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Theory of Characteristics

Description: The theory of characteristics will be presented generally for quasilinear differential equations of the second order in two variables. This is necessary because of the manifold requirements to be demanded from the theory of characteristics.
Date: September 1949
Creator: Tollmien, W.
Partner: UNT Libraries Government Documents Department

Evaporation, Heat Transfer, and Velocity Distribution in Two-Dimensional and Rotationally Symmetrical Laminar Boundary-Layer Flow

Description: The fundamental boundary layer equations for the flow, temperature and concentration fields are presented. Two dimensional symmetrical and unsymmetrical and rotationally symmetrical steady boundary layer flows are treated as well as the transfer boundary layer. Approximation methods for the calculation of the transfer layer are discussed and a brief survey of an investigation into the validity of the law that the Nusselt number is proportional to the cube root of the Prandtl number is presented.
Date: February 1958
Creator: Frössling, Nils
Partner: UNT Libraries Government Documents Department

Tunnel Correction for Compressible Subsonic Flow

Description: "This report presents a treatment of the effects of the tunnel walls on the flow velocity and direction in a compressible medium at subsonic speed by an approximate method. Calculations are given for the rotationally symmetric and two-dimensional problems of the flow past bodies, as well for the downwash effect in the tunnel with circular cross section" (p. 1).
Date: July 1947
Creator: v. Baranoff, A.
Partner: UNT Libraries Government Documents Department

NBS-INA -- The Institute for Numerical Analysis -- UCLA 1947-1954

Description: Abstract: This is the history of the Institute for Numerical Analysis (INA) with special emphasis in its research program during the period 1947 to 1956. The Institute for Numerical Analysis was located on the campus of the University of California, Los Angeles. It was a section of the National Applied Mathematics Laboratories, which formed the Applied Mathematics Division of the National Bureau of Standards (now the National Institute of Standards and technology), under the U.S. Department of Commerce.
Date: August 1991
Creator: Hestenes, Magnus Rudolph & Todd, John
Partner: UNT Libraries Government Documents Department

Algorithms of Schensted and Hillman-Grassl and Operations on Standard Bitableaux

Description: In this thesis, we describe Schensted's algorithm for finding the length of a longest increasing subsequence of a finite sequence. Schensted's algorithm also constructs a bijection between permutations of the first N natural numbers and standard bitableaux of size N. We also describe the Hillman-Grassl algorithm which constructs a bijection between reverse plane partitions and the solutions in natural numbers of a linear equation involving hook lengths. Pascal programs and sample output for both algorithms appear in the appendix. In addition, we describe the operations on standard bitableaux corresponding to the operations of inverting and reversing permutations. Finally, we show that these operations generate the dihedral group D_4
Date: August 1983
Creator: Sutherland, David C. (David Craig)
Partner: UNT Libraries

Two-Dimensional Irrotational Transonic Flows of a Compressible Fluid

Description: The methods of NACA TN No. 995 have been slightly modified and extended in include flows with circulation by considering the alteration of the singularities of the incompressible solution due to the presence of the hypergeometric functions in the analytic continuation of the solution. It was found that for finite Mach numbers the only case in which the nature of the singularity can remain unchanged is for a ratio of specific heats equal to -1. From a study of two particular flows it seems that the effect of geometry cannot be neglected, and the conventional "pressure-correction" formulas are not valid, even in the subsonic region if the body is thick, especially if there is a supersonic region in the flow.
Date: June 1948
Creator: Kuo, Yung-Huai
Partner: UNT Libraries Government Documents Department

Correlation of flame speed with stretch in turbulent premixed methane/air flames

Description: In the flamelet approach of turbulent premixed combustion, the flames are modeled as a wrinkled surface whose propagation speed, termed the {open_quotes}displacement speed,{close_quotes} is prescribed in terms of the local flow field and flame geometry. Theoretical studies suggest a linear relation between the flame speed and stretch for small values of stretch, S{sub L}/S{sub L}{sup 0} = 1 - MaKa, where S{sub L}{sup 0} is the laminar flame speed, Ka = {kappa}{delta}{sub F}/S{sub L}{sup 0} is the nondimensional stretch or the Karlovitz number, and Ma = L/{delta}{sub F} is the Markstein number. The nominal flame thickness, {delta}{sub F}, is determined as the ratio of the mass diffusivity of the unburnt mixture to the laminar flame speed. Thus, the turbulent flame model relies on an accurate estimate of the Markstein number in specific flame configurations. Experimental measurement of flame speed and stretch in turbulent flames, however, is extremely difficult. As a result, measurement of flame speeds under strained flow fields has been made in simpler geometries, in which the effect of flame curvature is often omitted. In this study we present results of direct numerical simulations of unsteady turbulent flames with detailed methane/air chemistry, thereby providing an alternative method of obtaining flame structure and propagation statistics. The objective is to determine the correlation between the displacement speed and stretch over a broad range of Karlovitz numbers. The observed response of the displacement speed is then interpreted in terms of local tangential strain rate and curvature effects. 13 refs., 3 figs.
Date: November 1, 1997
Creator: Chen, J.H. & Im, Hong G.
Partner: UNT Libraries Government Documents Department

Heat transfer at the mold-metal interface in permanent mold casting of aluminum alloys project. Annual project status report for the period October 1, 1997 to September 30, 1998

Description: In the first year of this three-year project, substantial progress has been achieved. This project on heat transfer coefficients in metal permanent mold casting is being conducted in three areas. They are the theoretical study at the University of Michigan, the experimental investigations of squeeze casting and semi-solid casting at CMI-Tech Center, and the experimental investigation of low pressure permanent mold casting at Amcast Automotive. U-M did an initial geometry which was defined for ProCAST to solve, and then a geometry half the size was defined and solved using the same boundary conditions. A conceptual mold geometry was examined and is represented as an axisymmetric element.Furthermore, the influences of the localized heat transfer coefficients on the casting process were carefully studied. The HTC Evaluator has been proposed and initially developed by the U-M team. The Reference and the Database Modules of the HTC Evaluator have been developed, and extensively tested. A series of technical barriers have been cited and potential solutions have been surveyed. At the CMI-Tech Center, the Kistler direct cavity pressure measurement system has been purchased and tested. The calibrations has been evaluated. The probe is capable of sensing a light finger pressure. The experimental mold has been designed and modified. The experimental mold has been designed and modified. The first experiment is scheduled for October 14, 1998. The geometry of the experimental hockey-puck casting has been given to the U-M team for numerical analysis.
Date: September 30, 1998
Creator: Pehlke, R.D. & Hao, S.W.
Partner: UNT Libraries Government Documents Department

Simulation of plasma based semiconductor processing using block structured locally refined grids

Description: We have described a new numerical method for plasma simulation. Calculations have been presented which show that the method is accurate and suggest the regimes in which the method provides savings in CPU time and memory requirements. A steady state simulation of a four centimeter domain was modeled with sheath scale (150 microns) resolution using only 40 grid points. Simulations of semiconductor processing equipment have been performed which imply the usefulness of the method for engineering applications. It is the author`s opinion that these accomplishments represent a significant contribution to plasma simulation and the efficient numerical solution of certain systems of non-linear partial differential equations. More work needs to be done, however, for the algorithm to be of practical use in an engineering environment. Despite our success at avoiding the dielectric relaxation timestep restrictions the algorithm is still conditionally stable and requires timesteps which are relatively small. This represents a prohibitive runtime for steady state solutions on high resolution grids. Current research suggests that these limitations may be overcome and the use of much larger timesteps will be possible.
Date: January 1, 1998
Creator: Wake, D.D.
Partner: UNT Libraries Government Documents Department

The Use of Chebyshev Polynomials in Numerical Analysis

Description: The purpose of this paper is to investigate the nature and practical uses of Chebyshev polynomials. Chapter I gives recognition to mathematicians responsible for studies in this area. Chapter II enumerates several mathematical situations in which the polynomials naturally arise and suggests reasons for the pursuance of their study. Chapter III includes: Chebyshev polynomials as related to "best" polynomial approximation, Chebyshev series, and methods of producing polynomial approximations to continuous functions. Chapter IV discusses the use of Chebyshev polynomials to solve certain differential equations and Chebyshev-Gauss quadrature.
Date: December 1975
Creator: Forisha, Donnie R.
Partner: UNT Libraries

Visualization of Instrumental Verification Information Details (VIVID) : code development, description, and usage.

Description: The formulation, implementation and usage of a numerical solution verification code is described. This code uses the Richardson extrapolation procedure to estimate the order of accuracy and error of a computational program solution. It evaluates multiple solutions performed in numerical grid convergence studies to verify a numerical algorithm implementation. Analyses are performed on both structured and unstructured grid codes. Finite volume and finite element discretization programs are examined. Two and three-dimensional solutions are evaluated. Steady state and transient solution analysis capabilities are present in the verification code. Multiple input data bases are accepted. Benchmark options are included to allow for minimal solution validation capability as well as verification.
Date: March 1, 2005
Creator: Roy, Christopher John; Bainbridge, Bruce L.; Potter, Donald L.; Blottner, Frederick G. & Black, Amalia Rebecca
Partner: UNT Libraries Government Documents Department

ML 3.1 developer's guide.

Description: ML development was started in 1997 by Ray Tuminaro and Charles Tong. Currently, there are several full- and part-time developers. The kernel of ML is written in ANSI C, and there is a rich C++ interface for Trilinos users and developers. ML can be customized to run geometric and algebraic multigrid; it can solve a scalar or a vector equation (with constant number of equations per grid node), and it can solve a form of Maxwell's equations. For a general introduction to ML and its applications, we refer to the Users Guide [SHT04], and to the ML web site, http://software.sandia.gov/ml.
Date: May 1, 2004
Creator: Sala, Marzio; Hu, Jonathan Joseph (Sandia National Laboratories, Livermore, CA) & Tuminaro, Raymond Stephen (Sandia National Laboratories, Livermore, CA)
Partner: UNT Libraries Government Documents Department

Real Beamline Optics from a Synthetic Beam

Description: The Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Lab can be described as a series of concatenated beamlines. Methods used to measure the Twiss parameters in closed orbit machines are not applicable in such open ended systems. We are using properly selected sets of real orbits in the accelerator, as one would for numerical analysis. The evolution of these trajectories along the beamline models the behavior of a synthetic beam which deterministically supplements beam profile-based Twiss parameter measurements and optimizes the efficiency of beamline tuning. Examples will be presented alongside a description of the process.
Date: May 1, 2010
Creator: Ryan Bodenstein,Michael Tiefenback,Yves Roblin
Partner: UNT Libraries Government Documents Department

Quantum crooks fluctuation theorem and quantum Jarzynski equality in the presence of a reservoir

Description: We consider the quantum mechanical generalization of Crooks Fluctuation and Jarzynski Equality Theorem for an open quantum system. The explicit expression for microscopic work for an arbitrary prescribed protocol is obtained, and the relation between quantum Crooks Fluctuation Theorem, quantum Jarzynski Equality and their classical counterparts are clarified. Numerical simulations based on a two-level toy model are used to demonstrate the validity of the quantum version of the two theorems beyond linear response theory regime.
Date: January 1, 2008
Creator: Quan, H T & Dong, H
Partner: UNT Libraries Government Documents Department

Numerical analysis of decoy state quantum key distribution protocols

Description: Decoy state protocols are a useful tool for many quantum key distribution systems implemented with weak coherent pulses, allowing significantly better secret bit rates and longer maximum distances. In this paper we present a method to numerically find optimal three-level protocols, and we examine how the secret bit rate and the optimized parameters are dependent on various system properties, such as session length, transmission loss, and visibility. Additionally, we show how to modify the decoy state analysis to handle partially distinguishable decoy states as well as uncertainty in the prepared intensities.
Date: January 1, 2008
Creator: Harrington, Jim W & Rice, Patrick R
Partner: UNT Libraries Government Documents Department

NUMERICAL FLOW AND TRANSPORT SIMULATIONS SUPPORTING THE SALTSTONE FACILITY PERFORMANCE ASSESSMENT

Description: The Saltstone Disposal Facility Performance Assessment (PA) is being revised to incorporate requirements of Section 3116 of the Ronald W. Reagan National Defense Authorization Act for Fiscal Year 2005 (NDAA), and updated data and understanding of vault performance since the 1992 PA (Cook and Fowler 1992) and related Special Analyses. A hybrid approach was chosen for modeling contaminant transport from vaults and future disposal cells to exposure points. A higher resolution, largely deterministic, analysis is performed on a best-estimate Base Case scenario using the PORFLOW numerical analysis code. a few additional sensitivity cases are simulated to examine alternative scenarios and parameter settings. Stochastic analysis is performed on a simpler representation of the SDF system using the GoldSim code to estimate uncertainty and sensitivity about the Base Case. This report describes development of PORFLOW models supporting the SDF PA, and presents sample results to illustrate model behaviors and define impacts relative to key facility performance objectives. The SDF PA document, when issued, should be consulted for a comprehensive presentation of results.
Date: February 28, 2009
Creator: Flach, G.
Partner: UNT Libraries Government Documents Department

Spatial Analysis of Emissions Sources for HCCI Combustion at Low Loads Using a Multi-Zone Model

Description: We have conducted a detailed numerical analysis of HCCI engine operation at low loads to investigate the sources of HC and CO emissions and the associated combustion inefficiencies. Engine performance and emissions are evaluated as fueling is reduced from typical HCCI conditions, with an equivalence ratio f = 0.26 to very low loads (f = 0.04). Calculations are conducted using a segregated multi-zone methodology and a detailed chemical kinetic mechanism for iso-octane with 859 chemical species. The computational results agree very well with recent experimental results. Pressure traces, heat release rates, burn duration, combustion efficiency and emissions of hydrocarbon, oxygenated hydrocarbon, and carbon monoxide are generally well predicted for the whole range of equivalence ratios. The computational model also shows where the pollutants originate within the combustion chamber, thereby explaining the changes in the HC and CO emissions as a function of equivalence ratio. The results of this paper contribute to the understanding of the high emission behavior of HCCI engines at low equivalence ratios and are important for characterizing this previously little explored, yet important range of operation.
Date: February 20, 2004
Creator: Aceves, S M; Flowers, D L; Espinosa-Loza, F; Martinez-Frias, J; Dec, J E; Sjoberg, M et al.
Partner: UNT Libraries Government Documents Department

USER 2.1; User Specified Estimation Routine, Techncial Manual 2003.

Description: This document is primarily a description of the user interface for USER2.1; it is not a description of the statistical theory and calculations behind USER. This project is funded by the Bonneville Power Administration, U.S. Department of Energy, under Contract No. 004126, Project No. 198910700 as part of the BPA's program to protect, mitigate, and enhance fish and wildlife affected by the development and operation of hydroelectric facilities on the Columbia River and its tributaries. The analysis of fish and wildlife data requires investigators to have the ability to develop statistical models tailored to their study requirements. Hence, a flexible platform to develop statistical likelihood models to estimate demographic parameters is necessary. To this end, Program USER (User Specified Estimation Routine) was developed to provide a convenient platform for investigators to develop statistical models and analyze tagging and count data. The program is capable of developing models and analyzing any count data that can be described by multinomial or product multinomial distributions. Such data include release-recapture studies using PIT-tags, radio-tags, balloon-tags, and acoustic-tags to estimate survival, movement, and demographic data on the age and/or sex structure of wild populations. The user of the program can specify the parameters and model structure at will to tailor the analyses to the specific requirements of the field sampling program, the data, and populations under investigation. All of this is available without the need for the user to know advanced programming languages or numerical analysis techniques, and without involving cumbersome software developed for extraneous purposes. Program USER represents a powerful statistical modeling routine that can be readily used by investigators with a wide range of interests and quantitative skills.
Date: July 1, 2003
Creator: Lady, James; Westhagen, Peter & Skalski, John
Partner: UNT Libraries Government Documents Department

A novel synthetic aperture technique for breast tomography with toroidal arrays

Description: Ultrasound is commonly used as an adjunct to mammography for diagnostic evaluation of suspicions arising from breast cancer screening. As an alternative to conventional sonography that uses hand-held transducers, toroidal array probes that encircle the breast immersed in a water bath have been investigated for ultrasound tomography. This paper introduces a new method for three-dimensional synthetic aperture diffraction tomography that maximizes the resolution in the scanning direction and provides quantitative reconstructions of the acoustic properties of the object. The method is validated by means of numerical simulations.
Date: January 1, 2009
Creator: Huang, Lianjie & Simonetti, Francesco
Partner: UNT Libraries Government Documents Department

Estimating maximum sustainable injection pressure duringgeological sequestration of CO2 using coupled fluid flow andgeomechanical fault-slip analysis

Description: This paper demonstrates the use of coupled fluid flow andgeomechanical fault slip (fault reactivation) analysis to estimate themaximum sustainable injection pressure during geological sequestration ofCO2. Two numerical modeling approaches for analyzing faultslip areapplied, one using continuum stress-strain analysis and the other usingdiscrete fault analysis. The results of these two approaches to numericalfault-slip analyses are compared to the results of a more conventionalanalytical fault-slip analysis that assumes simplified reservoirgeometry. It is shown that the simplified analytical fault-slip analysismay lead to either overestimation or underestimation of the maximumsustainable injection pressure because it cannot resolve importantgeometrical factors associated with the injection induced spatialevolution of fluid pressure and stress. We conclude that a fully couplednumerical analysis can more accurately account for the spatial evolutionof both insitu stresses and fluid pressure, and therefore results in amore accurate estimation of the maximum sustainable CO2 injectionpressure.
Date: October 17, 2006
Creator: Rutqvist, J.; Birkholzer, J.; Cappa, F. & Tsang, C.-F.
Partner: UNT Libraries Government Documents Department