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Generalized Courant-Snyder Theory and Kapchinskij-Vladimirskij Distribution For High-intensity Beams In A Coupled Transverse Focusing Lattice

Description: The Courant-Snyder (CS) theory and the Kapchinskij-Vladimirskij (KV) distribution for high-intensity beams in a uncoupled focusing lattice are generalized to the case of coupled transverse dynamics. The envelope function is generalized to an envelope matrix, and the envelope equation becomes a matrix envelope equation with matrix operations that are non-commutative. In an uncoupled lattice, the KV distribution function, first analyzed in 1959, is the only known exact solution of the nonlinear V… more
Date: July 18, 2011
Creator: QIn, Hong & Davidson, Ronald
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
open access

A TWO-DIMENSIONAL METHOD OF MANUFACTURED SOLUTIONS BENCHMARK SUITE BASED ON VARIATIONS OF LARSEN'S BENCHMARK WITH ESCALATING ORDER OF SMOOTHNESS OF THE EXACT SOLUTION

Description: The quantification of the discretization error associated with the spatial discretization of the Discrete Ordinate(DO) equations in multidimensional Cartesian geometries is the central problem in error estimation of spatial discretization schemes for transport theory as well as computer code verification. Traditionally fine mesh solutions are employed as reference, because analytical solutions only exist in the absence of scattering. This approach, however, is inadequate when the discretization… more
Date: May 1, 2011
Creator: Schunert, Sebastian & Azmy, Yousry Y.
Item Type: Refine your search to only Article
Partner: UNT Libraries Government Documents Department
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COMPARISON OF THE ACCURACY OF VARIOUS SPATIAL DISCRETIZATION SCHEMES OF THE DISCRETE ORDINATES EQUATIONS IN 2D CARTESIAN GEOMETRY

Description: We present a comprehensive error estimation of four spatial discretization schemes of the two-dimensional Discrete Ordinates (SN) equations on Cartesian grids utilizing a Method of Manufactured Solution (MMS) benchmark suite based on variants of Larsen’s benchmark featuring different orders of smoothness of the underlying exact solution. The considered spatial discretization schemes include the arbitrarily high order transport methods of the nodal (AHOTN) and characteristic (AHOTC) types, the d… more
Date: May 1, 2011
Creator: Schunert, Sebastian; Azmy, Yousry Y. & Fournier, Damien
Item Type: Refine your search to only Article
Partner: UNT Libraries Government Documents Department
open access

Status of Monte-Carlo Event Generators

Description: Recent progress on general-purpose Monte-Carlo event generators is reviewed with emphasis on the simulation of hard QCD processes and subsequent parton cascades. Describing full final states of high-energy particle collisions in contemporary experiments is an intricate task. Hundreds of particles are typically produced, and the reactions involve both large and small momentum transfer. The high-dimensional phase space makes an exact solution of the problem impossible. Instead, one typically reso… more
Date: August 11, 2011
Creator: Hoeche, Stefan
Item Type: Refine your search to only Article
Partner: UNT Libraries Government Documents Department
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A generalization of Reiner’s mathematical model for wet sand

Description: In this paper we modify the constitutive relation derived by Reiner (1945), to describe dilatancy in wet sand, by suggesting that the shear viscosity would depend on the shear rate and the volume fraction. We then look at the flow of a saturated densely packed bed of particles (with liquid in the pores) between two horizontal flat plates. We obtain exact solutions for a very special case.
Date: January 1, 2011
Creator: Massoudi, Mehrdad
Item Type: Refine your search to only Article
Partner: UNT Libraries Government Documents Department
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Discretization error estimation and exact solution generation using the method of nearby problems.

Description: The Method of Nearby Problems (MNP), a form of defect correction, is examined as a method for generating exact solutions to partial differential equations and as a discretization error estimator. For generating exact solutions, four-dimensional spline fitting procedures were developed and implemented into a MATLAB code for generating spline fits on structured domains with arbitrary levels of continuity between spline zones. For discretization error estimation, MNP/defect correction only require… more
Date: October 1, 2011
Creator: Sinclair, Andrew J. (Auburn University Auburn, AL); Raju, Anil (Auburn University Auburn, AL); Kurzen, Matthew J. (Virginia Tech Blacksburg, VA); Roy, Christopher John (Virginia Tech Blacksburg, VA) & Phillips, Tyrone S. (Virginia Tech Blacksburg, VA)
Item Type: Refine your search to only Report
Partner: UNT Libraries Government Documents Department
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