Showing papers on "Dynamic Monte Carlo method published in 1966"
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01 Nov 1966
TL;DR: In this article, a simulation study is made of vacancy migration in binary ordered alloys AB (simple cubic) and B3A (face-centred cubic), and the resulting self-diffusion is calculated and in the first case compares very favourably with the existing experimental results of Kuper et al.
Abstract: Using a Monte Carlo technique, a simulation study is made of vacancy migration in the binary ordered alloys AB (simple cubic) and B3A (face-centred cubic). The resulting self-diffusion is calculated and in the first case compares very favourably with the existing experimental results of Kuper et al. for a body-centred binary alloy. Quite different results are predicted for an alloy of form B3A and it is hoped that comparison with experiment will establish the importance of the isolated-vacancy mechanism as the means for producing self-diffusion.
301 citations
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108 citations
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66 citations
01 Jul 1966
TL;DR: In this paper, a Monte Carlo method was used to compute the molecular velocity distribution under conditions far from equilibrium, which is the only known method capable of computing the velocity distribution of dilute gases.
Abstract: : A Monte Carlo method of solving the fundamental equation of the kinetic theory of dilute gases has been developed and successfully applied to two problems, one involving translational relaxation of a spatially homogeneous gas and the other a plane steady shock of arbitrary strength (shock strength limited only by the fineness of the velocity space mesh) This is the first and only method capable of computing the molecular velocity distribution under conditions far from equilibrium The essence of the problem is evaluation of the non-linear five-dimensional collision integral Straight forward numerical quadrature would require about a year on the fastest present day computers The computation time is reduced to a practical value, of the order of an hour, by a statistical sampling technique closely resembling the real statistical collision phenomena in the gas Computations to date have been restricted to elastic sphere scattering of molecules without internal degrees of freedom Differential scattering cross-sections other than elastic sphere can be accommodated in the computer program without complications or computing time penalty Introduction of one or two internal molecular degrees of freedom will increase the complexity and computing time, but not to an impractical degree
54 citations
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TL;DR: In this paper, a theoretical model of a simple analogue of a system of hydrocarbon chains in which one end of each chain is fixed in a plane and in which the chains can coil and interact with each other is presented.
Abstract: A theoretical model system has been devised to act as a simple analogue of a system of hydrocarbon chains in which one end of each chain is fixed in a plane and in which the chains can coil and interact with each other. Using a Monte Carlo method, the end-to-end distance and other properties are determined as a function of their density using two different potential functions and restricting the chains to a two-dimensional hexagonal lattice. The possible relevance of the results obtained from this theoretical model to real physical situations, such as the configurations of chains in a monolayer, in bilayers and in biological membranes, is discussed.
38 citations
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TL;DR: In this article, a Monte Carlo procedure was used to simulate flexible branched macromolecules on a high speed digital computer and the effects of branching on these properties were discussed.
Abstract: A Monte Carlo procedure was used to simulate flexible branched macromolecules on a high‐speed digital computer. The molecules studied were of the regular‐comb type. Configurational and statistical thermodynamic properties were evaluated according to prescriptions used for linear flexible chains. The effects of branching on these properties are discussed.
36 citations
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TL;DR: The analysis of the classical four-body problem as applied by Monte Carlo techniques to chemical reactions of the type A+BCD→AB+CD is reported in this paper using a modified form of a Blais-Bunker interaction potential surface.
Abstract: The analysis of the classical four‐body problem as applied by Monte Carlo techniques to chemical reactions of the type A+BCD→AB+CD is reported. Using a modified form of a Blais—Bunker interaction potential surface, the model is applied to the reaction of K with C2H5I by approximating the C2H5 radical as being two carbon atoms, one of mass 14 amu, the other of mass 15 amu. Hamilton's equations are solved numerically, and by Monte Carlo averaging over the initial variables for 1060 different trajectories, various attributes of the reaction are calculated; these include the total reaction cross section, the differential reaction cross section, and the distribution of the heat of reaction among the available degrees of freedom of the products. It is found that the total reaction cross section is 15.9 A2. This result, which is less than that obtained by similar methods for the (K, CH3I) system, is interpreted as reflecting the increased steric hindrance present in the more bulky system.The differential reactio...
31 citations
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TL;DR: This chapter discusses the history of distribution sampling prior to the era of the computer and its relevance to simulation, and the role of Monte Carlo in this era.
Abstract: program. Proj. No. 90. 17-019(2), Appl. HeN. Lab., U. S. Steel, Monroeville, Pa., July 9, 1963. 57. McARTRVR, D.S. Strategy in research--alternative methods for design of experiments. Trans. Eng. Man. (1961), 34--40. 58. McMILLAN, CLAUDE, AND GONZALEZ, RICHARD ~. Systems Analysis. Richard D. Irwin, Inc., Homewood, Ill., 1965. 59. MARKOWITZ, H. M., HAUSNER, BERNARD, AND I~ARR, H. W. SIMSCRIPT: A simulation programming language. RM3310, Rand Corp., (Nov. 1962). 60. MARSHALL, A.W. Experimentation by simulation and Monte Carlo. P-1174, Rand Corp., Jan. 28, 1958. 61. MEYER, HERBERT A., ED. Symposium on Monte Carlo Methods. John Wiley, New York, 1956. 62. MOOD, A. M. Introduction to the Theory of Statistics. McGraw Hill, New York, 1950. 63. NAYLOR, THOMAS IH., BALINTFY, JOSEPH L., BURDICK, DONALD S., AND CHU, KONG. Computer Simulation Techniques. John Wiley, New York, 1966. 64. PARZEN, EMANUEL. Mathematical considerations in the estimation of spectra. Teehnometrics 3 (May, 1961), 167-190. 65. . Stochastic Processes. Holden-Day, San Francisco, 1962. 66. QUENOUILLE, M.H. The Design and Analysis of Experiment. Hafner, New York, 1953. 67. SIMPAC user's manual. TM 602/000/00, Systems Dec. Corp., Santa Monica, Calif., Apr. 15, 1962. 68. SOBEL, M., ANn WALD, A. A sequential decision procedure for choosing one of three hypotheses concerning the unknown mean of a normal distribution. Ann. Math. Statist. 10 (1939). 69. TEICHROEW, DANIEL. A history of distribution sampling prior to the era of the computer and its relevance to simulation. Amer. Statist. Ass. J. (Mar. 1965), 27---49. 70. AND LUBIN, JOHN F. Computer simulation: discussion of the technique and comparison of languages. Working Paper 20, Grad. Sch. Business, Stanford U., Stanford, Calif., Aug. 26, 1964. 71. TOCHER, K.D. The Art of Simulation. Van Nostrand, Princeton, N. J., 1963. 72. TVKEY, JOHN W. Discussion emphasizing the connection between analysis of variance and spectral analysis. Technometrics 3 (May, 1961), 191-220. 73. WALD, A. Sequential Analysis. John Wiley, New York, 1947. 74. WALSH, JOHN E. Use of linearized nonlinear regression for simulations involving Monte Carlo. Oper. Res. 11 (1963), 228-235. 75. WINER, B. J. Statistical Principles in Experimental Design. McGraw-Hill, New York, 1962. 76. WOrZNACOTT, THOMAS. Special analysis combining a bartlett window with an associated inner window. Technometrics 3 (May, 1961), 237-245. 77. YAG[L, S. Generation of input data for simulations. IBM Syst. J. 2 (1963), 286---296. 78. YAGLOM, A.M. An Introduction to the Theory of Stationary Random Functions. Prentice Hall, Englewood Cliffs, N. J., 1962.
23 citations
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07 Nov 1966TL;DR: From the Michigan study it became evident that a fast analog computer together with a small digital computer and a modest interface could obtain Monte Carlo solutions at rates competitive with standard finite-difference methods.
Abstract: In addition to finite-difference methods, Monte Carlo methods also are known for solving certain partial differential equations. When implemented on a digital computer, however, the Monte Carlo methods have generally proven to be very inefficient. In 1960, a study carried out at the University of Michigan described analog computer techniques for mechanizing Monte Carlo methods. From the Michigan study it became evident that a fast analog computer together with a small digital computer and a modest interface could obtain Monte Carlo solutions at rates competitive with standard finite-difference methods.
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TL;DR: In this article, the authors used the Monte Carlo method of stratified sampling to evaluate the dissociative recombination coefficient of positive-molecular-ion (mH ion) capture by molecular hydrogen ions.
Abstract: In a recent paper Bauer and Wu proposed a model which was self‐consistent for the application of perturbation theory to the problem of calculating the general order of magnitude of cross sections of electron—positive‐molecular‐ion dissociative recombination. In applying their model to the calculation on a hypothetical system of electron capture by molecular hydrogen ions it was necessary to make several approximations, without which it would have been exceedingly difficult to evaluate certain matrix elements. We show here that Monte Carlo methods can be used for evaluating these matrix elements without resorting to approximations other than the model itself. The Monte Carlo method of stratified sampling has been tested successfully on the problem of capture of electrons by molecular hydrogen ions. The dissociative recombination coefficient is found to be of the order of 3×10−8 cm3/sec at room temperature, which is in excellent agreement with reported experimental results.
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TL;DR: The feasibility of Monte Carlo linear extrapolation of multivariable functions is discussed and an effective truncation procedure is introduced, which not only economizes the machine time to a greet extent, but also serves for the purpose of variance reduction.
Abstract: The feasibility of Monte Carlo linear extrapolation of multivariable functions is discussed. The method considered is a modified version of the Monte Carlo method for linear interpolation. An effective truncation procedure is introduced, which not only economizes the machine time to a greet extent, but also serves for the purpose of variance reduction. A few examples were tested, all of which have shown that the method is promising.
17 Jan 1966
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Abstract: AN exact analysis of variance F-test can be obtained through a permutation procedure due to Fisher (1935), and from a theoretical point of view the normal theory P-test is an approximation to this exact test. Although a large number of computer programs exist for the usual normal-theory analysis of variance and its associated F-tests, only a single special purpose program has been reported for the F-test under permutation (Baker and Collier, 1961). The present paper describes a general purpose program for obtaining the empirical distributions of variance ratios under permutation for a wide class of experimental designs. I n order to clarify the nature of this computer program, a brief description of the permutation procedure is presented in the paragraph below. Under the permutation procedure the distribution of a particular variance ratio, say Ft, can be produced from just the data collected in a single experiment. The distribution is obtained by permuting the sample data in accordance with the constraints imposed by the experimental design and by computing Ft for that permutation pattern. The data are then repermuted, Ft recalculated, and the process repeated until a sufficient number of F,'s have been obtained to form the empirical distribution of Ft. One then defines a critical region on this distribution, say the upper five percent of the cases, and if the value of Ft yielded by the sample data falls in this region,
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TL;DR: In this paper, Monte Carlo calculations of deeply penetrating radiation fields are improved by using a transformation involving the factor e−cz, and the optimum value of c generally appears to be at or near the valu...
Abstract: Monte Carlo calculations of deeply penetrating radiation fields are improved by use of a transformation involving the factor e−cz. The optimum value of c generally appears to be at or near the valu...
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TL;DR: In this paper, the pseudo pair potential theory of mixtures developed by Salsburg was tested by carrying out Monte Carlo calculations for hard sphere systems of radius ratios 5 : 3 and 3 : 1 at low and moderate densities.
Abstract: The pseudo pair potential theory of mixtures developed by Salsburg1 has been tested by carrying out Monte Carlo calculations for hard sphere systems of radius ratios 5 : 3 and 3 : 1 at low and moderate densities. Comparison between the results obtained by use of the pseudo-potential model with those obtained earlier by direct Monte Carlo simulation studies2, 3 for such mixtures shows that the model is not a good approximation. An explanation of the observed discrepancies is proposed.
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01 Jan 1966
TL;DR: In this paper, the first and second moments of the electron distribution in depth, and for the second moment of the transverse distribution, as functions of atomic number and incident electron energy, are compared with some Monte Carlo calculations due to Bishop.
Abstract: On the basis of Lewis's theory of multiple scattering in an infinite medium, relatively simple expressions are obtained for the first and second moments of the electron distribution in depth, and for the second moment of the transverse distribution, as functions of atomic number and incident electron energy. The results are compared with some Monte Carlo calculations due to Bishop. These moments are then used to determine semi-empirical expressions for the distribution functions. These results are compared with the Monte Carlo distributions for copper, in which instance good agreement is found. Some discussion is given of the applicability of these results, and possible modifications, to the case of the semi-infinite medium.
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TL;DR: In this paper, a method for calculating properties of simple fluids by computer simulation appeared, which entails the generation of large numbers of configurations of N fluid particles by random displacements of one particle at a time.
Abstract: A METHOD of calculating properties of simple fluids by computer simulation appeared in 1953 (ref. 1). It entails the generation of large numbers of configurations of N fluid particles (represented by N triplets of co-ordinates) by random displacements of one particle at a time. The potential energy is calculated after each displacement; and, by rejecting appropriate fractions of all steps in which φ increases, one obtains a sequence of configurations which tends towards a Boltzmann distribution. The method has been applied, mainly by Wood et al., to calculate the equation of state of hard-sphere fluids2,3, the pressure, internal energy, specific heat and radial distribution function of argon (Lennard–Jones potential) at 55° C over a range of densities4 and the radial distribution junction of liquid argon at −146.5° C (ref. 5).
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TL;DR: A Monte Carlo calculation of the instrumental asymmetry in the correlation experiments described in the preceding paper is given in this article, which includes the effect of multiple scattering material in the path of the lower energy proton from the p-p scatteing.
01 Jan 1966
TL;DR: In this article, a number of methods of calculating the transport of neutrons and Y-rays, mainly in reactor shields, have been described, mainly based on the Monte-Carlo technique.
Abstract: A description is given of a number of methods of calculating the transport of neutrons and Y-rays, mainly in reactor shields. Emphasis has been laid on the Monte-Carlo technique. All the methods described have been programmed for the electronic computer GIER at Riso, and some of them also for the IBM 7090 computer at the Danish Technical University, Lyngby. A simple bulk shield programme system has been developed which calculates the penetration of neutrons as well as Y-rays throughout a reactor shield. The neutrons are treated according to the removal-diffusion theory with one removal and one diffusion group. The Y-ray calculation relies on the build-up concept. Animproved removal-diffusion neutron shielding programme has been worked out, permitting an arbitrary number of removal and diffusion groups. A cross-section library with the elements most frequently encountered in shielding has been prepared. A general outline of the Monte-Carlo calculation method for problems in nuclear particle transport is given. Some minor reactor problems concerning self-absorption of Y-rays in fuel rods and distribution of the energy deposition on the various components of a fuel lattice cell are solved by the Monte-Carlo method.
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TL;DR: An algorithm, based on Monte Carlo techniques, is presented for the design and analysis of a crystal controlled oscillator that should yield improved frequency stability and reduced cost compared with results obtained from conventional design methods.
Abstract: An algorithm, based on Monte Carlo techniques, is presented for the design and analysis of a crystal controlled oscillator. A digital computer simulates the oscillator as its circuit components change in accordance with their probability distributions. Selection of the final oscillator design is based on the probability of circuit failure as calculated by the computer. This method should yield improved frequency stability and reduced cost compared with results obtained from conventional design methods.
01 Feb 1966
TL;DR: The Monte Carlo computer program for transmission probability for gas molecular flow through two coaxial cylinders in series shows good consistency with known experimental results.
Abstract: Monte Carlo computer program for transmission probability for gas molecular flow through two coaxial cylinders in series