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On Carrier Facilitated Transport Through Membranes

Description: Facilitated transport is a process, whereby the diffusion of a solute across a membrane is chemically enhanced. In this report an analysis is given of a facilitated transport system involving a volatile species A which reacts with a nonvolatile carrier species B to form the nonvolatile product AB.
Date: June 1980
Creator: Kaper, H. G.; Leaf, G. K. & Matkowsky, Bernard J.
Partner: UNT Libraries Government Documents Department

9-Zoom : A One-Dimensional, Multigroup, Neutron Diffusion Theory Reactor Code for the IBM 709

Description: The following document describes the usage and purpose of the neutron diffusion theory reactor program 9-Zoom, a memory-contained program that takes advantage of 709 features such as, for example, preferential order of multiply by zero, and for small problems approaches input-output limitations with excellent convergence properties.
Date: August 25, 1959
Creator: Stone, S. P.; Collins, E. T. & Lenihan, S. R..
Partner: UNT Libraries Government Documents Department

Multigroup Methods for Neutron Diffusion Problems

Description: Abstract: "The age-diffusion is adequate to describe the neutron behavior of a very large class of nonthermal reactors (all except those whose dimensions are comparable to the neutron mean free path). Thus, a convenient means of obtaining an accurate solution to this equation is very useful for general reactor calculations. Methods for reducing the age-diffusion equation to a finite set of coupled ordinary differential equations, called multigroup equations, are described. The relative merits of several alternate schemes are discussed. The multigroup equations may be solved by iterative procedures based on an assumed spatial distribution of the fission source neutrons. In practice the initially assumed source shape is accurate enough so that additional iterations are unnecessary. Analytical and numerical methods for solving the multigroup equations with the assumed source are discussed. The adjoint equations are also reduced to multigroup form, and examples of the adjoint function in obtaining improved reactivity values are given."
Date: August 20, 1953
Creator: Hurwitz, H. & Ehrlich, R.
Partner: UNT Libraries Government Documents Department

NUMERICAL SOLUTION OF TRANSIENT AND STEADY-STATE NEUTRON TRANSPORT PROBLEMS

Description: A general numerical procedure, called the discrete S/sub n/ method, for solving the neutron transport equation is described. The main topics relate to the derivation of suitable difference equations, and to the problem of solving these, while maintaining generality, accuracy, and reasonable computing speed. A few comparisons with other methods are made. (auth)
Date: May 16, 1959
Creator: Carlson, B.
Partner: UNT Libraries Government Documents Department

Multigroup discrete ordinates solution of Boltzmann-Fokker-Planck equations and cross section library development of ion transport

Description: We have developed and successfully implemented a two-dimensional bilinear discontinuous in space and time, used in conjunction with the S{sub N} angular approximation, to numerically solve the time dependent, one-dimensional, one-speed, slab geometry, (ion) transport equation. Numerical results and comparison with analytical solutions have shown that the bilinear-discontinuous (BLD) scheme is third-order accurate in the space ad time dimensions independently. Comparison of the BLD results with diamond-difference methods indicate that the BLD method is both quantitavely and qualitatively superior to the DD scheme. We note that the form of the transport operator is such that these conclusions carry over to energy dependent problems that include the constant-slowing-down-approximation term, and to multiple space dimensions or combinations thereof. An optimized marching or inversion scheme or a parallel algorithm should be investigated to determine if the increased accuracy can compensate for the extra overhead required for a BLD solution, and then could be compared to other discretization methods such as nodal or characteristic schemes.
Date: August 1, 1995
Creator: Prinja, A.K.
Partner: UNT Libraries Government Documents Department

Delta f Monte Carlo Calculation Of Neoclassical Transport In Perturbed Tokamaks

Description: Non-axisymmetric magnetic perturbations can fundamentally change neoclassical transport in tokamaks by distorting particle orbits on deformed or broken flux surfaces. This so-called non-ambipolar transport is highly complex, and eventually a numerical simulation is required to achieve its precise description and understanding. A new delta#14;f particle code (POCA) has been developed for this purpose using a modi ed pitch angle collision operator preserving momentum conservation. POCA was successfully benchmarked for neoclassical transport and momentum conservation in axisymmetric con guration. Non-ambipolar particle flux is calculated in the non-axisymmetric case, and results show a clear resonant nature of non-ambipolar transport and magnetic braking. Neoclassical toroidal viscosity (NTV) torque is calculated using anisotropic pressures and magnetic fi eld spectrum, and compared with the generalized NTV theory. Calculations indicate a clear #14;B2 dependence of NTV, and good agreements with theory on NTV torque pro les and amplitudes depending on collisionality.
Date: April 11, 2012
Creator: Kimin Kim, Jong-Kyu Park, Gerrit Kramer and Allen H. Boozer
Partner: UNT Libraries Government Documents Department

An Expression for the Temperature Gradient in Chaotic Fields

Description: A coordinate system adapted to the invariant structures of chaotic magnetic fields is constructed. The coordinates are based on a set of ghost-surfaces, defined via an action-gradient flow between the minimax and minimizing periodic orbits. The construction of the chaotic coordinates allows an expression describing the temperature gradient across a chaotic magnetic field to be derived. The results are in close agreement with a numerical calculation.
Date: December 22, 2008
Creator: Hudson, S.R.
Partner: UNT Libraries Government Documents Department

Using the Schwinger variational functional for the solution of inverse transport problems

Description: A new iterative inverse method for gama-ray transport problems is presented. The method, based on a novel application of the Schwinger variational functional, is developed as a perturbation problem in which the current model (in the iterative process) is considered the initial, unperturbed system, and the actual model is considered the perturbed system. The new method requires the solution of a set of uncoupled one-group forward and adjoint transport equations in each iteration. Four inverse problems are considered: determination of (1) interface locations in a multilayer sourcehhield system; (2) the isotopic composition of an unknown source (including inert elements); (3) interface locations and the source composition simultaneously; and (4) the composition of an unknown layer in the shield. Only the first two problems were actually solved in numerical one-dimensional (spherical) test cases. The method worked well for the unknown interface location problem and extremely well for the unknown source composition problem. Convergence of the method was heavily dependent on the initial guess.
Date: January 1, 2002
Creator: Favorite, J. A. (Jeffrey A.)
Partner: UNT Libraries Government Documents Department

A REMARK ON THE SECOND FUNDAMENTAL THEOREM IN ONE-VELOCITY TRANSPORT THEORY

Description: In one-velocity transport theory with linearly anisotropic scattering, the second fundamental theorem always gives an under-estimate of the average nonescape probability of neutrons from critical slabs, spheres, and cylinders if the buckling is calculated with zero extrapolation length. (auth)
Date: October 31, 1962
Creator: Dresner, L.
Partner: UNT Libraries Government Documents Department

THE MULTIGROUP DIFFUSION EQUATIONS OF REACTOR PHYSICS

Description: The partial differential equations of the multigroup diffusion model of reactor physics are shown to have solutions both in the time-independent and timedependent problems, and the usually assumed behavior of these solutions is shown to be mathematically valid. The method of spectral representation is developed for the multigroup diffusion operator. (auth)
Date: July 28, 1958
Creator: Habetler, G.J. & Martino, M.A.
Partner: UNT Libraries Government Documents Department

Corn Pone: A Multigroup, Multiregion Reactor Code

Description: Report covering the development of a set of difference equations for machine solution. In addition, this report serves as user's manual for Corn Pone, which is a code for the Oracle, the Oak Ridge National Laboratory computer.
Date: 1961?
Creator: Kinney, W. E. & Coveyou, R. R.
Partner: UNT Libraries Government Documents Department