Showing papers on "Dynamic Monte Carlo method published in 1969"

Application of Monte Carlo to Heat Transfer Problems

Abstract: Publisher Summary This chapter presents a view of the problems that have been solved by Monte Carlo in certain areas of heat transfer, and the techniques used in their solution. Only the straightforward Monte Carlo approach has been given. The machine running time of Monte Carlo programs have been discussed. No definitive method of predicting running time exists for most problems. The time used will depend, of course, on the machine used, and perhaps more strongly on the ability of the programmer to pick methods and shortcuts that will reduce the burden on the machine. An example of such a shortcut is the use of special subroutines for computation of such functions as sine and cosine. These routines sacrifice some accuracy to a gain in speed. If problem answers accurate to a few per cent are desired, then the use of eight-place functions from a relatively slow subroutine is a needless luxury, especially if the subroutine is to be used tens of thousands of times. The chapter discusses the fruitless argument as to whether Monte Carlo or some other method is a “better” way of attacking a given problem.

Monte Carlo of Chains with Excluded Volume: a Way to Evade Sample Attrition

Abstract: A new method for the generation of long self‐avoiding walks on lattice is described: Short self‐avoiding walks—say of length N = 50—are generated by direct Monte Carlo method, then linked in pairs to form “dimers.” Each dimer is tested for intersections between its two halves—those passing the test giving a sample of self‐avoiding walks N = 100, which is dimerized in turn, etc. In this manner the repeated checking for intersections formed with only a few steps (short loops) is substantially avoided, while precisely such intersections are responsible for the heavy attrition with the direct Monte Carlo method. Thus the attrition accompanying the dimerization is quite insignificant even for very large N. With the help of this method walks N = 50 × 27 = 6400 were generated on the 4‐choice cubic lattice, for which the expansion coefficient of the end to end distance is α = 2.2. (The limit reached by others is N ≃ 2000 on the tetrahedral lattice, corresponding to only α ≃ 1.6, while α = 2.2 would require a leng...

Pair and triplet interactions in argon

Abstract: Thermodynamic properties of dense gaseous and liquid argon are calculated using perturbation theory based on the hard-sphere potential, together with an accurately determined pair potential function and the triple-dipole dispersion three-body interaction. The first-order contribution of the three-body interaction is calculated both by a Monte Carlo method and by the use of the superposition approximation for the three-body distribution function, with good agreement. Monte Carlo estimates are also found for second-order contributions of the three-body interactions, which prove to be small. Agreement with experiment is excellent at high temperatures and good at low temperatures. Slight discrepancies at low temperatures are probably due partly to the use of the ‘local compressibility’ approximation and perhaps partly to slight uncertainty in the pair potential in the neighbourhood of its zero.

Monte Carlo simulation of electrical discharges in gases

Abstract: New Monte Carlo methods of calculation for tracing the motion of electrons in gases are described. Two problems have been treated by these methods, and the techniques applied to electron swarms in neon. Firstly, the probability of back-scatter of electrons to the cathode has been estimated for values of E/p0 between 10 and 200 V cm-1 torr-1 (E is the electric field and p0 the pressure reduced to 0 °C) and for emission energies up to the lowest excitation potential. Secondly, Townsend primary ionization coefficients α/p0 and drift velocities have been evaluated for values of E/p0 from 20 to 400 V cm-1 torr-1. It is shown that the use of the ergodic hypothesis is not valid, yielding values of α/p0 which are up to 40% too high in neon, and that entire avalanches must be simulated before meaningful results can be obtained. The present results agree well with those obtained recently at Swansea using the Boltzmann equation, indicating that the Lorentz approximation employed in the latter method leads to only small errors in estimates of the mean properties of the electron swarms. The equilibrium of the swarm with the field is considered in detail. It is shown that, for uniform fields, deviations from exponential growth of current with increasing electrode separation occur if the interelectrode voltage is not at least three times the mean energy of electrons impinging on the anode.

The Monte Carlo technique applied to radiative transfer.

Abstract: A general review is given of the application of the Monte Carlo method to the numerical calculations of non-equilibrium radiation transport. With the aid of a general flow chart, the various steps required in such Monte Carlo calculations are detailed. Advanced techniques which improve efficiency of calculations such as weighting and biasing are also discussed. Although specific results are not given in the text, references to recent Monte Carlo calculations of radiation transport are included.

Studies in applied mathematics 3.

Abstract: : Contents: The mathematical basis of Monte Carlo and quasi Monte Carlo methods; Foundations of the theory of branching processes; Some molecular applications of Monte Carlo methods; The application of Monte Carlo techniques to problems of linear transport of elementary particles; Practical uses of the Monte Carlo method in neutronics calculations; The Monte Carlo method in quantum statistics; Random number generation is too important to be left chance; Monte Carlo computation on classical fluids; The dynamics of variable stars; and Rotating fluids: A survey of phenomena and theory

Monte Carlo Integration of the Adjoint Neutron Transport Equation

Abstract: The integral equation adjoint to the linear transport equation for neutrons is formulated and prescriptions given for its solution by Monte Carlo methods. The process of tracking is the same as for...

Study of Some of the Parameters Affecting Knudsen Effusion. VI. Monte Carlo Analyses of Channel Orifices

Abstract: Techniques for Monte Carlo simulation of real particle behavior have been extended to study the performance of channel orifices. Transmission coefficient calculations and wall‐flux gradient behavior are considered. For the particular case L / R = 4.0, functions are derived to allow for variable orifice‐to‐collimator distances when the target collection method is used. A “state‐of‐the‐art” discussion on orifice behavior is included to help delineate the purposes of this study. It is concluded that use of both knife‐edged and channel orifices is sometimes necessary to establish the cell‐orifice behavior of some systems; information derived from experimental studies, and from Monte Carlo analysis of flux relationships appropriate to the geometry of the system, seems to indicate that the channel orifice is a better choice for most effusion work.

The Monte Carlo method. Plotting the course of complex reactions.

Abstract: Introduces the Monte Carlo method applied to the problem of the probability that a given molecule will spontaneously decompose in a monomolecular reaction process, or that two molecules of the same

A Monte Carlo method for quantum chemistry

Abstract: A Monte Carlo method is described for evaluating quantities such as E = / and other expectation values. The method is in principle applicable to a wave function of any number of electrons. As an example, a two-parameter wave function for helium is studied.

Probability distributions and error estimates for Monte Carlo solutions of radiation problems

Abstract: Probability distributions and error estimates for Monte Carlo solutions of radiation heat transfer problems, considering wavelength and direction of emitted photon bundles