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Monte Carlo Methods

Description: Abstract: "The paper is concerned with the basic concepts and techniques of Monte Carlo, such as the generation of random numbers, the construction of samples from a given distribution, and techniques for reducing the variances of the estimates. The latter include the expected values method, systematic and stratified sampling, importance sampling, splitting and Russian roulette, conditional Monte Carlo, and correlation and regression. These are discussed with reference to two examples: a system comprising a roulette wheel and three urns, and a simplified neutron shielding problem. For the two-stage sampling in the first example, the inequalities among the variances of ten of the estimates obtained by various methods are investigated."
Date: September 1958
Creator: Kaplan, Edward L.
Partner: UNT Libraries Government Documents Department

Study of a like-sign dilepton search for chargino-neutralino production at CDF

Description: We propose a like-sign dilepton search for chargino-neutralino production in p#22; p collisions at ps = 1:8 TeV, which complements the previously published trilepton search by the CDF detector using Fermilab Run I data. Monte Carlo predictions for the signal and background e#14;ciencies indicate a signi#12;cant increase in sensitivity to chargino-neutralino production compared to the traditional trilepton analysis alone.
Date: March 2, 1999
Creator: Worcester, Matthew
Partner: UNT Libraries Government Documents Department

A Monte Carlo Calculation of the Neutron Detection Efficiency of a Hydrogen Bubble Chamber

Description: Abstract: "The calculation of the efficiency of the Los Alamos hydrogen bubble chamber for detection of neutrons in the energy range 5 to 35 MeV has been done using a "Monte Carlo" technique. The detection efficiency is calculated as a function of energy of the neutron and angle of the proton recoil."
Date: September 1962
Creator: Wooten, J. K. & Bryant, H. C.
Partner: UNT Libraries Government Documents Department

Monte Carlo-Based Validation of the ENDF/MC²-II/SDX Cell Homogenization Path

Description: The results are presented of a program of validation of the unit cell homogenization prescriptions and codes used for the analysis of Zero Power Reactor (ZPR) fast breeder reactor critical experiments. The ZPR drawer loading patterns comprise both plate type and pin-calandria type unit cells. A prescription is used to convert the three dimensional physical geometry of the drawer loadings into one dimensional calculational models. The ETOE-II/MC²-II/SDX code sequence is used to transform ENDF/B basic nuclear data into unit cell average broad group cross sections based on the 1D models. Cell average, broad group anisotropic diffusion coefficients are generated using the methods of Benoist or of Gelbard. The resulting broad (approx. 10 to 30) group parameters are used in multigroup diffusion and S(su n) transport calculations of full core XY or RZ models which employ smeared atom densities to represent the contents of the unit cells.
Date: April 1979
Creator: Wade, D. C.
Partner: UNT Libraries Government Documents Department

The Evaluation of Definite Integrals, and a Quasi-Monte-Carlo Method Based on the Properties of Algebraic Numbers

Description: A formula is given for the approximate evaluation of multiple definite integrals using the ergodic property of a certain transformation of the unit cube into itself. Estimates of the rate of convergence are made for sufficiently smooth integrand. The work was motivated by a belief, that appeared at one time justified, that a substantial improvement of the accuracy of Monte Carlo method would result from use of the principles described herein. Although that belief proved groundless in numerical tests, it is deemed worthwhile to give this report of the work. Part of the theoretical development, the work of L.G. Peck, will be reported independently. (auth)
Date: October 13, 1951
Creator: Richtmyer, R. D.
Partner: UNT Libraries Government Documents Department

Monte Carlo Methods and Applications for the Nuclear Shell Model

Description: The shell-model Monte Carlo (SMMC) technique transforms the traditional nuclear shell-model problem into a path-integral over auxiliary fields. We describe below the method and its applications to four physics issues: calculations of sd-pf-shell nuclei, a discussion of electron-capture rates in pf-shell nuclei, exploration of pairing correlations in unstable nuclei, and level densities in rare earth systems.
Date: August 10, 1998
Creator: Dean, D.J. & White, J.A.
Partner: UNT Libraries Government Documents Department

Particle-transport simulation with the Monte Carlo method

Description: Attention is focused on the application of the Monte Carlo method to particle transport problems, with emphasis on neutron and photon transport. Topics covered include sampling methods, mathematical prescriptions for simulating particle transport, mechanics of simulating particle transport, neutron transport, and photon transport. A literature survey of 204 references is included. (GMT)
Date: January 1, 1975
Creator: Carter, L.L. & Cashwell, E.D.
Partner: UNT Libraries Government Documents Department

Isotopic depletion with Monte Carlo

Description: This work considers a method to deplete isotopes during a time- dependent Monte Carlo simulation of an evolving system. The method is based on explicitly combining a conventional estimator for the scalar flux with the analytical solutions to the isotopic depletion equations. There are no auxiliary calculations; the method is an integral part of the Monte Carlo calculation. The method eliminates negative densities and reduces the variance in the estimates for the isotope densities, compared to existing methods. Moreover, existing methods are shown to be special cases of the general method described in this work, as they can be derived by combining a high variance estimator for the scalar flux with a low-order approximation to the analytical solution to the depletion equation.
Date: June 1, 1996
Creator: Martin, W.R. & Rathkopf, J.A.
Partner: UNT Libraries Government Documents Department

A Set of Monte Carlo Subroutines for Treating the Physics of Compton Scattering

Description: A set of portable Monte Carlo subroutines is presented to treat the physics of Compton scattering. Electron binding energies are included by the modification of the Klein-Nishina probability distribution by the incoherent scattering function. In addition the scattered photon's energy is calculated by taking into account the momentum distribution of the electron. These subroutines have been verified and validated by calculating the total cross section over incident photon energies of 10 keV to 100 MeV for elements of Z=l to Z=l 00 and are within 1.08% of published values.
Date: December 1, 1998
Creator: Lestone, John; Earnhart, Jonathan & Prettyman, Thomas
Partner: UNT Libraries Government Documents Department

Efficient single scatter electron Monte Carlo

Description: A single scatter electron Monte Carlo code (SSMC), CREEP, has been written which bridges the gap between existing transport methods and modeling real physical processes. CREEP simulates ionization,elastic and bremsstrahlung events individually. Excitation events are usually treated with an excitation-only stopping power, although simulation of individual excitation events is possible. Agreement of these quantities with experimental values is generally quite good.One application of this code is the generation of probability distribution functions (PDFs) to describe the phase space of a single electron emerging from a sphere of a given material and radius. A library of data sets for such spheres (or ``kugels``) is being computed for a variety of incident energies, material types, and sizes. The final goal of this work is to achieve extremely accurate transport results with an efficiency that is similar to that of condensed history methods.
Date: November 3, 1997
Creator: Svatos, M.M. & Rathkopf, J.A.
Partner: UNT Libraries Government Documents Department

Fermion Monte Carlo

Description: We review the fundamental challenge of fermion Monte Carlo for continuous systems, the "sign problem". We seek that eigenfunction of the many-body Schriodinger equation that is antisymmetric under interchange of the coordinates of pairs of particles. We describe methods that depend upon the use of correlated dynamics for pairs of correlated walkers that carry opposite signs. There is an algorithmic symmetry between such walkers that must be broken to create a method that is both exact and as effective as for symmetric functions, In our new method, it is broken by using different "guiding" functions for walkers of opposite signs, and a geometric correlation between steps of their walks, With a specific process of cancellation of the walkers, overlaps with antisymmetric test functions are preserved. Finally, we describe the progress in treating free-fermion systems and a fermion fluid with 14 <sup>3</sup>He atoms.
Date: December 1, 1998
Creator: Kalos, M. H. & Pederiva, F.
Partner: UNT Libraries Government Documents Department

Shell model the Monte Carlo way

Description: The formalism for the auxiliary-field Monte Carlo approach to the nuclear shell model is presented. The method is based on a linearization of the two-body part of the Hamiltonian in an imaginary-time propagator using the Hubbard-Stratonovich transformation. The foundation of the method, as applied to the nuclear many-body problem, is discussed. Topics presented in detail include: (1) the density-density formulation of the method, (2) computation of the overlaps, (3) the sign of the Monte Carlo weight function, (4) techniques for performing Monte Carlo sampling, and (5) the reconstruction of response functions from an imaginary-time auto-correlation function using MaxEnt techniques. Results obtained using schematic interactions, which have no sign problem, are presented to demonstrate the feasibility of the method, while an extrapolation method for realistic Hamiltonians is presented. In addition, applications at finite temperature are outlined.
Date: March 1, 1995
Creator: Ormand, W.E.
Partner: UNT Libraries Government Documents Department

Proceedings of the Nuclear Criticality Technology Safety Workshop

Description: This document contains summaries of most of the papers presented at the 1995 Nuclear Criticality Technology Safety Project (NCTSP) meeting, which was held May 16 and 17 at San Diego, Ca. The meeting was broken up into seven sessions, which covered the following topics: (1) Criticality Safety of Project Sapphire; (2) Relevant Experiments For Criticality Safety; (3) Interactions with the Former Soviet Union; (4) Misapplications and Limitations of Monte Carlo Methods Directed Toward Criticality Safety Analyses; (5) Monte Carlo Vulnerabilities of Execution and Interpretation; (6) Monte Carlo Vulnerabilities of Representation; and (7) Benchmark Comparisons.
Date: April 1, 1998
Creator: Sanchez, Rene G.
Partner: UNT Libraries Government Documents Department

Evolution of 2D Potts Model Grain Microstructures from an Initial Hillert Size Distribution

Description: Grain growth experiments and simulations exhibit self-similar grain size distributions quite different from that derived via a mean field approach by Hillert [ 1]. To test whether this discrepancy is due to insufficient anneal times, two different two-dimensional grain structures with realistic topologies and Hillert grain size distributions are generated and subjected to grain growth via the Monte Carlo Potts Model (MCPM). In both cases, the observed self-similar grain size distributions deviate from the initial Hillert form and conform instead to that observed in MCPM grain growth simulations that start from a random microstructure. This suggests that the Hillert grain size distribution is not an attractor.
Date: October 19, 1998
Creator: Battaile, C.C. & E.A., Holm
Partner: UNT Libraries Government Documents Department

Verification of the MCNP (TM) Perturbation Correction Feature for Cross-Section Dependent Tallies

Description: The Monte Carlo N-Particle Transport Code MCNP version 4B perturbation capability has been extended to cross-section dependent tallies and to the track-length estimate of Iqff in criticality problems. We present the complete theory of the MCNP perturbation capability including the correction to MCNP4B which enables cross-section dependent perturbation tallies. We also present the MCNP interface as an upgrade to the MCNP4B manual. Finally, we present test results demonstrating the validity of the perturbation capability in MCNP, particularly cross-section dependent problems.
Date: October 1, 1998
Creator: Hess, A. K.; McKinney, G. W.; Hendricks, J. S. & Carter, L. L.
Partner: UNT Libraries Government Documents Department


Description: Paper presented at Shielding Information Meeting, May 14-15, 1956, Marietta, Ga. This code employs special techniques for the express purpcse of tryirg to obtain reasonable estimates of deep penetrations of gamma rays in an infinite medium emitted from a point monoenergetic source. The code is presently in the debugging'' stage and wlll be tested agninst well known standards before it is used for production. (auth)
Date: June 1, 1958
Creator: Penny, S.K.
Partner: UNT Libraries Government Documents Department


Description: The need for random numbers, particularly in regard to Monte Carlo applications, andd the multiplicative mixed congruential methods most commonly used to obtain random numbers are discussed. Both methods involve somewhat arbitrary parameters. Proofs for the lengths of period for both methods and a derivation of an expression for the serial correlation coefficient in terms of the parameters of the mixed congruential method are presented. The results of a series of statistical tests made to determine satisfactory parameters are listed. The length of run test was found to be the most powerful test in that it rejected the largest number of parameters as unsatisfactory. The multiplicative method (for the parameters tested) was superior to the mixed congruential method. The multiplicative method multiplier lambda = 2/sup 18/ + 3 satisfactorily passed all tests and has a short multiply time. (auth)
Date: August 1, 1963
Creator: Gannon, L.J. & Schmittroth, L.A.
Partner: UNT Libraries Government Documents Department

Improved criticality convergence via a modified Monte Carlo iteration method

Description: Nuclear criticality calculations with Monte Carlo codes are normally done using a power iteration method to obtain the dominant eigenfunction and eigenvalue. In the last few years it has been shown that the power iteration method can be modified to obtain the first two eigenfunctions. This modified power iteration method directly subtracts out the second eigenfunction and thus only powers out the third and higher eigenfunctions. The result is a convergence rate to the dominant eigenfunction being |k{sub 3}|/k{sub 1} instead of |k{sub 2}|/k{sub 1}. One difficulty is that the second eigenfunction contains particles of both positive and negative weights that must sum somehow to maintain the second eigenfunction. Summing negative and positive weights can be done using point detector mechanics, but this sometimes can be quite slow. We show that an approximate cancellation scheme is sufficient to accelerate the convergence to the dominant eigenfunction. A second difficulty is that for some problems the Monte Carlo implementation of the modified power method has some stability problems. We also show that a simple method deals with this in an effective, but ad hoc manner.
Date: January 1, 2009
Creator: Booth, Thomas E & Gubernatis, James E
Partner: UNT Libraries Government Documents Department

Asymptotic analysis of spatial discretizations in implicit Monte Carlo

Description: We perform an asymptotic analysis of spatial discretizations in Implicit Monte Carlo (IMC). We consider two asymptotic scalings: one that represents a time step that resolves the mean-free time, and one that corresponds to a fixed, optically large time step. We show that only the latter scaling results in a valid spatial discretization of the proper diffusion equation, and thus we conclude that IMC only yields accurate solutions when using optically large spatial cells if time steps are also optically large. We demonstrate the validity of our analysis with a set of numerical examples.
Date: January 1, 2009
Creator: Densmore, Jeffery D
Partner: UNT Libraries Government Documents Department