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416

May 6, 2010
05/10

by
Sack, R. A

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Generalization of laplace expansion to arbitrary powers and functions of distance between two points

Topics: DISTANCE, LAPLACE EQUATION, LAPLACE EQUATION

Analytical solution of Laplace equation using variable separation method, consists of two velocity potentials. However, only one component has been used. This research used both velocity potential equation components. With the potential equation, water wave surface equation and the related wave constants were formulated using kinematic free surface boundary condition and surface momentum equation. The characteristic of water wave surface that was produced was observed, both in deep water and...

Topics: Complete Solutionof Laplace Equation, Water wave surface equation.

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399

May 6, 2010
05/10

by
Wagner, C. A

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Gravitational potential of triaxial earth

Topics: EARTH (PLANET), ECCENTRICITY, GRAVITATIONAL FIELDS, LAPLACE EQUATION, EARTH, GRAVITATIONAL POTENTIAL

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236

Jun 27, 2010
06/10

by
Marko, W

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Moving long cylindrical model for aerobraking tests at high speed in drop wire facility

Topics: LAPLACE EQUATION, MATHEMATICAL MODELS, TIDES, ANTISYMMETRY, HARMONIC FUNCTIONS, OSCILLATIONS, WAVE...

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214

Jun 12, 2011
06/11

by
Eckert, Klaus; Juedes, David; Welch, Lonnie; Chelberg, David; Bruggerman, Carl; Drews, Frank; Fleeman, David; Parrott, David; Pfarr, Barbar

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Abstract. This paper presents a model that is useful for developing resource allocation algorithms for distributed real-time systems .that operate in dynamic environments. Interesting aspects of the model include dynamic environments, utility and service levels, which provide a means for graceful degradation in resource-constrained situations and support optimization of the allocation of resources. The paper also provides an allocation algorithm that illustrates how to use the model for...

Topics: CRAY COMPUTERS, COMPUTER SYSTEMS PERFORMANCE, PARALLEL PROCESSING (COMPUTERS), LAPLACE EQUATION,...

1,104
1.1K

Jun 21, 2010
06/10

by
Kuznetsova, T. D., et al

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Tables of characteristic exponents of Mathieu equations

Topics: APPROXIMATION, AXISYMMETRIC FLOW, HYDRODYNAMICS, INCOMPRESSIBLE FLUIDS, DIFFERENTIAL EQUATIONS,...

421
421

Jun 13, 2011
06/11

by
Davis, Brian A

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Previous work at NASA Langley Research Center (LaRC) involved fabrication and testing of composite beams with embedded, pre-strained shape memory alloy (SMA) ribbons. That study also provided comparison of experimental results with numerical predictions from a research code making use of a new thermoelastic model for shape memory alloy hybrid composite (SMAHC) structures. The previous work showed qualitative validation of the numerical model. However, deficiencies in the experimental-numerical...

Topics: COMPUTATIONAL FLUID DYNAMICS, CONVERGENCE, BOUNDARY CONDITIONS, LAPLACE EQUATION, ALGORITHMS,...

161
161

May 23, 2011
05/11

by
Chu, Barbara C. F.; Orgel, Leslie E

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Conjugates of biotin with the decamer of glutamic acid (glu(sub 10)) and the trimer of D,L-2-amino-5-phosphonovaleric acid (I) have been synthesized, and it has been shown that they mediate the binding of avidin to hydroxylapatite. In a similar way a conjugate of methotrexate with glu(sub 10) mediates the binding of dihydrofolate reductase to the mineral. The presentation of ligands on the hydroxylapatite component of bone may find applications in clinical medicine.

Topics: GRID GENERATION (MATHEMATICS), PREDICTOR-CORRECTOR METHODS, WINGS, COMPUTATIONAL GRIDS, LAPLACE...

774
774

Jul 11, 2010
07/10

by
Dvorak, F. A.; Woodward, F. A

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An analysis method and computer program have been developed for the calculation of the viscosity dependent aerodynamic characteristics of multi-element infinite swept wings in incompressible flow. The wing configuration consisting at the most of a slat, a main element and double slotted flap is represented in the method by a large number of panels. The inviscid pressure distribution about a given configuration in the normal chord direction is determined using a two dimensional potential flow...

Topics: INTERFERENCE DRAG, SWEPTBACK WINGS, TRANSONIC FLIGHT, AERODYNAMIC CHARACTERISTICS, ANGLE OF ATTACK,...

618
618

Feb 8, 2022
02/22

by
M. M. Lavrentiev

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This monograph deals with the problems of mathematical physics which are improperly posed in the sense of Hadamard. The first part covers various approaches to the formulation of improperly posed problems. These approaches are illustrated by the example of the classical improperly posed Cauchy problem for the Laplace equation. The second part deals with a number of problems of analytic continuations of analytic and harmonic functions. The third part is concerned with the investigation of the...

Topics: mathematical physics, Hadamard problem, Cauchy Problems, Laplace Equation, inverse problems,...

A general technique for expanding an unknown potential field in terms of a linear summation of weighted dipole or quadrupole fields is described. Computational methods were developed for the iterative addition of dipole fields. Various solution potentials were compared inside the boundary with a more precise calculation of the potential to derive optimal schemes for locating the singularities of the dipole fields. Then, the problem of determining solutions to Laplace's equation on an unbounded...

Topics: NASA Technical Reports Server (NTRS), ELECTROSTATICS, POTENTIAL FIELDS, QUADRUPOLES, DIPOLES,...

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208

Jun 20, 2010
06/10

by
Polyak, M. P.; Zysina-Molozhen, L. M

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Temperature field calculation for effective cooling of blades in gas turbines

Topics: COOLING SYSTEMS, GAS TURBINES, TEMPERATURE DISTRIBUTION, TURBINE BLADES, COMPUTER PROGRAMMING,...

296
296

Jun 1, 2011
06/11

by
Johnson, Wayne; Yamauchi, Gloria K.; Derby, Michael R.; Wadcock, Alan J

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Wind tunnel measurements and calculations of the aerodynamic interactions between two tiltrotor aircraft in helicopter mode are presented. The measured results include the roll moment and thrust change on the downwind aircraft, as a function of the upwind aircraft position (longitudinal, lateral, and vertical). Magnitudes and locations of the largest interactions are identified. The calculated interactions generally match the measurements, with discrepancies attributed to the unsteadiness of...

Topics: ALGORITHMS, KERNEL FUNCTIONS, METHODOLOGY, MATHEMATICAL MODELS, NORMAL DENSITY FUNCTIONS,...

289
289

Jun 11, 2011
06/11

by
MacConochie, Ian O.; Stnaley, Douglas O

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A single-stage-to-orbit launch vehicle is used to assess the applicability of Soviet Energia high-pressure-hydrocarbon engine to advanced U.S. manned space transportation systems. Two of the Soviet engines are used with three Space Shuttle Main Engines. When applied to a baseline vehicle that utilized advanced hydrocarbon engines, the higher weight of the Soviet engines resulted in a 20 percent loss of payload capability and necessitated a change in the crew compartment size and location from...

Topics: BAYES THEOREM, STEREOSCOPIC VISION, SHAPES, ITERATION, PARAMETERIZATION, MATHEMATICAL MODELS,...

A computer software system is described which computes global numerical solutions of the integro-differential Laplace tidal equations, including dissipation terms and ocean loading and self-gravitation effects, for arbitrary diurnal and semidiurnal tidal constituents. The integration algorithm features a successive approximation scheme for the integro-differential system, with time stepping forward differences in the time variable and central differences in spatial variables. Solutions for M2,...

Topics: NASA Technical Reports Server (NTRS), COMPUTERS, NUMERICAL ANALYSIS, OCEANS, TIDES, GRAVITATION,...

341
341

Jun 11, 2011
06/11

by
Meyers, James F

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The development of Doppler global velocimetry is described. Emphasis is placed on the modifications necessary to advance this nonintrusive laser based measurement technique from a laboratory prototype to a viable wind tunnel flow diagnostics tool. Several example wind tunnel flow field investigations are described to illustrate the versatility of the technique. Flow conditions ranged from incompressible to Mach 2.8 with measurement distances extending from 1 to 15 m.

Topics: THREE DIMENSIONAL FLOW, NAVIER-STOKES EQUATION, NUMERICAL ANALYSIS, INCOMPRESSIBLE FLOW, INVISCID...

This paper helps the reader understand the characteristics of the Cray X1 vector supercomputer system, and provides hints and information to enable the reader to port codes to the system. It provides a comparison between the basic performance of the X1 platform and other platforms that are available at NASA Ames Research Center. A set of codes, solving the Laplacian equation with different parallel paradigms, is used to understand some features of the X1 compiler. An example code from the NAS...

Topics: NASA Technical Reports Server (NTRS), CRAY COMPUTERS, COMPUTER SYSTEMS PERFORMANCE, PARALLEL...

A boundary integral numerical method for the dynamics of nonspherical cavitation bubbles in inviscid incompressible liquids is described. Only surface values of the velocity potential and its first derivatives are involved. The problem of solving the Laplace equation in the entire domain occupied by the liquid is thus avoided. The collapse of a bubble in the vicinity of a solid wall and the collapse of three bubbles with collinear centers are considered.

Topics: NASA Technical Reports Server (NTRS), BUBBLES, CAVITATION FLOW, INCOMPRESSIBLE FLUIDS, INTEGRAL...

A general theory for indicial-potential-compressible aerodynamics around complex configurations is presented. The motion is assumed to consist of constant subsonic or supersonic speed (steady state) and small perturbations around the steady state. Using the finite-element method to discretize the space problem, a set of differential-difference equations in time relating the potential to its normal derivative on the surface of the body was obtained. The aerodynamics transfer function was derived...

Topics: NASA Technical Reports Server (NTRS), AERODYNAMIC CONFIGURATIONS, FINITE ELEMENT METHOD, SUBSONIC...

Equations are derived for the approximate calculation of the air gap configuration of a hollow-rotor clutch.

Topics: NASA Technical Reports Server (NTRS), CLUTCHES, LAPLACE EQUATION, MAGNETIC FIELDS,...

The lunar magnetic dipole moment is discussed. It is proposed that if a primordial core magnetic field existed, it would give rise to a present day nonzero external dipole magnetic field. This conclusion is based on the assumption that the lunar mantle is at least slightly ferromagnetic, and thus would maintain a permanent magnetization after the disappearance of the core magnetic field. Using a simple mathematical model of the moon, calculations are performed which support this hypothesis.

Topics: NASA Technical Reports Server (NTRS), LUNAR MAGNETIC FIELDS, POTENTIAL THEORY, LAPLACE EQUATION,...

A complete derivation of the geopotential function and its gradient is presented. Also included is the transformation of Laplace's equation from Cartesian to spherical coordinates. The analytic solution to Laplace's equation is obtained from the transformed version, in the classical manner of separating the variables. A cursory introduction to the method devised by Pines, using direction cosines to express the orientation of a point in space, is presented together with sample computer program...

Topics: NASA Technical Reports Server (NTRS), GEOPOTENTIAL, GRAVITATIONAL FIELDS, ORBIT CALCULATION,...

Ocean tidal signals appear in many geophysical measurements. Geophysicists need realistic tidal models to aid in interpretation of their data. Because of the closeness to resonance of dissipationless ocean tides, it is difficult for numerical models to correctly represent the actual open ocean tide. As an approximate solution to this problem, test functions derived by solving Laplace's Tidal Equations with ocean loading and self gravitation are used as a basis for least squares dynamic...

Topics: NASA Technical Reports Server (NTRS), EARTH TIDES, OCEAN MODELS, COASTAL PLAINS, LAPLACE EQUATION,...

A representative class of elliptic equations is treated by a dissipative compact finite difference scheme and a general solution technique by relaxation methods is discussed in detail for the Laplace equation.

Topics: NASA Technical Reports Server (NTRS), ELLIPTIC FUNCTIONS, FINITE DIFFERENCE THEORY, LAPLACE...

A method was developed for determining the fundamental tidal frequencies for closed basins of water, by means of an eigenvalue analysis. The mathematical model employed, was the Laplace tidal equations.

Topics: NASA Technical Reports Server (NTRS), FINITE ELEMENT METHOD, NASTRAN, STRUCTURAL BASINS, TIDES,...

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238

May 22, 2011
05/11

by
Ozhogin, V

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The research projects and new technological developments that have occured in Russia are highlighted in this document. Some of the research discussed includes: x-ray structure analysis of YBCO superconducting single crystals and accompanying phase transformations; the role of electron-electron interaction in High Temperature Superconductors (HTSC); the formation of Cooper pairs in crystals; the synthesis and research on a new family of superconductors based on complex copper and mercury oxides...

Topics: COMPUTATIONAL FLUID DYNAMICS, GALERKIN METHOD, GRID GENERATION (MATHEMATICS), LAPLACE EQUATION,...

Procedures are given for calculating thermal fields and associated thermal deformations in astronomical mirrors. A technique is described for thermal strain simulation when complex thermal fields develop in astronomical mirrors. Thermal strains in pyroceramic, quartz and pyrex mirrors can be effectively determined at temperatures ranging from -70 to 150 C by this technique.

Topics: NASA Technical Reports Server (NTRS), MIRRORS, TELESCOPES, TEMPERATURE EFFECTS, THERMAL STRESSES,...

Measurements of rotating equilibrium bubble shapes in the low-gravity environment of a free-falling aircraft are presented. Emphasis is placed on bubbles which intersect the container boundaries. These data are compared with theoretical profiles derived from Laplace's formula and are in good agreement with the measurements. Two types of instability are explored. The first occurs when the baffle spacing is too large for the bubble to intersect both the top and bottom boundaries. The second...

Topics: NASA Technical Reports Server (NTRS), BUBBLES, FLUID MECHANICS, GRAVITATION, MICROGRAVITY, SHAPES,...

A variety of increasingly intricate container geometries are under consideration for the passive manipulation of liquids aboard spacecraft where the impact of gravity may be neglected. In this study we examine the mean curvature of a liquid volume confined within a radial array of disconnected vanes of infinite extent. This particular geometry possesses a number of desirable characteristics relevant to waste water treatment aboard spacecraft for life support. It is observed that under certain...

Topics: NASA Technical Reports Server (NTRS), WEIGHTLESSNESS, LIQUIDS, VANES, CASES (CONTAINERS), MEAN FREE...

In detached Bridgman crystal growth, most of the melt is in contact with the ampoule wall, but the crystal is separated from the wall by a small gap, typically 1-100 micrometers. A liquid free surface, or meniscus, bridges across this gap at the position of the melt-crystal interface. Meniscus shapes have been calculated for the case of detached Bridgman growth in cylindrical ampoules by solving the Young-Laplace equation. Key parameters affecting meniscus shapes are the growth angle, contact...

Topics: NASA Technical Reports Server (NTRS), BRIDGMAN METHOD, CRYSTAL GROWTH, MELTS (CRYSTAL GROWTH),...

An existence result was obtained for a nonlinear second-order equation in an exterior domain of IR(3). The proof relies on a variational formulation in weighted Sobolev spaces.

Topics: NASA Technical Reports Server (NTRS), DIRICHLET PROBLEM, ELLIPSES, THEOREM PROVING, VARIATIONAL...

We present a new method for density estimation based on Mercer kernels. The density estimate can be understood as the density induced on a data manifold by a mixture of Gaussians fit in a feature space. As is usual, the feature space and data manifold are defined with any suitable positive-definite kernel function. We modify the standard EM algorithm for mixtures of Gaussians to infer the parameters of the density. One benefit of the approach is it's conceptual simplicity, and uniform...

Topics: NASA Technical Reports Server (NTRS), ALGORITHMS, KERNEL FUNCTIONS, METHODOLOGY, MATHEMATICAL...

The convergence properties of numerical schemes for partial differential equations are studied by examining the eigensystem of the discrete operator. This method of analysis is very general, and allows the effects of boundary conditions and grid nonuniformities to be examined directly. Algorithms for the Laplace equation and a two equation model hyperbolic system are examined.

Topics: NASA Technical Reports Server (NTRS), COMPUTATIONAL FLUID DYNAMICS, CONVERGENCE, BOUNDARY...

We present a new Bayesian vision technique that aims at recovering a shape from two or more noisy observations taken under similar lighting conditions. The shape is parametrized by a piecewise linear height field, textured by a piecewise linear irradiance field, and we assume Gaussian Markovian priors for both shape vertices and irradiance variables. The observation process. also known as rendering, is modeled by a non-affine projection (e.g. perspective projection) followed by a convolution...

Topics: NASA Technical Reports Server (NTRS), BAYES THEOREM, PARAMETERIZATION, MATHEMATICAL MODELS,...

The procedure to generate the grid around a complex wing configuration is presented in this report. The automatic grid generation utilizes the Modified Advancing Front Method as a predictor and an elliptic scheme as a corrector. The scheme will advance the surface grid one cell outward and the newly obtained grid is corrected using the Laplace equation. The predictor-corrector step ensures that the grid produced will be smooth for every configuration. The predictor-corrector scheme is extended...

Topics: NASA Technical Reports Server (NTRS), GRID GENERATION (MATHEMATICS), PREDICTOR-CORRECTOR METHODS,...

The problem of an elastic solid containing a semi-infinite plane crack subjected to concentrated shears parallel to the edge of the crack is considered. A closed form solution using four distinct harmonic functions (none of which can be taken arbitrarily) is found to satisfy the finite displacement and inverse square root stress singularity at the edge of the crack. Explicit expressions in terms of elementary functions are given for the distribution of stress and displacement in the solid....

Topics: NASA Technical Reports Server (NTRS), CRACK PROPAGATION, FRACTURE MECHANICS, HARMONIC FUNCTIONS,...

An analysis was made of the potential flow behavior for an initially uniform flow passing over a single axisymmetric hill, an oval mound, and a combination of two hills. Small perturbation theory was used, and the resulting Laplace equation for the perturbation velocity potential was solved by using either a product solution or a Green's function. The three dimensional solution is of interest in calculating the pressure distribution around obstacles, the flow of pollutants carried by the wind,...

Topics: NASA Technical Reports Server (NTRS), MATHEMATICAL MODELS, THREE DIMENSIONAL FLOW, TURBULENT...

Two trends evident in global tidal modelling since the first GEOP conference in 1972 are described. The first centers on the incorporation of terms for ocean loading and gravitational self attraction into Laplace's tidal equations. The second centers on a better understanding of the problem of near resonant modelling and the need for realistic maps of tidal elevation for use by geodesists and geophysicists. Although new models still show significant differences, especially in the South...

Topics: NASA Technical Reports Server (NTRS), GEODYNAMICS, GRAVITATIONAL EFFECTS, MATHEMATICAL MODELS,...

An important goal of geodesy is to determine the anomalous potential and its derivatives outside of the earth. Representing the surface anomalies by a series of spherical harmonics is useful since it is then possible to do a term by term solution of Laplace's equation and upward continuation. The problem of finding such a spherical harmonic series for anomaly values given on an equiangular surface grid is addressed. (This is a first step toward the more complicated problem of finding a function...

Topics: NASA Technical Reports Server (NTRS), COEFFICIENTS, COMPUTATIONAL GRIDS, GEODESY, GRAVITY...

A computer software system is described which computes global numerical solutions of the integro-differential Laplace tidal equations, including dissipation terms and ocean loading and self-gravitation effects, for arbitrary diurnal and semidiurnal tidal constituents. The integration algorithm features a successive approximation scheme for the integro-differential system, with time stepping forward differences in the time variable and central differences in spatial variables.

Topics: NASA Technical Reports Server (NTRS), COMPUTER SYSTEMS PROGRAMS, GRAVITATIONAL EFFECTS, INTEGRATED...

On a macroscopic scale, a nonreactive liquid partially covering a homogeneous solid surface will intersect the solid at an angle called the contact angle. For molten metals and semiconductors, the contact angle is materially dependent upon both the solid and liquid and typical values fall in the range 80-170 deg, depending on the crucible material. On a microscopic scale, there does not exist a precise and sharp contact angle but rather the liquid and solid surfaces merge smoothly and...

Topics: NASA Technical Reports Server (NTRS), CRYSTAL GROWTH, ELECTROMAGNETIC FIELDS, LIQUID SURFACES,...

A rapid procedure for generating C-type cascade grids suitable for viscous flow computations in turbomachinery blade rows is presented. The resulting mesh is periodic from one blade passage to the next, nearly orthogonal, and continuous across the wake downstream of a blade. The procedure employs a pair of conformal mappings that take the exterior of the cascade into the interior of an infinite strip with curved boundaries. The final transformation to a rectangular computational domain is...

Topics: NASA Technical Reports Server (NTRS), CASCADE FLOW, COMPUTATION, COORDINATES, GRID GENERATION...

A cubic spline collocation procedure was developed for the numerical solution of partial differential equations. This spline procedure is reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy of a nonuniform mesh. Solutions using both spline procedures, as well as three-point finite difference methods, are presented for...

Topics: NASA Technical Reports Server (NTRS), CUBIC EQUATIONS, NUMERICAL ANALYSIS, SPLINE FUNCTIONS,...

Formulations for a general theory of thermoelasticity to generate accurate thermal stresses for structural members of aeronautical vehicles were developed in 1954 by Boley. The formulation also provides three normal stresses and a shear stress along the entire length of the beam. The Poisson effect of the lateral and transverse normal stresses on a thermally loaded beam is taken into account in this theory by employing an Airy stress function. The Airy stress function enables the reduction of...

Topics: NASA Technical Reports Server (NTRS), THERMAL STRESSES, THERMOELASTICITY, MECHANICAL PROPERTIES,...

Various artificial compressibility methods for calculating the three-dimensional incompressible Navier-Stokes equations are compared. Each method is described and numerical solutions to test problems are conducted. A comparison based on convergence behavior, accuracy, and robustness is given.

Topics: NASA Technical Reports Server (NTRS), THREE DIMENSIONAL FLOW, NAVIER-STOKES EQUATION, NUMERICAL...

Indirect mapping ocean tides by means of land and island-based tidal gravity measurements is presented. The inverse scheme of linear programming is used for indirect mapping of ocean tides. Open ocean tides were measured by the numerical integration of Laplace's tidal equations.

Topics: NASA Technical Reports Server (NTRS), EARTH TIDES, LINEAR PROGRAMMING, OCEAN CURRENTS, GRAVIMETRY,...

An analytical solution was obtained for the perturbation velocity potential for transonic flow about lifting wing-body configurations with order-one span-length ratios and small reduced-span-length ratios and equivalent-thickness-length ratios. The analysis is performed with the method of matched asymptotic expansions. The angles of attack which are considered are small but are large enough to insure that the effects of lift in the region far from the configuration are either dominant or...

Topics: NASA Technical Reports Server (NTRS), BODY-WING CONFIGURATIONS, LIFTING BODIES, SLENDER BODIES,...

A Poisson equation on a rectangular domain is solved by coupling two methods: the domain is divided in two squares, a finite element approximation is used on the first square and a spectral discretization is used on the second one. Two kinds of matching conditions on the interface are presented and compared. In both cases, error estimates are proved.

Topics: NASA Technical Reports Server (NTRS), COUPLING, FINITE ELEMENT METHOD, SPECTRAL METHODS,...

Preconditioned conjugate gradient methods for solving sparse symmetric and positive finite systems of linear equations are described. Necessary and sufficient conditions are given for when these preconditioners can be used and an analysis of their effectiveness is given. Efficient computer implementations of these methods are discussed and results on the CYBER 203 and the Finite Element Machine under construction at NASA Langley Research Center are included.

Topics: NASA Technical Reports Server (NTRS), CONJUGATE GRADIENT METHOD, ITERATIVE SOLUTION, LINEAR...

NASTRAN solution techniques are shown for a numerical analysis of a class of coupled vector flow processes described by simultaneous parabolic differential equations. To define one physical problem type where equations of this form arise, the differential equations describing the coupled transfers of heat and mass in mechanical equilibrium with negligible mass average velocity are presented and discussed. Also shown are the equations describing seepage when both electrokinetic and hydrodynamic...

Topics: NASA Technical Reports Server (NTRS), COMPUTER PROGRAMS, FINITE ELEMENT METHOD, PARABOLIC...