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Experimental computation with oscillatory integrals

Description: A previous study by one of the present authors, together with D. Borwein and I. Leonard [8], studied the asymptotic behavior of the p-norm of the sinc function: sinc(x) = (sin x)/x and along the way looked at closed forms for integer values of p. In this study we address these integrals with the tools of experimental mathematics, namely by computing their numerical values to high precision, both as a challenge in itself, and also in an attempt to recognize the numerical values as closed-form constants. With this approach, we are able to reproduce several of the results of [8] and to find new results, both numeric and analytic, that go beyond the previous study.
Date: June 26, 2009
Creator: Bailey, David H. & Borwein, Jonathan M.
Partner: UNT Libraries Government Documents Department

Estimation of Damage Preference From Strike Parameters

Description: Estimation of an opponent's damage preference is illustrated by discussing the sensitivity of stability indices and strike parameters to it and inverting the results to study the sensitivity of estimates to uncertainties in strikes. Costs and stability indices do not generally have the monotonicity and sensitivity needed to support accurate estimation. First and second strikes do. Second strikes also have proportionality, although they are not unambiguously interpretable. First strikes are observable and have the greatest overall power for estimation, whether linear or numerical solutions are used.
Date: September 11, 1998
Creator: Canavan, G. H.
Partner: UNT Libraries Government Documents Department

Comparison of Numerical Methods for Solving the Second-Order Differential Equations of Molecular Scattering Theory

Description: The numerical solution of coupled, second-order differential equations is a fundamental problem in theoretical physics and chemistry. There are presently over 20 commonly used methods. Unbiased comparisons of the methods are difficult to make and few have been attempted. Here we report a comparison of 11 different methods applied to 3 different test problems. The test problems have been constructed to approximate chemical systems of current research interest and to be representative of the state of the art in inelastic molecular collisions. All calculations were done on the same computer and the attempt was made to do all calculations to the same level of accuracy. The results of the initial tests indicated that an improved method might be obtained by using different methods in different integration regions. Such a hybrid program was developed and found to be at least 1.5 to 2.0 times faster than any individual method.
Date: July 1, 1980
Creator: Thomas, L.D.; Alexander, M.H.; Johnson, B.R.; Lester Jr., W. A.; Light, J.C.; McLenithan, K.D. et al.
Partner: UNT Libraries Government Documents Department

Numerical image restoration by the method of singular-value decomposition

Description: BS>From seventh international conference on system sciences; Honolulu, Hawaii, USA (8 Jan 1974). The numerical image restoration problem is considered for the case of shift-variant imaging. The solution formalism presented is based on the method of singular-value decomposition. Some special-case versions of the formalism are considered. (auth)
Date: October 31, 1973
Creator: Ekstrom, M.P.
Partner: UNT Libraries Government Documents Department

Modeling broadband poroelastic propagation using an asymptotic approach

Description: An asymptotic method, valid in the presence of smoothly-varying heterogeneity, is used to derive a semi-analytic solution to the equations for fluid and solid displacements in a poroelastic medium. The solution is defined along trajectories through the porous medium model, in the manner of ray theory. The lowest order expression in the asymptotic expansion provides an eikonal equation for the phase. There are three modes of propagation, two modes of longitudinal displacement and a single mode of transverse displacement. The two longitudinal modes define the Biot fast and slow waves which have very different propagation characteristics. In the limit of low frequency, the Biot slow wave propagates as a diffusive disturbance, in essence a transient pressure pulse. Conversely, at low frequencies the Biot fast wave and the transverse mode are modified elastic waves. At intermediate frequencies the wave characteristics of the longitudinal modes are mixed. A comparison of the asymptotic solution with analytic and numerical solutions shows reasonably good agreement for both homogeneous and heterogeneous Earth models.
Date: May 1, 2009
Creator: Vasco, Donald W.
Partner: UNT Libraries Government Documents Department

A pore-scale model of two-phase flow in water-wet rock

Description: A finite-difference discretization of Stokes equations is used to simulate flow in the pore space of natural rocks. Numerical solutions are obtained using the method of artificial compressibility. In conjunction with Maximal Inscribed Spheres method, these computations produce relative permeability curves. The results of computations are in agreement with laboratory measurements.
Date: February 1, 2009
Creator: Silin, Dmitriy & Patzek, Tad
Partner: UNT Libraries Government Documents Department

Correspondence of the Gardner and van Genuchten/Mualem relativepermeability function parameters

Description: The Gardner and van Genuchten models of relativepermeability are widely used in analytical and numerical solutions toflow problems. However, the applicab ility of the Gardner model to realproblems is usually limited, because empirical relative permeability datato calibrate the model are not routinely available. In contrast, vanGenuchten parameters can be estimated using more routinely availablematric potential and saturation data. However, the van Genuchten model isnot amenable to analytical solutions. In this paper, we introducegeneralized conversion formulae that reconcile these two models. Ingeneral, we find that the Gardner parameter alpha G is related to the vanGenuchten parameters alpha vG and n by alpha G=alpha vG ~; 1:3 n. Thisconversion rule will allow direct recasting of Gardner-based analyticalsolutions in the van Genuchten parameter space. The validity of theproposed formulae was tested by comparing the predicted relativepermeability of various porous media with measured values.
Date: January 3, 2007
Creator: Ghezzehei, Teamrat A.; Kneafsey, Timothy J. & Su, Grace W.
Partner: UNT Libraries Government Documents Department

Accurate Iterative Analysis Solution of theKapchinskij-Vladimirskij Equations for the Case of a Matched Beam

Description: The well-known Kapchinskij-Vladimirskij (KV) equations are difficult to solve in general, but the problem is simplified for the matched-beam case with sufficient symmetry. They show that the interdependence of the two KV equations is eliminated, so that only one needs to be solved--a great simplification. They present an iterative method of solution which can potentially yield any desired level of accuracy. The lowest level, the well-known smooth approximation, yields simple, explicit results with good accuracy for weak or moderate focusing fields. The next level improves the accuracy for high fields; they previously showed [Part. Accel. 52, 133 (1996)] how to maintain a simple explicit format for the results. That paper used expansion in a small parameter to obtain results of second-level accuracy. The present paper, using straightforward iteration, obtains equations of first, second, and third levels of accuracy. For a periodic lattice with beam matched to lattice, they use the lattice and beam parameters as input and solve for phase advances and envelope functions. They find excellent agreement with numerical solutions over a wide range of beam emittances and intensities.
Date: January 31, 2007
Creator: Anderson, O.A.
Partner: UNT Libraries Government Documents Department

Modeling Gas-Phase Transport in Polymer-Electrolyte FuelCells

Description: In this transaction, the equations and methodology for modeling convection and ordinary, Knudsen, and pressure diffusion of gases in a fuel-cell gas-diffusion layer are described. Some results examining the magnitudes of the various terms are also made. This derivation results in a self-consistent description of the various transport mechanisms and is robust for numerical solutions, especially for conditions involving different flow regimes or where the regime is not known a priori.
Date: August 17, 2006
Creator: Weber, A.Z. & Newman, J.
Partner: UNT Libraries Government Documents Department


Description: A possible phase transition in liquid He{sup 3} has been investigated theoretically by generalizing the Bardeen, Cooper, and Schrieffer equations for the transition temperature in the manner suggested by Cooper, Mills, and Sessler. The equations are transformed into a form suitable for numerical solution and an expression is given for the transition temperature at which liquid He{sup 3} will change to highly correlated phase. Following a suggestion of Hottelson, it is shown that the phase transition is a consequence of the interaction of particles in relative D-states. The predicted value of the transition temperature depends on the assumed form of the effective single-particle potential and the interaction between He{sup 3} atoms. The most important aspects of the single-particle potential are related to the thermodynamic properties of the liquid just above the transition temperature. Two choices of the two-particle interaction, oonstituent with experiments, yield a second-order transition at a temperature between approximately 0.01 K and 0.1 K. The highly correlated phase should exhibit enhanced fluidity.
Date: January 29, 1960
Creator: Emery, V.J. & Sessler, A.M.
Partner: UNT Libraries Government Documents Department

An Explicit Time-Domain Hybrid Formulation Based on the Unified Boundary Condition

Description: An approach to stabilize the two-surface, time domain FEM/BI hybrid by means of a unified boundary condition is presented. The first-order symplectic finite element formulation [1] is used along with a version of the unified boundary condition of Jin [2] reformulated for Maxwell's first-order equations in time to provide both stability and accuracy over the first-order ABC. Several results are presented to validate the numerical solutions. In particular the dipole in a free-space box is analyzed and compared to the Dirchlet boundary condition of Ziolkowski and Madsen [3] and to a Neuman boundary condition approach.
Date: February 28, 2007
Creator: Madsen, N; Fasenfest, B J; White, D; Stowell, M; Jandhyala, V; Pingenot, J et al.
Partner: UNT Libraries Government Documents Department

Two-body bound states & the Bethe-Salpeter equation

Description: The Bethe-Salpeter formalism is used to study two-body bound states within a scalar theory: two scalar fields interacting via the exchange of a third massless scalar field. The Schwinger-Dyson equation is derived using functional and diagrammatic techniques, and the Bethe-Salpeter equation is obtained in an analogous way, showing it to be a two-particle generalization of the Schwinger-Dyson equation. The authors also present a numerical method for solving the Bethe-Salpeter equation without three-dimensional reduction. The ground and first excited state masses and wavefunctions are computed within the ladder approximation and space-like form factors are calculated.
Date: January 18, 1995
Creator: Pichowsky, M.; Kennedy, M. & Strickland, M.
Partner: UNT Libraries Government Documents Department

2D Numerical Simulation of the Resistive Reconnection Layer

Description: In this paper we present a two-dimensional numerical simulation of a reconnection current layer in incompressible resistive magnetohydrodynamics with uniform resistivity in the limit of very large Lundquist numbers. We use realistic boundary conditions derived consistently from the outside magnetic field, and we also take into account the effect of the back pressure from flow into the separatrix region. We find that within a few Alfvén times the system reaches a steady state consistent with the Sweet-Parker model, even if the initial state is Petschek-like.
Date: March 1, 1999
Creator: Kulsrud, R. M. & Uzdensky, D. A.
Partner: UNT Libraries Government Documents Department

Silicon crystal surface temperature: Computational and radiometric studies

Description: The surface temperature of the three-channel, gallium cooled Cornell silicon crystal was evaluated for the given system configuration and specifications. The THTB thermal-hydraulic program is used for the numerical solution of the problem, and the results are to be compared with the radiometric measurements obtained at Cornell.
Date: December 1, 1988
Creator: Khounsary, A.M.; Kuzay, T.M. & Forster, G.A.
Partner: UNT Libraries Government Documents Department

Image enhancement by edge-preserving filtering

Description: Image enhancement is useful when the details in an image are lost due to various reasons. It is common to subtract a mask from a given image to enhance the details. The trick is how to obtain a good mask. We describe here how an edge-preserving filter can be used to generate a mask which is smooth over areas with fine details, yet preserving most of the edges. Experiments with real images show that our scheme is very effective.
Date: November 1, 1994
Creator: Wong, Yiu-fai
Partner: UNT Libraries Government Documents Department

Singular eigenfunctions for shearing fluids I

Description: The authors construct singular eigenfunctions corresponding to the continuous spectrum of eigenvalues for shear flow in a channel. These modes are irregular as a result of a singularity in the eigenvalue problem at the critical layer of each mode. They consider flows with monotonic shear, so there is only a single critical layer for each mode. They then solve the initial-value problem to establish that these continuum modes, together with any discrete, growing/decaying pairs of modes, comprise a complete basis. They also view the problem within the framework of Hamiltonian theory. In that context, the singular solutions can be viewed as the kernel of an integral, canonical transformation that allows us to write the fluid system, an infinite-dimensional Hamiltonian system, in action-angle form. This yields an expression for the energy in terms of the continuum modes and provides a means for attaching a characteristic signature (sign) to the energy associate with each eigenfunction. They follow on to consider shear-flow stability within the Hamiltonian framework. Next, the authors show the equivalence of integral superpositions of the singular eigenfunctions with the solution derived with Laplace transform techniques. In the long-time limit, such superpositions have decaying integral averages across the channel, revealing phase mixing or continuum damping. Under some conditions, this decay is exponential and is then the fluid analogue of Landau damping. Finally, the authors discuss the energetics of continuum damping.
Date: February 1, 1995
Creator: Balmforth, N.J. & Morrison, P.J.
Partner: UNT Libraries Government Documents Department

Numerical analysis of the ultraprecision machining of copper

Description: Modeling of the ultraprecision machining process can aid in the understanding of the relative importance of various process parameters and ultimately lead to improved methods of generating ultraprecision surfaces such as those required for metal optics and single crystal microelectronics substrates. Any modeling method should be verified by direct comparison to experimental data. Until recently it has been difficult to accurately measure the cutting edge, or sharpness, of a diamond tool; and therefore, most models have assumed an infinitely sharp cutting tip. With the relatively new technology of the Atomic Force Microscope (AFM), the cutting edge of single crystal diamond tools can be quantitatively described. Ultraprecision machining experiments using an AFM characterized cutting tool and orthogonal geometry have been performed. These experiments have resulted in measured cutting and thrust forces for different depths of cut in copper (Te-Cu: 99.4-99.5% Cu, 0.5-0.6% Te, 4-5 micron grain size, 225 MPa yield strength) with a well characterized diamond tool. By using this actual tool tip geometry the authors have been able to develop a model that can predict cutting and thrust forces for depths of cut on the order of the sharpness of the tool. Forces predicted by this numerical model are compared to the experimentally measured forces.
Date: March 1, 1995
Creator: Stevens, R.; Anderson, C.; Rhorer, R. & Lucca, D.
Partner: UNT Libraries Government Documents Department