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At least 595 records · Page 33

Getting granite dikes out of the source region

Whether a dike can propagate far from a magma reservoir depends upon the competition between the rate at which propagation widens the dike and the rate at which freezing constricts the aperture available for magma flow. Various formulations are developed for a viscous fluid at temperature T(sub m) intruding a growing crack in an elastic solid. The initial solid temperature equals T(sub m) at the source and decreases linearly with distance from the source. If T(sub m) is the unique freezing temperature of the fluid, dike growth is initially self-similar and an essentially exact solution is obtained; if T(sub m) is above the solidus temperature, the solution is approximate but is designed to overestimate the distance the dike may propagate. The ability of a dike to survive thermally depends primarily upon a single parameter that is a measure of the ratio of the dike frozen margin thickness to elastic thickness. Perhaps more intuitively, one may define a minimum distance from the essentially solid reservoir wall to the point at which the host rock temperature drops below the solidus, necessary for dikes to propagate far into subsolidus rock. It is concluded that for reasonable material properties and source conditions, most basalt dikes will have little difficulty leaving the source region, but most rhyolite dikes will be halted by freezing soon after the magma encounters rock at temperatures below the magma solidus. While these results can explain why granitic dikes are common near granitic plutons but rare elsewhere, the potentially large variation in magmatic systems makes it premature to rule out the possibility that most granites are transported through the crust in dikes. Nonetheless, these results highlight difficulties with such proposals and suggest that it may also be premature to rule out the possibility that most granite plutons ascend as more equidimensional bodies.

Rubin, Allan M.↗

Transverse shear stresses and their sensitivity coefficients in multilayered composite panels

A computational procedure is presented for the accurate determination of transverse shear stresses and their sensitivity coefficients in flat multilayered composite panels subjected to mechanical and thermal loads. The sensitivity coefficients measure the sensitivity of the transverse shear stresses to variations in the different lamination and material parameters of the panel. The panel is discretized by using either a three-field mixed finite element model based on a two-dimensional first- order shear deformation plate theory or a two-field degenerate solid element with each of the displacement components having a linear variation throughout the thickness of the laminate. The evaluation of transverse shear stresses can be conveniently divided into two phases. The first phase consists of using a superconvergent recovery technique for evaluating the in-plane stresses in the different layers. In the second phase, the transverse shear stresses are evaluated by using piecewise integration, in the thickness direction, of the three-dimensional equilibrium equations. The same procedure is used for evaluating the sensitivity coefficients of the transverse shear stresses. The effectiveness of the computational procedure is demonstrated by means of numerical examples of multilayered cross-ply panels subjected to transverse loading, uniform temperature change, and uniform temperature gradient through the thickness of the panel. In each case the standard of the comparison is taken to be the exact solution of the three dimensional thermoelasticity equations of the panel.

Noor, Ahmed K.↗

Buckling of imperfect, anisotropic, ring-stiffened cylinders under combined loads

The objective of this study is to develop an anlysis to predict buckling loads of ring-stiffened anisotropic cylinders subject to axial compression, torsion, and internal pressure. This structure is modeled as a branched shell. A nonlinear axisymmetric prebuckling equilibrium state is assumed which is amenable to an exact solution within each branch. Axisymmetric geometric imperfections are included. Buckling displacements are represented by a Fourier series in the circumferential coordination and the finite-element method in the axial coordinate. Application of the Trefftz criterion to the second variation of the total potential energy leads to a nonlinear eigenvalue problem for the buckling load and mode. Results are presented for both unstiffened and ring-stiffened cylinders in the form of buckling interaction diagrams. Imperfections can cause an unexpected buckling mode in the ring web which would not occur for the perfect structure, and pressurization diminishes the benefit of adding rings to the unstiffened shell to increase the buckling load. The implementation of the analysis methodology into a structural sizing algorithm is discussed.

Ley, Robert P.↗

Investigation of dispersion-relation-preserving scheme and spectral analysis methods for acoustic waves

Important characteristics of the aeroacoustic wave propagation are mostly encoded in their dispersion relations. Hence, a computational aeroacoustic (CAA) algorithm, which reasonably preserves these relations, was investigated. It was derived using an optimization procedure to ensure, that the numerical derivatives preserved the wave number and angular frequency of the differential terms in the linearized, 2-D Euler equations. Then, simulations were performed to validate the scheme and a compatible set of discretized boundary conditions. The computational results were found to agree favorably with the exact solutions. The boundary conditions were transparent to the outgoing waves, except when the disturbance source was close to a boundary. The time-domain data generated by such CAA solutions were often intractable until their spectra was analyzed. Therefore, the relative merits of three different methods were included in the study. For simple, periodic waves, the periodogram method produced better estimates of the steep-sloped spectra than the Blackman-Tukey method. Also, for this problem, the Hanning window was more effective when used with the weighted-overlapped-segment-averaging and Blackman-Tukey methods gave better results than the periodogram method. Finally, it was demonstrated that the representation of time domain-data was significantly dependent on the particular spectral analysis method employed.

Vanel, Florence O.↗

New higher-order Godunov code for modelling performance of two-stage light gas guns

A new quasi-one-dimensional Godunov code for modeling two-stage light gas guns is described. The code is third-order accurate in space and second-order accurate in time. A very accurate Riemann solver is used. Friction and heat transfer to the tube wall for gases and dense media are modeled and a simple nonequilibrium turbulence model is used for gas flows. The code also models gunpowder burn in the first-stage breech. Realistic equations of state (EOS) are used for all media. The code was validated against exact solutions of Riemann's shock-tube problem, impact of dense media slabs at velocities up to 20 km/sec, flow through a supersonic convergent-divergent nozzle and burning of gunpowder in a closed bomb. Excellent validation results were obtained. The code was then used to predict the performance of two light gas guns (1.5 in. and 0.28 in.) in service at the Ames Research Center. The code predictions were compared with measured pressure histories in the powder chamber and pump tube and with measured piston and projectile velocities. Very good agreement between computational fluid dynamics (CFD) predictions and measurements was obtained. Actual powder-burn rates in the gun were found to be considerably higher (60-90 percent) than predicted by the manufacturer and the behavior of the piston upon yielding appears to differ greatly from that suggested by low-strain rate tests.

Bogdanoff, D. W.↗

Computing Noise Temperature In A Beam Waveguide

Method of computing noise temperature in beam waveguide system involves both theoretical and experimental elements. Circumvents problem of computing noise temperature exactly from first principles: in case of typical practical system, noise-temperature problem so complex and difficult exact solution impossible.

Veruttipong, Watt↗

Damped Oscillator with Delta-Kicked Frequency

Exact solutions of the Schrodinger equation for quantum damped oscillator subject to frequency delta-kick describing squeezed states are obtained. The cases of strong, intermediate, and weak damping are investigated.

Manko, O. V.↗

Reflection Spectrum of Two Level Atoms by an Evanescent Laser Wave

An exact solution and numerical calculation of the reflection of two level atoms by atomic mirror are presented. The curve of reflection coefficient against Rabi frequency calculated shows some new features, and the physical machanism underlying is analyzed.

Tan, Weihan↗

Layerwise mechanics and finite element for the dynamic analysis of piezoelectric composite plates

Laminate and structural mechanics for the analysis of laminated composite plate structures with piezoelectric actuators and sensors are presented. The theories implement layerwise representations of displacements and electric potential, and can model both the global and local electromechanical response of smart composite laminates. Finite-element formulations are developed for the quasi-static and dynamic analysis of smart composite structures containing piezoelectric layers. Comparisons with an exact solution illustrate the accuracy, robustness and capability of the developed mechanics to capture the global and local response of thin and/or thick laminated piezoelectric plates. Additional correlations and numerical applications demonstrate the unique capabilities of the mechanics in analyzing the static and free-vibration response of composite plates with distributed piezoelectric actuators and sensors.

Saravanos, Dimitris A.↗

Fully-Explicit and Self-Consistent Algebraic Reynolds Stress Models

A fully-explicit, self-consistent algebraic expression for the Reynolds stress, which is the exact solution to the Reynolds stress transport equation in the 'weak equilibrium' limit for two-dimensional mean flows for all linear and some quasi-linear pressure-strain models, is derived. Current explicit algebraic Reynolds stress models derived by employing the 'weak equilibrium' assumption treat the production-to-dissipation (P/epsilon) ratio implicitly, resulting in an effective viscosity that can be singular away from the equilibrium limit. In the present paper, the set of simultaneous algebraic Reynolds stress equations are solved in the full non-linear form and the eddy viscosity is found to be non-singular. Preliminary tests indicate that the model performs adequately, even for three dimensional mean flow cases. Due to the explicit and non-singular nature of the effective viscosity, this model should mitigate many of the difficulties encountered in computing complex turbulent flows with the algebraic Reynolds stress models.

Girimaji, Sharath S.↗

Nonstandard Finite Difference Schemes: Relations Between Time and Space Step-Sizes in Numerical Schemes for PDE's That Follow from Positivity Condition

A large class of physical phenomena can be modeled by evolution and wave type Partial Differential Equations (PDE). Few of these equations have known explicit exact solutions. Finite-difference techniques are a popular method for constructing discrete representations of these equations for the purpose of numerical integration. However, the solutions to the difference equations often contain so called numerical instabilities; these are solutions to the difference equations that do not correspond to any solution of the PDE's. For explicit schemes, the elimination of this behavior requires functional relations to exist between the time and space steps-sizes. We show that such functional relations can be obtained for certain PDE's by use of a positivity condition. The PDE's studied are the Burgers, Fisher, and linearized Euler equations.

Mickens, Ronald E.↗

Application of AWE for RCS Frequency Response Calculations Using Method of Moments

An implementation of the Asymptotic Waveform Evaluation (AWE) technique is presented for obtaining the frequency response of the Radar Cross Section (RCS) of arbitrarily shaped, three-dimensional perfect electric conductor (PEC) bodies. An Electric Field Integral Equation (EFIE) is solved using the Method of Moments (MoM) to compute the RCS. The electric current, thus obtained, is expanded in a Taylor series around the frequency of interest. The coefficients of the Taylor series (called 'moments') are obtained using the frequency derivatives of the EFIE. Using the moments, the electric current on the PEC body is obtained over a frequency band. Using the electric current at different frequencies, RCS of the PEC body is obtained over a wide frequency band. Numerical results for a square plate, a cube, and a sphere are presented over a bandwidth. A good agreement between AWE and the exact solution over the bandwidth is observed.

Reddy, C. J.↗

Asymptotic Waveform Evaluation (AWE) Technique for Frequency Domain Electromagnetic Analysis

The Asymptotic Waveform Evaluation (AWE) technique is applied to a generalized frequency domain electromagnetic problem. Most of the frequency domain techniques in computational electromagnetics result in a matrix equation, which is solved at a single frequency. In the AWE technique, the Taylor series expansion around that frequency is applied to the matrix equation. The coefficients of the Taylor's series are obtained in terms of the frequency derivatives of the matrices evaluated at the expansion frequency. The coefficients hence obtained will be used to predict the frequency response of the system over a frequency range. The detailed derivation of the coefficients (called 'moments') is given along with an illustration for electric field integral equation (or Method of Moments) technique. The radar cross section (RCS) frequency response of a square plate is presented using the AWE technique and is compared with the exact solution at various frequencies.

Cockrell, C. R.↗

Time Dependent Models of Grain Formation Around Carbon Stars

Carbon-rich Asymptotic Giant Branch stars are sites of dust formation and undergo mass loss at rates ranging from 10(exp -7) to 10(exp -4) solar mass/yr. The state-of-the-art in modeling these processes is time-dependent models which simultaneously solve the grain formation and gas dynamics problem. We present results from such a model, which also includes an exact solution of the radiative transfer within the system.

Egan, M. P.↗

Frequency Response Calculations of Input Characteristics of Cavity-Backed Aperture Antennas Using AWE with Hybrid FEM/MoM Technique

Application of Asymptotic Waveform Evaluation (AWE) is presented in conjunction with a hybrid Finite Element Method (FEM)/Method of Moments (MoM) technique to calculate the input characteristics of cavity-backed aperture antennas over a frequency range. The hybrid FEM/MoM technique is used to form an integro-partial-differential equation to compute the electric field distribution of the cavity-backed aperture antenna. The electric field, thus obtained, is expanded in a Taylor series around the frequency of interest. The coefficients of 'Taylor series (called 'moments') are obtained using the frequency derivatives of the integro-partial-differential Equation formed by the hybrid FEM/MoM technique. Using the moments, the electric field in the cavity is obtained over a frequency range. Using the electric field at different frequencies, the input characteristics of the antenna are obtained over a wide frequency band. Numerical results for an open coaxial line, probe fed cavity, and cavity-backed microstrip patch antennas are presented. Good agreement between AWE and the exact solution over the frequency range is observed.

Reddy, C. J.↗

Non-Linear Cosmological Power Spectra in Real and Redshift Space

We present an expression for the non-linear evolution of the cosmological power spectrum based on Lagrangian trajectories. This is simplified using the Zel'dovich approximation to trace particle displacements, assuming Gaussian initial conditions. The model is found to exhibit the transfer of power from large to small scales expected in self-gravitating fields. Some exact solutions are found for power-law initial spectra. We have extended this analysis into red-shift space and found a solution for the non-linear, anisotropic redshift-space power spectrum in the limit of plane-parallel redshift distortions. The quadrupole-to-monopole ratio is calculated for the case of power-law initial spectra. We find that the shape of this ratio depends on the shape of the initial spectrum, but when scaled to linear theory depends only weakly on the redshift-space distortion parameter, beta. The point of zero-crossing of the quadrupole, kappa(sub o), is found to obey a simple scaling relation and we calculate this scale in the Zel'dovich approximation. This model is found to be in good agreement with a series of N-body simulations on scales down to the zero-crossing of the quadrupole, although the wavenumber at zero-crossing is underestimated. These results are applied to the quadrupole-to-monopole ratio found in the merged QDOT plus 1.2-Jy-IRAS redshift survey. Using a likelihood technique we have estimated that the distortion parameter is constrained to be beta greater than 0.5 at the 95 percent level. Our results are fairly insensitive to the local primordial spectral slope, but the likelihood analysis suggests n = -2 un the translinear regime. The zero-crossing scale of the quadrupole is k(sub 0) = 0.5 +/- 0.1 h Mpc(exp -1) and from this we infer that the amplitude of clustering is sigma(sub 8) = 0.7 +/- 0.05. We suggest that the success of this model is due to non-linear redshift-space effects arising from infall on to caustic and is not dominated by virialized cluster cores. The latter should start to dominate on scales below the zero-crossing of the quadrupole, where our model breaks down.

Taylor, A. N.↗

Diffraction of a Gaussian Beam by a Spherical Obstacle

The Kirchhoff integral for diffraction in the near-forward direction is derived from the exact solution of the electromagnetic boundary value problem of a focused Gaussian laser beam incident on a spherical particle. The diffracted intensity in the vicinity of the particle is computed and the way in which the features of the diffraction pattern depend on the width of the Gaussian beam is commented on.

Lock, James A.↗