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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. Revised formulation of the kinetic plasma theory

    Neufeld, Jacob - International Journal of Electronics
    Using the Maxwellian macroscopic approach and analysing the formulation of the dielectric constant, it is shown that the concept of energy has not been properly incorporated into the current kinetic plasma theory. The difficulties are due to the Boltzmann collisional term (∂F/∂t)coll which accounts for a change in the velocity distribution due to collisions alone. If one attempts to rephrase the Boltzmann-Vlasov theory in terms of the Maxwellian macroscopic formulation, one obtains an expression for energy which is not consistent with the meaning of this concept in generalized dynamics. In a revised version developed in this analysis the Boltzmann collisionalmore » term has been eliminated and an appropriate collisional operator is introduced which is believed to describe more adequately collisional processes in a plasma. Here, it is assumed that the collisional operator can be applied directly to the electrical intensity of the field interacting with the plasma and is effective in transforming the intensity in a collisionless plasma into a corresponding intensity in a collisional plasma. At the same time the relationship between the electron velocity distribution function and the field intensity is considered to be the same, whether there are collisions or not. In other words, not only a collisionless but also a collisional plasma are assumed to be controlled by a Vlasov type mechanism which does not take into account explicitly the Boltzmann term (∂F/∂t)coll.« less

  4. Some fundamental ideas in topology and their application to problems in metallurgy

    Barrett, Lida K. ; Yust, C. S. - Scripta Metallurgica
    The topological ideas and results that have been used by metallurgists, together with several results not previously presented in the metallurgical literature, are developed in a systematic manner. Based on this presentation, a review is given of the use of topology in metallurgy. The additional topology that is introduced includes the Alexander duality theorem, the Euler-Poincare formula, and the concept of deformation retract. Further, these concepts are used to establish interrelationships among the results of several papers and to clarify the mathematical treatment.

  5. Some Extensions of an Algorithm for Sparse Linear Least Squares Problems

    Heath, Michael T. - SIAM Journal on Scientific and Statistical Computing
    In this paper several algorithms are developed which extend the method of George and Heath for sparse linear least squares problems to include rank deficient problems, linear equality constrained problems, and updating of solutions. An application of these methods to the solution of sparse square nonsymmetric linear systems is also presented.

  6. Unitary Irreducible Representations of SU(2, 2). III. Reduction with Respect to an Iso-Poincaré Subgroup

    Yao, Tsu - Journal of Mathematical Physics
    The unitary irreducible representations of SU(2, 2), the covering group of the conformal group, are reduced with respect to an iso-Poincaré subgroup E(3, 1). Explicit representations of the 15 generators of SU(2, 2) in terms of differential operators in the function space of |η,ξ,ε;s,t,m$$\rangle$$, |ω,ξ,ε;r,t,m$$\rangle$$, and |ξ,ε;t,m$$\rangle$$, the basis vectors for "timelike,'' "spacelike,'' and "lightlike'' UIR's of E(3, 1), respectively, are given. The matrix elements between a basis vector in the maximal compact subgroup SU(2) × SU(2) × U(1) and a basis vector in E(3, 1) are calculated for all 14 different classes of UIR's of SU(2, 2). He wemore » find that two classes are reducible with respect to "lightlike'' representations, two classes are reducible with respect to "timelike'' representations, eight classes are reducible with respect to ``spacelike'' representations, and two classes contain both "timelike'' and "spacelike'' representations of E(3, 1).« less

  7. Complete Continuity of the Inverse of the Laplacian and Green’s Function

    Fink, James P. - SIAM Review
    In this paper, we apply the theory of strictly positive definite operators and completely continuous symmetric operators on a Hilbert space to certain boundary value problems in mathematical physics. Here we discuss in detail the application to the eigenvalue problem for the vibrating membrane.

  8. Current-Commutator Derivation of Mass-Difference Relations

    Goyal, Ashok ; Li, Gino Fong ; Segrè, Gino - Physical Review. D, Particles Fields
    Here we investigate the consequences of the vanishing of certain double commutators to examine the consistency of SU⁡(3) × SU⁡(3)-breaking models. We also calculate the contribution to ΔI = 2 mass differences of isospin-violating terms other than the electromagnetic interactions, in the Hamiltonian.

  9. Application of a Relativistic Resonance Formula to the e+⁢e-→π+⁢π- Experiment

    Parkinson, Michael - Physical Review. D, Particles Fields
    The present data for the reaction e+⁢e-→π+⁢π- are analyzed with the aid of a general effective-range resonance formula for the ρ meson. It is concluded that (a) mρ = 769 ± 5 MeV and Γρ = 109 ± 10 MeV provide a reasonable explanation of the present experimental points; (b) the full width at half-maximum regardless of the peak height should give an excellent estimate of the ρ width; (c) it is hard to escape $$|F_π$$$$(m_ρ$$$$^2|$$^2$ $$= m_ρ$$$$^2$$$$/Γ_ρ$$$$^2$; (d) the effects of final-state interactions on resonance shape ought to be investigated.

  10. Broken Chiral Symmetry and the Veneziano Model

    Cronin, Jeremiah A. ; Kang, Kyungsik - Physical Review Letters
    We investigate chiral-symmetry breaking within the Kπ system when a Veneziano model is assumed for various off-mass-shell extrapolations. Here, we derive expressions for the matrix elements of σ terms and the divergence of the strangeness-changing current and discuss the implications to chiral-symmetry-breaking interactions. Application of our results to the $$\mathrm{K}$$$$\mathcal{l}$$3 form factors gives $$(\frac{fk}{fπf+(0)})$$ =1.35 and the relation $$(\frac{fk}{fπ})$$2 = cos⁡[αK* $$\prime$$ (0) (μK2 - μπ2)].
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