applied to structured cluster problems (bond and site) on various twoand threedimensional lattices; see, for example, Frisch, Sonnenblick, Vyssotsky & Hammersley (1961), Frisch, Hammersley & Welsh (1962), Dean (1963). Estimates have been obtained for the expected cluster size, the probability that a point belongs to an infinite cluster, and the critical probability at which infinite clusters occur. In this paper we discuss a twodimensional unstructured cluster problem, i.e. one in which there is no underlying lattice structure as there is in the structured case. It is interesting to note the similarity between the structured and unstructured cases. Consider an infinite plane on which are scattered discs of radius R whose centres are points distributed according to the Poisson law with density A, i.e. the probability that the centre of a disc lies in a small area &A equals A &A + o(6A). A cluster of size n is defined as a set of n discs each of which overlaps at least one other member of the set and none of which overlaps a disc which is not a member of the set. Although the probability of a cluster of size n and the expected number of discs in a cluster depend on the two variables A and R, dimensional analysis suggests that they are functions of only one composite variable t = AR2. This can also be verified by evaluating the probability of a cluster of size n for small values of n. Let pn(t) be the probability of a non-zero cluster of size n, and let e(t) be the expected number of discs in a non-zero cluster. There exists a critical value t = tc at which e(t) becomes infinite (Gilbert, 1961). For t > t, infinite clusters occur. We obtain a graph of e(t) as a function of t and estimate t, by extrapolation. As in the structured cases the difficulties of a direct approach prove insurmountable and hence a Monte Carlo solution is used. Gilbert (1961) has considered this problem in relation to communication networks and the spread of contagious disease. He uses the notation E = 4lTt. He is interested in P,'(E), the probability that a particle belongs to an infinite cluster. This is clearly zero for E < E,. By approximating P,,(E) by PN(E) which is the probability that a particle belongs to a cluster of size N or more, and evaluating PN(E) by a Monte Carlo procedure, he obtains an estimate Ec = 3X2, te = 0255. Section 2 describes a Monte Carlo technique to evaluate e(t) and a graph of e(t) as a
27 citations
25 citations
Journal Article•
20 citations
TL;DR: In this article, a Monte Carlo method for the numerical solution of nonlinear, frequency-dependent, radiative transfer problems is described and the accuracy of the method is investigated with respect to the number of particles required, propagation of statistical error, truncation error and convergence to a known solution.
TL;DR: In this paper, a computational technique based on the method of path integral is studied with a view to finding approximate solutions of a class of two-point boundary-value problems, which are "rough" solutions by Monte Carlo sampling.
Abstract: A computational technique based on the method of path integral is studied with a view to finding approximate solutions of a class of two-point boundary-value problems. These solutions are "rough" solutions by Monte Carlo sampling. From the computational point of view, however, once these rough solutions are obtained for any nonlinear cases, they serve as good starting approximations for improving the solutions to higher accuracy. Numerical results of a few examples are also shown.
TL;DR: In this article, a detailed Monte Carlo analysis in one, two, and three dimensions with different multigroup scattering kernels is presented for a number of actual reactor systems, and several variance reducing sam...
Abstract: A detailed Monte Carlo analysis in one, two, and three dimensions and with different multigroup scattering kernels is presented for a number of actual reactor systems. Several variance reducing sam...
TL;DR: The analog-hybrid computer Monte Carlo technique for solving elliptic and parabolic partial differential equations has been implemented on a new hybrid computer capable of taking statistics over 1000 two-or three-dimensional random walks per second.
Abstract: The analog-hybrid computer Monte Carlo technique for solving elliptic and parabolic partial differential equations has been implemented on a new hybrid computer capable of taking statistics over 1000 two-or three-dimensional random walks per second. This exceptional computing speed and flexible digital control permit direct plotting of partial differential equation solutions; of perhaps even greater interest is the incorporation of such Monte Carlo routines in real-time analog computer setups in process control applications. In this connection, the Monte Carlo method has been extended to a wider class of problems, and is especially applicable to heat conduction/diffusion problems.
TL;DR: In this article, a combination of Monte Carlo and analytical methods is used to calculate the angular distribution of the neutrons in the various orders of scattering, which can be applied to much thicker scattering samples and is much less time consuming than the correction procedures which use the Monte Carlo random walk methods throughout.
01 Jan 1967
TL;DR: In this article, the effect of the grazing flux on the surface-crossing flux estimator and the pillbox track-length estimator used in Monte Carlo calculations was investigated. But it was found that the effect was negligible.
Abstract: Calculations were set up to determine the effect of the grazing flux on the surface-crossing flux estimator and the pillbox track-length estimator used in Monte Carlo calculations. It was found tha...
TL;DR: Two variance reducing techniques, control variates and importance sampling, are described in this paper, which are used in increasing the efficiency of a Monte Carlo evaluation of an integral, are shown under very general conditions that the Bernstein polynomials can serve as both a control variate and an importance sampling function.
Abstract: Two variance reducing techniques, the method of control variates and the method of importance sampling, which are used in increasing the efficiency of a Monte Carlo evaluation of an integral, are described. It is shown under very general conditions that the Bernstein polynomials can serve as both a control variate and an importance sampling function. In addition these methods can also be combined to further increase the efficiency of the Monte Carlo evaluation. An example is given to illustrate the method.
01 Jan 1967
TL;DR: In this paper, the main parameters of cryogenic vacuum chambers are examined and the possibility of their calculation by the Monte Carlo method is shown, and an algorithm for calculating the parameters and its realization on a computer are described.
Abstract: The main parameters of cryogenic vacuum chambers are examined and the possibility of their calculation by the Monte Carlo method is shown. An algorithm for calculating the parameters and its realization on a computer are described.
TL;DR: In this article, a method was described for predicting the neutron multiplication factor of geometrically complicated configurations of unreflected unmoderated enriched-uranium metal from the results of two delayed computations.
Abstract: A method is described for predicting the neutron multiplication factors of geometrically complicated configurations of unreflected unmoderated enriched-uranium metal from the results of two delayed...
TL;DR: A method is given for generating Monte Carlo final states with unit weight, distributed according to Lorentz invariant phase space, and as a result the computer time to generate one event varies only linearly with the number of particles.
01 Jan 1967
TL;DR: Histogram construction via algebraic Monte Carlo method, determining simultaneous effect of several input statistical variables on output variable.
Abstract: Histogram construction via algebraic Monte Carlo method, determining simultaneous effect of several input statistical variables on output variable
TL;DR: In this paper, a Monte Carlo calculation based on a collision density approach was made of the energy and spatial flux distribution in water from a 14.7 MeV neutron fusion source, compared with an earlier moments method solution of the Boltzmann equation.
Abstract: Detailed knowledge of fast neutron interactions is important for conceptual designs of blankets for thermonuclear reactors. A Monte Carlo calculation, based on a collision density approach, was made of the energy and spatial flux distribution in water from a 14.7 MeV neutron fusion source. The results are compared with an earlier moments method solution of the Boltzmann equation. A concurrent experimental study by a threshold detector technique proved relatively ineffective at determining accurate flux spectra near the neutron source because of the dominant influence of uncollided flux. Reasonable agreement between experiment and theory was found, however, in a comparison of measured activation integrals and ones computed from both the Monte Carlo and the moments method results.