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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

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

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

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

A POSSIBLE PHASE TRANSITION IN LIQUID He3

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

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

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

Computational experience with a dense column feature for interior-point methods

Description: Most software that implements interior-point methods for linear programming formulates the linear algebra at each iteration as a system of normal equations. This approach can be extremely inefficient when the constraint matrix has dense columns, because the density of the normal equations matrix is much greater than the constraint matrix and the system is expensive to solve. In this report the authors describe a more efficient approach for this case, that involves handling the dense columns by using a Schur-complement method and conjugate gradient interaction. The authors report numerical results with the code PCx, into which the technique now has been incorporated.
Date: August 1, 1997
Creator: Wenzel, M.; Czyzyk, J. & Wright, S.
Partner: UNT Libraries Government Documents Department

Study of transverse loss factor for the tapered sections in the APS storage ring

Description: In the 7-GeV Advanced Photon Source (APS) storage ring, the tapered sections are considered to be the main contributor to the transverse impedance. The large tube represents the beam chamber, and the small one the insertion device section. Both are connected by a tapered transition with angle {theta}. This note presents a power law dependence of the transverse loss factor on the taper angle for this structure.
Date: June 6, 1990
Partner: UNT Libraries Government Documents Department

Toward an extended-geostrophic Euler-Poincare model for mesoscale oceanographic flow

Description: The authors consider the motion of a rotating, continuously stratified fluid governed by the hydrostatic primitive equations (PE). An approximate Hamiltonian (L1) model for small Rossby number {var_epsilon} is derived for application to mesoscale oceanographic flow problems. Numerical experiments involving a baroclinically unstable oceanic jet are utilized to assess the accuracy of the L1 model compared to the PE and to other approximate models, such as the quasigeostrophic (QG) and the geostrophic momentum (GM) equations. The results of the numerical experiments for moderate Rossby number flow show that the L1 model gives accurate solutions with errors substantially smaller than QG or GM.
Date: July 1998
Creator: Allen, J. S.; Newberger, P. A. & Holm, D. D.
Partner: UNT Libraries Government Documents Department

A neural computation approach to the set covering problem

Description: This paper presents a neural network algorithm which is capable of finding approximate solutions for unicost set covering problems. The network has two types of units (neurons), with different dynamics and activation functions. One type represents the objects to be covered (the rows in the matrix representation of the problem) and another represents the ``covering`` sets (the 0,1 variables). They are connected as a bipartite graph which represents the incidence relations between objects and sets (i.e the 0,1 adjacency matrix). When the parameters of the units are correctly tuned, the stable states of the system correspond to the minimal covers. I show that in its basic mode of operation, descent dynamics, when the network is set in an arbitrary initial state it converges in less than 2n steps (where n is the number of variables), to a stable state which represents a valid solution. In this mode, the network implements a greedy heuristic in which the choice function is based on the unit inputs (which are determined by the activation functions and the network state). On top of the basic network dynamics, the algorithm applies an adaptive restart procedure which helps to search more effectively for ``good`` initial states and results in better performance.
Date: July 1, 1995
Creator: Grossman, T.
Partner: UNT Libraries Government Documents Department

Overture: an objectoriented framework for solving partial differential equations on overlapping grids

Description: The Overture framework is an object-oriented environment for solving partial differential equations in two and three space dimensions. It is a collection of C++ libraries that enables the use of finite difference and finite volume methods at a level that hides the details of the associated data structures. Overture can be used to solve problems in complicated, moving geometries using the method of overlapping grids. It merges geometry, grid generation, difference operators, boundary conditions, data-base access and graphics into an easy to use high level interface.
Date: September 22, 1998
Creator: Brown, D L; Henshaw, W D & Quinlan , D J
Partner: UNT Libraries Government Documents Department

Numerical anomalies mimicking physical effects

Description: Numerical simulations of flows with shock waves typically use finite-difference shock-capturing algorithms. These algorithms give a shock a numerical width in order to generate the entropy increase that must occur across a shock wave. For algorithms in conservation form, steady-state shock waves are insensitive to the numerical dissipation because of the Hugoniot jump conditions. However, localized numerical errors occur when shock waves interact. Examples are the ``excess wall heating`` in the Noh problem (shock reflected from rigid wall), errors when a shock impacts a material interface or an abrupt change in mesh spacing, and the start-up error from initializing a shock as a discontinuity. This class of anomalies can be explained by the entropy generation that occurs in the transient flow when a shock profile is formed or changed. The entropy error is localized spatially but under mesh refinement does not decrease in magnitude. Similar effects have been observed in shock tube experiments with partly dispersed shock waves. In this case, the shock has a physical width due to a relaxation process. An entropy anomaly from a transient shock interaction is inherent in the structure of the conservation equations for fluid flow. The anomaly can be expected to occur whenever heat conduction can be neglected and a shock wave has a non-zero width, whether the width is physical or numerical. Thus, the numerical anomaly from an artificial shock width mimics a real physical effect.
Date: September 1, 1995
Creator: Menikoff, R.
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

Mechanisms affecting kinetic energies of laser-ablated materials

Description: Laser materials processing techniques are expected to have a dramatic impact on materials science and engineering in the near future and beyond. One of the main laser materials processing techniques is Pulsed Laser Deposition (PLD) for thin film growth. While experimentalists search for optimal approaches for thin film growth with pulsed laser deposition (PLD), a systematic effort in theory and modeling of various processes during PLD is needed. The quality of film deposited depends critically on the range and profile of the kinetic energy and density of the ablated plume. While it is to the advantage of pulsed laser deposition to have high kinetic energy, plumes that are too energetic causes film damage. A dynamic source effect was found to accelerate the plume expansion velocity much higher than that from a conventional free expansion model. A self-similar theory and a hydrodynamic model are developed to study this effect, which may help to explain experimentally observed high front expansion velocity. Background gas can also affect the kinetic energies. High background gas may cause the ablated materials to go backward. Experimentally observed plume splitting is also discussed.
Date: December 1995
Creator: Chen, K. R.; Leboeuf, J. N.; Wood, R. F.; Geohegan, D. B.; Donato, J. M.; Liu, C. L. et al.
Partner: UNT Libraries Government Documents Department

Global coupling and decoupling of the APS storage ring

Description: This Paper describes a study of controlling the coupling between the horizontal and the vertical betatron oscillations in the APS storage ring. First, we investigate the strengthening of coupling using two families of skew quadrupoles. Using smooth approximation, we obtained the formulae to estimate the coupling ratio defined as the ratio of the vertical and horizontal emittances or, for a single particle, the ratio of the maximum values of the Courant Snyder invariants. Since we knew that the coupling is mostly enhanced by the 21st harmonic content of skew quadrupole distribution, we carried out the harmonic analysis in order to find the optimum arrangement of the skew quadrupoles. The numerical results from tracking a single particle are presented for the various configurations of skew quadrupoles. Second, we describe the global decoupling procedure to minimize the unwanted coupling effects. These are mainly due to the random roll errors of normal quadrupoles. It is shown that even with the rather large rms roll error of 2 mrad we can reduce the Coupling from 70 percent to 10 percent with a skew quadrupole strength which is one order of magnitude lower than the typical normal quadrupole strength.
Date: July 1, 1995
Creator: Chae, Yong-Chul; Liu, Jianyang & Teng, L.C.
Partner: UNT Libraries Government Documents Department

Rapid asymmetric inflation and early cosmology in theories with sub-millimeter dimensions

Description: It was recently pointed out that the fundamental Planck mass could be close to the TeV scale with the observed weakness of gravity at long distances being due the existence of new sub-millimeter spatial dimensions. In this picture the standard model fields are localized to a (3+1)-dimensional wall or ''3-brane''. We show that in such theories there exist attractive models of inflation that occur while the size of the new dimensions are still small. We show that it is easy to produce the required number of efoldings, and further that the density perturbations {delta}{rho}/{rho} as measured by COBE can be easily reproduced, both in overall magnitude and in their approximately scale-invariant spectrum. In the minimal approach, the inflaton field is just the moduli describing the size of the internal dimensions, the role of the inflationary potential being played by the stabilizing potential of the internal space. We show that under quite general conditions, the inflationary era is followed by an epoch of contraction of our world on the brane, while the internal dimensions slowly expand to their stabilization radius. We find a set of exact solutions which describe this behavior, generalizing the well-known Kasner solutions. During this phase, the production of bulk gravitons remains suppressed. The period of contraction is terminated by the blue-shifting of Hawking radiation left on our wall at the end of the inflationary de Sitter phase. The temperature to which this is reheated is consistent with the normalcy bounds. We give a precise definition of the radion moduli problem.
Date: March 15, 1999
Creator: Arkani-Hamed, Nima
Partner: UNT Libraries Government Documents Department

QCD Evolution equations: Numerical algorithms from the Laguerre expansion

Description: A complete numerical implementation, in both singlet and non-singlet sectors, of a very elegant method to solve the QCD Evolution equations, due to Furmanski and Petronzio, is presented. The algorithm is directly implemented in x-space by a Laguerre expansion of the parton distributions. All the leading-twist distributions are evolved: longitudinally polarized, transversely polarized and unpolarized, to NLO accuracy. The expansion is optimal at finite x, up to reasonably small x-values (x{approx}10{sup {minus}3}), below which the convergence of the expansion slows down. The polarized evolution is smoother, due to the less singular structure of the anomalous dimensions at small-x. In the region of fast convergence, which covers most of the usual perturbative applications, high numerical accuracy is achieved by expanding over a set of approximately 30 polynomials, with a very modest running time.
Date: March 1, 1998
Creator: Coriano, Claudio & Savkli, Cetin
Partner: UNT Libraries Government Documents Department

A Full-Order, Almost Deterministic Optical Matching Algorithm

Description: An algorithm was developed for beam envelope matching with fixed geometry, taking into account the full order behavior of the quadrupoles and their compounded effects. The algebraic complexity of the system has hitherto defied attempts to obtain global solutions in any deterministic manner. In the present approach an algorithm to systematically reduce the overall system of equations has resulted in a system of two 8th order equations in only two variables in the thin lens approximation, and a system of two 12th order equations in two variables in the semi-thin lens approximation. The former displays a high degree of robustness in providing true global solutions, while the latter can be deterministically iterated to approach the exact thick lens solution to very high accuracy, and can be applied to configurations with arbitrary non-dispersive intervening optics. At the numerical level these 2 reduced systems are input to an equation solver in Mathematica 4.0 based on Grobner-basis techniques, capable of providing global solutions to such algebraic systems. The combined application of these 2 systems of equations has resulted in a very robust and effective algorithm for on-line optical beam envelope matching. The global nature of the algorithm also may point to possible deficiencies in the optical system configuration when no solution in real numbers exists. This affords a higher degree of insight and confidence than is possible with local-root-searching algorithms. An on-line high precision transfer matrix measurement program was developed in conjunction to provide input to this algorithm. Preliminary on-line testing on the CEBAF accelerator at the Thomas Jefferson National Accelerator Facility has positively demonstrated the effectiveness of this method. Direction for further enhancement of the algorithm will also be discussed.
Date: June 1, 2001
Creator: Chao, Yu-Chiu
Partner: UNT Libraries Government Documents Department