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  1. Adjoint and Importance in Monte Carlo Application

    Coveyou, R. R. ; Cain, V. R. ; Yost, K. J. - Nuclear Science and Engineering
    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 economical or even feasible. This paper presents an exposition of the most useful methods of variance reduction. The exposition is unified by consistent exploitation of adjoint formulations to estimate expected values, as in previous work, and further to evaluate the variance of the resulting estimates., The connection between adjoint formulations and the choice of biasing schemes is also investigated. In particular, it is shown that the value functionmore » (the solution of the integral equation of the adjoint formulation) is always a good choice for importance function biasing; a sharp upper bound, independent of the particular problem, is found for the resulting variance. Predicted (analytic) and experimental (Monte Carlo) results are also given for a simple one-dimensional problem.« less

  2. Moments Calculations of the Fermi Age in Moderators and Moderator-Metal Mixtures

    Joanou, G. D. ; Goodjohn, A. J. ; Wikner, N. F. - Nuclear Science and Engineering
    Essentially exact calculations of the Fermi age in the pure moderators and in moderator-metal mixtures have been performed by computing the first few moments of the slowing-down distribution. Here, the treatment of energy degradation takes into account the anisotropy of the elastic scattering to sixth order in a Legendre expansion, using data not previously available. Energy degradation through inelastic and (n, 2n) processes is explicitly included.

  3. Performance of packed columns. II. Wetted and effective‐interfacial areas, gas ‐ and liquid‐phase mass transfer rates

    Shulman, H. L. ; Ullrich, C. F. ; Proulx, A. Z. ; ... - AIChE Journal
    AbstractA study was made of separating the volumetric mass transfer coefficients, kGa and kLa, into their components kG, kL, and a so that the effects of variables might be determined separately for each component. Mass transfer rates for four packings, 1/2‐ and 1 1/2‐in. Raschig rings and 1/2‐in. and 1‐in. Berl saddles, made of naphthalene, were determined by vaporization into air at gas rates from 100 to 1,000 1b./(hr.) (sq. ft.).The correlation for kGa was used to determine the wetted areas of those packings when irrigated with water and to calculate the effective interfacial areas, a, from Fellinger's data formore » ammonia absorption. These effective areas were then used to evaluate kL from previously published kLa data, and a correlation was obtained for all packings.The correlations for kGa and kLand the effective‐interfacial‐area data make possible a more rigorous method for the design of packed columns than was heretofore available.« less

  4. Spectra of High-Energy Electron Beams in Water

    Kessaris, Nikitas D. - Radiation Research
    The spectra of electrons in the energy range 10-20 MeV incident on water are obtained theoretically by solving the appropriate transport equation by the moment method. The spectra of the primary (incident) electrons as a function of depth are obtained first, and they subsequently serve as the source of secondaries for which an analogous equation is solved.

  5. Ground-State Energy Eigenvalues and Eigenfunctions for an Electron in an Electric-Dipole Field

    Turner, J. E. ; Anderson, V. E. ; Fox, Kenneth - Physical Review
    Ground-state energy eigenvalues and eigenfunctions are obtained by a variational method for an electron in the field of a finite, stationary, permanent electric dipole. The dipole moments studied cover the range from the minimum value required for binding (Dmin =0.6393 ea0) to D =400 ea0, where the system is equivalent to the hydrogen atom perturbed slightly by a distant stationary negative charge. The eigenvalues obtained agree with those reported by Wallis, Herman, and Milnes, who determined them by another method in the range D =0.84ea0 to 30⁢ea0. The normalized eigenfunctions display the manner in which the electronic charge density changesmore » from that of the hydrogen atom at very large D to a flat distribution approaching that which is characteristic of a zero-energy continuum state as the minimum moment is approached from above. Optimized variational wave functions for different values of D are presented for use in other calculations. Contour maps and profiles of electronic charge density are shown for a number of values of D. Mean values of the powers -1, 1, and 2 of the distances of the electron from the dipole charges are also calculated.« less

  6. Model for Dynamical Calculation of Inelasticity

    Islam, M. M. ; Kang, Kyungsik - Physical Review
    Here we propose a model in which inelasticity can be calculated dynamically. By this we mean, given the left-hand cut contribution (or force), our model gives a prescription for calculating inelasticity $$η_l⁡(=e^{–2⁢δ_l^I}$$ where $$δ_l^I$$ is ⁢the ⁢imaginary ⁢part⁢ of ⁢the⁢ phase ⁢shift). The basic assumption of the model is that there is one inelastic vi above which a large number of reaction channels open, so that the partial-wave amplitude is essentially imaginary in the inelastic region. Our amplitude satisfies elastic unitarity below the inelastic threshold and inelastic unitarity above it. We illustrate the use of the model by applying itmore » to the π –π p-wave system, where we approximate the left-hand-cut contribution by one pole and by two poles.« less

  7. Numerical studies of frontal motion in the atmosphere-I

    Kasahara, A. ; Isaacson, E. ; Stoker, J. J. - Tellus. Series A, Dynamic Meteorology and Oceanography (Online)
    The motion of frontal disturbances in the atmosphere is studied by the numerical solution of differential equations based upon a two-layer model of an incompressible fluid on a rotating earth. The density of each layer is assumed to be constant. The upper and lower fluids correspond respectively to warm and cold air. In this first attempt, only the motion of the lower cold air layer is studied by assuming, in effect, that the dynamics of the perturbations in the upper warm air layer can be neglected. The numerical study of this simple mechanical model shows that even though thermodynamic processesmore » have been ignored, the occlusion process, characteristic for warm and cold fronts, develops from an initially sinusoidal frontal pattern. Two cases of different initial conditions are examined. Case A: Only the east-west component of wind velocity is initially geostrophic. Case B: Both east-west and north-south components are initially geostrophic. In both cases, computations indicate that the cold front propagates faster than the warm front and that a relatively strong mass convergence zone appears behind the cold front only. This fact suggests the occurrence of severe storms associated with cold fronts, but not with warm fronts in the atmosphere. The numerical method developed here to calculate the movement of the front is based on following the motion of the material “particles” at the front. This method has applications to the numerical solution of a certain class of hydrodynamic flow problems in which the entire boundary of the domain of integration is not given a priori, but must be determined (so-called free-boundary problems).« less

  8. Calculation of Exact Eigenfunctions of Spin and Orbital Angular Momentum Using the Projection Operator Method

    Rotenberg, Aubey - Journal of Chemical Physics
    Using the projection operator technique a code has been written for the IBM-7090 to generate electronic wavefunctions which are eigenfunctions of both spin and orbital angular momentum. All the functions which arise in the L—S coupling of any allowed system of electrons in a single s, p, d, or f shell can be computed as well as some functions for a few electrons in the g shell. Also, functions arising in the coupling of electrons in different shells are obtained, and these eigenfunctions are of particular interest in configuration interaction studies of atomic structure. A few representative eigenfunctions are listed.more » In addition an auxiliary code was written to give the terms arising in L—S coupling.« less

  9. Hyperon-nucleon scattering

    de Swart, J. J. ; Dullemond, C. - Annals of Physics
    The hyperon-nucleon scattering is calculated for Λ-laboratory energies up to 315 Mev. The potentials used were those linear combinations of the nucleon-nucleon potentials as prescribed by global symmetry. Here, we have taken the mass difference between the Λ- and Σ-hyperon exactly into account in the kinematics. However, the mass differences between the Σ-hyperons and between the nucleons are neglected. Angular distributions and total cross sections are given for all possible hyperon-nucleon scattering reactions. Where possible a comparison with experiment is made.

  10. Remark on the radiative muon decay in the theory with an intermediate vector meson

    Biaalynicka-Birula, Z. - Nuovo Cimento
    The problem of explaining the lack of radiative muon decay in an intermediate charged vector meson theory is discussed. A possible way of introducing the charged vector meson to the theory of weak interactions is outlined in which renormalization is retained. However, if this way is used, the anomalous magnetic moment is calculated to be large, which is in contradiction with expectation.
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