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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

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

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

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

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

FLUID DYNAMICS MODEL FOR SALT-DOME EVOLUTION

Description: A fluid dynamics model for the evolution of salt domes and ridges is presented. The model assumes a rigid substrate, finite thickness of both strata with no slip and a rigid or free surface of overburden. Inertial terms in the Navier-Stokes equations are neglected due to the large viscosities considered and the initial perturbation is taken to be sinusoidal. Finite sine and cosine transforms are used to solve the flow equations and the resulting systems of equations reproduces the velocity field equation of Ramberg's model. Assuming an initial interface, the infinite series solution is truncated to obtain the constants of the integration from the boundary conditions. The interface is then moved to a new position. Thus, the new shape for the interface can be traced for any time. For small perturbations, we obtain results that are approximately those obtained by the linear theory. Results of the numerical solution of the model for both large and small perturbations are presented.
Date: August 1, 1977
Creator: Nasir, N. E. & Dabbousi, O. B.
Partner: UNT Libraries Government Documents Department

An Analytical Model for Solute Transport in Unsaturated Flowthrough a Single Fracture and Porous Rock Matrix

Description: Exact analytical solutions are presented for solute transport in an unsaturated fracture and porous rock matrix. The problem includes advective transport in the fracture and rock matrix as well as advective and diffusive fracture-matrix exchange. Linear sorption in the fracture and matrix and radioactive decay are also treated. The solution is for steady, uniform transport velocities within the fracture and matrix, but allows for independent specification of each of the velocities. The problem is first solved in terms of the solute concentrations that result from an instantaneous point source. Superposition integrals are then used to derive the solute mass flux at a fixed downstream position from an instantaneous point source and for the solute concentrations that result from a continuous point source. Solutions are derived for cases with the solute source in the fracture and the solute source in the matrix. The analytical solutions are closed-form and are expressed in terms of algebraic functions, exponentials, and error functions. Comparisons between the analytical solutions and numerical simulations, as well as sensitivity studies, are presented. Increased sensitivity to cross-flow and solute source location is found for increasing Peclet number. The numerical solutions are found to compare well with the analytical solutions at lower Peclet numbers ,but show greater deviation at higher Peclet numbers.
Date: September 16, 2004
Creator: Houseworth, J.E.
Partner: UNT Libraries Government Documents Department

Accurate iterative analytic 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 how to maintain a simple explicit format for the results. That paper used expansion in a small parameter to obtain the second level. 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 waveforms. They find excellent agreement with numerical solutions over a wide range of beam emittances and intensities.
Date: August 6, 2006
Creator: Anderson, Oscar A.
Partner: UNT Libraries Government Documents Department

The Role of Nuclear Motion in the Photo-Double Ionization ofMolecular Hydrogen

Description: We examine the origin of recently observed variations with internuclear distance (R) of the fully differential cross sections for double ionization of aligned H2 by absorption of a single photon. Using the results of fully converged numerical solutions of the Schroedinger equation, we show that these variations arise primarily from pronounced differences in the R-dependence of the parallel and perpendicular components of the ionization amplitude. We also predict that R-dependences should be readily observable in the asymmetry parameter for photo-double ionization, even in experimental measurements that are not differential in the energy sharings between ejected photo-electrons.
Date: October 26, 2006
Creator: Horner, Daniel A.; Vanroose, Wim; Rescigno, Thomas N.; Martin,Fernando & McCurdy, C. William
Partner: UNT Libraries Government Documents Department

NUMERICAL SOLUTION FOR THE POTENTIAL AND DENSITY PROFILE OF A THERMAL EQUILIBRIUM SHEET BEAM

Description: In a recent paper, S. M. Lund, A. Friedman, and G. Bazouin, Sheet beam model for intense space-charge: with application to Debye screening and the distribution of particle oscillation frequencies in a thermal equilibrium beam, in press, Phys. Rev. Special Topics - Accel. and Beams (2011), a 1D sheet beam model was extensively analyzed. In this complementary paper, we present details of a numerical procedure developed to construct the self-consistent electrostatic potential and density profile of a thermal equilibrium sheet beam distribution. This procedure effectively circumvents pathologies which can prevent use of standard numerical integration techniques when space-charge intensity is high. The procedure employs transformations and is straightforward to implement with standard numerical methods and produces accurate solutions which can be applied to thermal equilibria with arbitrarily strong space-charge intensity up to the applied focusing limit.
Date: April 1, 2011
Creator: Bazouin, Steven M. Lund, Guillaume & Bazouin, Guillaume
Partner: UNT Libraries Government Documents Department

Group velocity and pulse lengthening of mismatched laser pulses in plasma channels

Description: Analytic solutions are presented to the non-paraxial wave equation describing an ultra-short, low-power, laser pulse propagating in aplasma channel. Expressions for the laser pulse centroid motion and laser group velocity are derived, valid for matched and mismatchedpropagation in a parabolic plasma channel, as well as in vacuum, for an arbitrary Laguerre-Gaussian laser mode. The group velocity of amismatched laser pulse, for which the laser spot size is strongly oscillating, is found to be independent of propagation distance andsignificantly less than that of a matched pulse. Laser pulse lengthening of a mismatched pulse owing to laser mode slippage isexamined and found to dominate over that due to dispersive pulse spreading for sufficiently long pulses. Analytic results are shown tobe in excellent agreement with numerical solutions of the full Maxwell equations coupled to the plasma response. Implications for plasmachannel diagnostics are discussed.
Date: July 7, 2011
Creator: Schroeder, Carl; Benedetti, Carlo; Esarey, Eric; van Tilborg, Jeroen & Leemans, Wim
Partner: UNT Libraries Government Documents Department