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Practical error estimates for Reynolds' lubrication approximation and its higher order corrections

Description: Reynolds lubrication approximation is used extensively to study flows between moving machine parts, in narrow channels, and in thin films. The solution of Reynolds equation may be thought of as the zeroth order term in an expansion of the solution of the Stokes equations in powers of the aspect ratio {var_epsilon} of the domain. In this paper, we show how to compute the terms in this expansion to arbitrary order on a two-dimensional, x-periodic domain and derive rigorous, a-priori error bounds … more
Date: December 10, 2008
Creator: Wilkening, Jon
Partner: UNT Libraries Government Documents Department
open access

Discretizing gravity in warped spacetime

Description: We investigate the discretized version of the compact Randall-Sundrum model. By studying the mass eigenstates of the lattice theory, we demonstrate that for warped space, unlike for flat space, the strong coupling scale does not depend on the IR scale and lattice size. However, strong coupling does prevent us from taking the continuum limit of the lattice theory. Nonetheless, the lattice theory works in the manifestly holographic regime and successfully reproduces the most significant features … more
Date: July 11, 2005
Creator: Schwartz, Matthew; Randall, Lisa; Schwartz, Matthew D. & Thambyahpillai, Shiyamala
Partner: UNT Libraries Government Documents Department
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On prediction of wind-borne plumes with simple models of turbulenttransport

Description: The dispersion of pollutants from the ground by turbulent winds is difficult to model in general. However, for flat homogeneous terrain and steady wind conditions, if the wind profile is modeled with a power-law dependence on height, the advection-dispersion equation has an exact solution. In this paper the analytical solution is compared to a numerical simulation of the coupled air-ground system for a leaking underground gas storage, with a power-law velocity profile that was fit to the logari… more
Date: June 21, 2006
Creator: Schwarz, Katherine; Patzek, Tad & Silin, Dmitriy
Partner: UNT Libraries Government Documents Department
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Global paths of time-periodic solutions of the Benjamin-Ono equation connecting arbitrary traveling waves

Description: We classify all bifurcations from traveling waves to non-trivial time-periodic solutions of the Benjamin-Ono equation that are predicted by linearization. We use a spectrally accurate numerical continuation method to study several paths of non-trivial solutions beyond the realm of linear theory. These paths are found to either re-connect with a different traveling wave or to blow up. In the latter case, as the bifurcation parameter approaches a critical value, the amplitude of the initial condi… more
Date: December 11, 2008
Creator: Ambrose, David M. & Wilkening, Jon
Partner: UNT Libraries Government Documents Department
open access

On Sub-linear Convergence for Linearly Degenerate Waves in Capturing Schemes

Description: A common attribute of capturing schemes used to find approximate solutions to the Euler equations is a sub-linear rate of convergence with respect to mesh resolution. Purely nonlinear jumps, such as shock waves produce a first-order convergence rate, but linearly degenerate discontinuous waves, where present, produce sub-linear convergence rates which eventually dominate the global rate of convergence. The classical explanation for this phenomenon investigates the behavior of the exact solution… more
Date: March 17, 2008
Creator: Banks, J W; Aslam, T & Rider, W J
Partner: UNT Libraries Government Documents Department
open access

Parallel Computation of Three-Dimensional Flows using Overlapping Grids with Adaptive Mesh Refinement

Description: This paper describes an approach for the numerical solution of time-dependent partial differential equations in complex three-dimensional domains. The domains are represented by overlapping structured grids, and block-structured adaptive mesh refinement (AMR) is employed to locally increase the grid resolution. In addition, the numerical method is implemented on parallel distributed-memory computers using a domain-decomposition approach. The implementation is flexible so that each base grid wit… more
Date: November 15, 2007
Creator: Henshaw, W & Schwendeman, D
Partner: UNT Libraries Government Documents Department
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Optimal Chunking of Large Multidimensional Arrays for Data Warehousing

Description: Very large multidimensional arrays are commonly used in data intensive scientific computations as well as on-line analytical processingapplications referred to as MOLAP. The storage organization of such arrays on disks is done by partitioning the large global array into fixed size sub-arrays called chunks or tiles that form the units of data transfer between disk and memory. Typical queries involve the retrieval of sub-arrays in a manner that access all chunks that overlap the query results. An… more
Date: February 15, 2008
Creator: Otoo, Ekow J.; Otoo, Ekow J.; Rotem, Doron & Seshadri, Sridhar
Partner: UNT Libraries Government Documents Department
open access

Exact solution of the envelope equations for a matched quadrupole-focused beam in the low space-charged limit

Description: The Kapchinskij-Vladimirskij equations are widely used to study the evolution of the beam envelopes in a periodic system of quadrupole focusing cells. In this paper, we analyze the case of a matched beam. Our model is analogous to that used by Courant and Snyder [E.D. Courant and H.S. Snyder, Ann. Phys. 3, 1 (1958)]in obtaining a first-order approximate solution for a synchrotron. Here, we treat a linear machine and obtain an exact solution. The model uses a full occupancy, piecewise-constant f… more
Date: September 23, 2008
Creator: Anderson, O. A. & LoDestro, L. L.
Partner: UNT Libraries Government Documents Department
open access

Exact solution of the envelope equations for a matchedquadrupole-focused beam in the zero space-charge limit

Description: The Kapchinskij-Vladimirskij equations are widely used to study the evolution of the beam envelopes in a periodic system of quadrupole focusing cells. In this paper, we analyze the case of a matched beam. Our model is analogous to that used by Courant and Snyder [E.D. Courant and H.S. Snyder, Ann. Phys. 3, 1 (1958)] in obtaining a first-order approximate solution for a synchrotron. Here, we treat a linear machine and obtain an exact solution. The model uses a full occupancy, piecewise-constant … more
Date: November 7, 2008
Creator: Anderson, Oscar A. & LoDestro, L. L.
Partner: UNT Libraries Government Documents Department
open access

An Exact Solution of Transport in Porous Media with Equilibrium and Kinetic Reactions

Description: This paper presents an analytical solution of reactive transport with equilibrium and kinetic reactions. A benchmark model of A {leftrightarrow} B {leftrightarrow} C {yields} chain reactions is developed for the purpose of verifying numerical computer codes and qualifying mathematical models. A reaction matrix is derived for both the equilibrium and first-order kinetic reactions and further decoupled as a diagonal matrix. Therefore, the partial differential equations (PDEs) coupled by the react… more
Date: April 12, 2006
Creator: Lu, X. & Sun, Y.
Partner: UNT Libraries Government Documents Department
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Exact solutions in a model of vertical gas migration

Description: This work is motivated by the growing interest in injectingcarbon dioxide into deep geological formations as a means of avoidingatmospheric emissions of carbon dioxide and consequent global warming.One of the key questions regarding the feasibility of this technology isthe potential rate of leakage out of the primary storage formation. Weseek exact solutions in a model of gas flow driven by a combination ofbuoyancy, viscous and capillary forces. Different combinations of theseforces and charact… more
Date: June 27, 2006
Creator: Silin, Dmitriy B.; Patzek, Tad W. & Benson, Sally M.
Partner: UNT Libraries Government Documents Department
open access

A Quantitative Comparison of Numerical Methods for the Compressible Euler Equations: Fifth-order WENO and Piecewise-Linear Godunov

Description: A numerical study is undertaken comparing a fifth-order version of the weighted essentially non-oscillatory numerical (WENO5) method to a modern piecewise-linear, second-order, version of Godunov's (PLMDE) method for the compressible Euler Equations. A series of one-dimensional test problems are examined beginning with classical linear problems and ending with complex shock interactions. The problems considered are: (1) linear advection of a Gaussian pulse in density, (2) Sod's shock tube probl… more
Date: November 5, 2003
Creator: Greenough, J A & Rider, W J
Partner: UNT Libraries Government Documents Department
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Low-frequency fluid waves in fractures and pipes

Description: Low-frequency analytical solutions have been obtained for phase velocities of symmetrical fluid waves within both an infinite fracture and a pipe filled with a viscous fluid. Three different fluid wave regimes can exist in such objects, depending on the various combinations of parameters, such as fluid density, fluid viscosity, walls shear modulus, channel thickness, and frequency. Equations for velocities of all these regimes have explicit forms and are verified by comparisons with the exact s… more
Date: September 1, 2010
Creator: Korneev, Valeri
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.
Partner: UNT Libraries Government Documents Department
open access

ALFVEN-WAVE OSCILLATIONS IN A SPHERE, WITH APPLICATIONS TO ELECTRON-HOLE DROPS IN Ge

Description: The problem of Alfven-wave oscillations in an anisotropic sphere is studied, and two solutions are presented. One solution is exact, involving an expansion of the current inside the sphere in a series of orthonormal modes. The second is approximate, based on a perturbation expansion of the induced fields and currents in powers of the sphere radius. The approximate solution can be applied to a material having a completely general conductivity tensor, while the exact solution is restricted to sit… more
Date: January 1, 1978
Creator: Markiewicz, R. S.
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
Partner: UNT Libraries Government Documents Department
open access

Exact Magnetic Diffusion Solutions for Magnetohydrodynamic Code Verification

Description: In this paper, the authors present several new exact analytic space and time dependent solutions to the problem of magnetic diffusion in R-Z geometry. These problems serve to verify several different elements of an MHD implementation: magnetic diffusion, external circuit time integration, current and voltage energy sources, spatially dependent conductivities, and ohmic heating. The exact solutions are shown in comparison with 2D simulation results from the Ares code.
Date: December 3, 2010
Creator: Miller, D. S.
Partner: UNT Libraries Government Documents Department
open access

Development of a thermal equilibrium prediction algorithm.

Description: A thermal equilibrium prediction algorithm is developed and tested using a heat conduction model and data sets from calorimetric measurements. The physical model used in this study is the exact solution of a system of two partial differential equations that govern the heat conduction in the calorimeter. A multi-parameter estimation technique is developed and implemented to estimate the effective volumetric heat generation and thermal diffusivity in the calorimeter measurement chamber, and the e… more
Date: January 1, 2001
Creator: Aviles-Ramos, C. (Cuauhtemoc)
Partner: UNT Libraries Government Documents Department
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Time-Resolved Photoemission of Correlated Electrons Driven Out of Equilibrium

Description: We describe the temporal evolution of the time-resolved photoemission response of the spinless Falicov-Kimball model driven out of equilibrium by strong, applied fields. The model is one of the few possessing a metal-insulator transition and admitting an exact solution in the time domain. The nonequilibrium dynamics, evaluated using an extension of dynamical mean-field theory, show how the driven system differs from two common viewpoints - a quasi-equilibrium system at an elevated, effective te… more
Date: February 15, 2010
Creator: Moritz, B.; /SLAC, SIMES; Devereaux, T.P.; /SLAC, SIMES /Stanford U., Geballe Lab.; Freericks, J.K. & U., /Georgetown
Partner: UNT Libraries Government Documents Department
open access

Analytic Solution of the Envelope Equations for an Undepressed Matched Beam in a FODO Quadrupole Channel

Description: In 1958, Courant and Snyder analyzed the problem of alternating-gradient beam transport and treated a model without focusing gaps or space charge. Recently we revisited their work and found the exact solution for matchedbeam envelopes in a linear quadrupole lattice [O.A. Anderson and L.L. LoDestro, Phys. Rev. ST Accel. Beams, 2009]. We extend that work here to include the effect of asymmetric drift spaces. We derive the solution and show exact envelopes for the first two solution bands and the … more
Date: April 29, 2009
Creator: Anderson, Oscar & LoDestro, L. L.
Partner: UNT Libraries Government Documents Department
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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
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
Partner: UNT Libraries Government Documents Department
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Heavy-Ion-Fusion-Science: Summary of U.S. Progress

Description: Over the past two years noteworthy experimental and theoretical progress has been made towards the top-level scientific question for the U.S. program in Heavy Ion Fusion Science and High Energy Density Physics: ''How can heavy ion beams be compressed to the high intensity required to create high energy density matter and fusion conditions''? [1]. New results in transverse and longitudinal beam compression, beam-target interaction, high-brightness transport, beam production, as well as a new sch… more
Date: April 16, 2006
Creator: Yu, Simon S.; Logan, B. G.; Barnard, J. J.; Bieniosek, F. M.; Davidson, R. C.; Friedman, A. et al.
Partner: UNT Libraries Government Documents Department
open access

SUDOKU A STORY & A SOLVER

Description: Sudoku, also known as Number Place, is a logic-based placement puzzle. The aim of the puzzle is to enter a numerical digit from 1 through 9 in each cell of a 9 x 9 grid made up of 3 x 3 subgrids (called ''regions''), starting with various digits given in some cells (the ''givens''). Each row, column, and region must contain only one instance of each numeral. Completing the puzzle requires patience and logical ability. Although first published in a U.S. puzzle magazine in 1979, Sudoku initially … more
Date: April 1, 2006
Creator: GARDNER, P.R.
Partner: UNT Libraries Government Documents Department
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