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At least 559 records · Page 31

An exactly solvable model for calculating critical misfit and thickness in epitaxial superlattices. II - Layers of unequal elastic constants and thicknesses

The theoretical model developed by van der Merwe and Jesser (1988) is extended to permit the exact determination of the critical misfit and critical thickness of an epitaxially grown superlattice made up of layers with differing elastic constants and thicknesses. Lateral force balances are maintained by means of an explicit relationship between the homogeneous misfit strains and the thicknesses and moduli. A number of simplifying approximations are introduced, and sample numerical results are presented in graphs.

Jesser, W. A.↗

A hybrid perturbation-Galerkin method for differential equations containing a parameter

A two-step hybrid perturbation-Galerkin method to solve a variety of differential equations which involve a parameter is presented and discussed. The method consists of: (1) the use of a perturbation method to determine the asymptotic expansion of the solution about one or more values of the parameter; and (2) the use of some of the perturbation coefficient functions as trial functions in the classical Bubnov-Galerkin method. This hybrid method has the potential of overcoming some of the drawbacks of the perturbation method and the Bubnov-Galerkin method when they are applied by themselves, while combining some of the good features of both. The proposed method is illustrated first with a simple linear two-point boundary value problem and is then applied to a nonlinear two-point boundary value problem in lubrication theory. The results obtained from the hybrid method are compared with approximate solutions obtained by purely numerical methods. Some general features of the method, as well as some special tips for its implementation, are discussed. A survey of some current research application areas is presented and its degree of applicability to broader problem areas is discussed.

Geer, James F.↗

Optimal model reduction and frequency-weighted extension

In this paper the quadratically optimal model reduction problem for single-input, single-output systems is considered. The reduced order model is determined by minimizing the integral of the magnitude-squared of the transfer function error. It is shown that the numerator coefficients of the optimal approximant satisfy a weighted least squares problem and, on this basis, a two-step iterative algorithm is developed combining a least squares solver with a gradient minimizer. The existence of globally optimal stable solutions to the optimization problem is established, and convergence of the algorithm to stationary values of the cost function is proved. The formulation is extended to handle the frequency-weighted optimal model reduction problem. Three examples demonstrate the optimization algorithm.

Spanos, J. T.↗

A new treatment of the albedo radiation pressure in the case of a uniform albedo and of a spherical satellite

The purpose of this paper is to present a model for the radiation pressure acceleration of a spherical satellite, due to the radiation reflected by a planet with a uniform albedo. A particular choice of variables allows one to reduce the surface integrals over the lit portion of the planet visible to the satellite to one-dimensional integrals. Exact analytical expressions are found for the integrals corresponding to the case where the spacecraft does not 'see' the terminator. The other integrals can be computer either numerically, or analytical in an approximate form. The results are compared with those of Lochry (1966). The model is applied to Magellan, a spacecraft orbiting Venus.

Borderies, Nicole↗

The gabbro-eclogite phase transition and the elevation of mountain belts on Venus

Among the four mountain belts surrounding Lakshmi Planum, Maxwell Montes is the highest and stands up to 11 km above the mean planetary radius and 7 km above Lakshmi Planum. The bulk composition and radioactive heat production of the crust on Venus, where measured, are similar to those of terrestrial tholeiitic basalt. Because the thickness of the low-density crust may be limited by the gabbro-garnet granulite-eclogite phase transitions, the 7-11 km maximum elevation of Maxwell Montes is difficult to understand except in the unlikely situation that the crust contains a large volume of magma. A possible explanation is that the base of the crust is not in phase equilibrium. It has been suggested that under completely dry conditions, the gabbro-eclogite phase transition takes place by solid-state diffusion and may require a geologically significant time to run to completion. Solid-state diffusion is a strongly temperature-dependent process. In this paper we solve the thermal evolution of the mountain belt to attempt to constrain the depth of the gabbro-eclogite transition and thus to assess this hypothesis quantitatively. The one-dimensional heat equation is solved numerically by a finite difference approximation. The deformation of the horizontally shortening crustal and mantle portions of the thermal boundary layer is assumed to occur by pure shear, and therefore the vertical velocity is given by the product of the horizontal strain rate and depth.

Namiki, Noriyuki↗

BLSTA: A boundary layer code for stability analysis

A computer program is developed to solve the compressible, laminar boundary-layer equations for two-dimensional flow, axisymmetric flow, and quasi-three-dimensional flows including the flow along the plane of symmetry, flow along the leading-edge attachment line, and swept-wing flows with a conical flow approximation. The finite-difference numerical procedure used to solve the governing equations is second-order accurate. The flow over a wide range of speed, from subsonic to hypersonic speed with perfect gas assumption, can be calculated. Various wall boundary conditions, such as wall suction or blowing and hot or cold walls, can be applied. The results indicate that this boundary-layer code gives velocity and temperature profiles which are accurate, smooth, and continuous through the first and second normal derivatives. The code presented herein can be coupled with a stability analysis code and used to predict the onset of the boundary-layer transition which enables the assessment of the laminar flow control techniques. A user's manual is also included.

Wie, Yong-Sun↗

Polynomial approximation of Poincare maps for Hamiltonian system

Different methods are proposed and tested for transforming a non-linear differential system, and more particularly a Hamiltonian one, into a map without integrating the whole orbit as in the well-known Poincare return map technique. We construct piecewise polynomial maps by coarse-graining the phase-space surface of section into parallelograms and using either only values of the Poincare maps at the vertices or also the gradient information at the nearest neighbors to define a polynomial approximation within each cell. The numerical experiments are in good agreement with both the real symplectic and Poincare maps.

Froeschle, Claude↗

A new algorithm for L2 optimal model reduction

In this paper the quadratically optimal model reduction problem for single-input, single-output systems is considered. The reduced order model is determined by minimizing the integral of the magnitude-squared of the transfer function error. It is shown that the numerator coefficients of the optimal approximant satisfy a weighted least squares problem and, on this basis, a two-step iterative algorithm is developed combining a least squares solver with a gradient minimizer. Convergence of the proposed algorithm to stationary values of the quadratic cost function is proved. The formulation is extended to handle the frequency-weighted optimal model reduction problem. Three examples demonstrate the optimization algorithm.

Spanos, J. T.↗

Mount Rainier active cascade volcano

Mount Rainier is one of about two dozen active or recently active volcanoes in the Cascade Range, an arc of volcanoes in the northwestern United States and Canada. The volcano is located about 35 kilometers southeast of the Seattle-Tacoma metropolitan area, which has a population of more than 2.5 million. This metropolitan area is the high technology industrial center of the Pacific Northwest and one of the commercial aircraft manufacturing centers of the United States. The rivers draining the volcano empty into Puget Sound, which has two major shipping ports, and into the Columbia River, a major shipping lane and home to approximately a million people in southwestern Washington and northwestern Oregon. Mount Rainier is an active volcano. It last erupted approximately 150 years ago, and numerous large floods and debris flows have been generated on its slopes during this century. More than 100,000 people live on the extensive mudflow deposits that have filled the rivers and valleys draining the volcano during the past 10,000 years. A major volcanic eruption or debris flow could kill thousands of residents and cripple the economy of the Pacific Northwest. Despite the potential for such danger, Mount Rainier has received little study. Most of the geologic work on Mount Rainier was done more than two decades ago. Fundamental topics such as the development, history, and stability of the volcano are poorly understood.

Source record↗

Analytic model of aurorally coupled magnetospheric and ionospheric electrostatic potentials

This paper describes modest but significant improvements on earlier studies of electrostatic potential structure in the auroral region using the adiabatic auroral arc model. This model has crucial nonlinearities (connected, for example. with aurorally produced ionization) which have hampered analysis; earlier work has either been linear, which I will show is a poor approximation or, if nonlinear, either numerical or too specialized to study parametric dependencies. With certain simplifying assumptions I find new analytic nonlinear solutions fully exhibiting the parametric dependence of potentials on magnetospheric (e.g.. cross-tail potential) and ionospheric (e.g., recombination rate) parameters. No purely phenomenological parameters are introduced. The results are in reasonable agreement with observed average auroral potential drops, inverted-V scale sizes, and dissipation rates. The dissipation rate is quite comparable to tail energization and transport rates and should have a major effect on tail and magnetospheric dynamics. This paper gives various relations between the cross-tail potential and auroral parameters (e.g., total parallel currents and potential drops) which can be studied with existing data sets.

Cornwall, J. M.↗

Numerical Simulation of the Instability of an Inviscid Liquid Jet in a Coflowing Compressible Airstream

The nonlinear interfacial instability of a liquid jet in a coflowing compressible airstream is studied numerically. A high-resolution scheme which has second-order accuracy in space and time is coupled with a Lagrangian marker particle algorithm to visualize the large-scale motion of the interfaces in compressible flow. A numerical algorithm based on an approximate equation of state of a compressible liquid is developed to allow this two-fluid system to be governed by the nonlinear unsteady Euler equations in conservative form. The initial growth of small disturbances given by the simulations agrees well with linear theory. The process of jet disruption in compressible flow is demonstrated to consist of the formation of liquid spikes, interweaving of the gas and liquid and stretching and detachment of the liquid main center core.

Li, H. -S.↗

A Rigorous Framework for Optimization of Expensive Functions by Surrogates

The goal of the research reported here is to develop rigorous optimization algorithms to apply to some engineering design problems for which design application of traditional optimization approaches is not practical. This paper presents and analyzes a framework for generating a sequence of approximations to the objective function and managing the use of these approximations as surrogates for optimization. The result is to obtain convergence to a minimizer of an expensive objective function subject to simple constraints. The approach is widely applicable because it does not require, or even explicitly approximate, derivatives of the objective. Numerical results are presented for a 31-variable helicopter rotor blade design example and for a standard optimization test example.

Booker, Andrew J.↗

Nonlinear Waves and Particle Heating in the Auroral Ionosphere

In the two year period, the researchers have developed innovative 2-D simulation codes for modeling the interaction between electron beams and plasma waves and particles in the auroral ionosphere. These new simulations include kinetic wave particles as well as wave-wave interactions near and above approximately 500 km. The principal numerical model consists of partial-differential equations which evolve large amplitude magnetized 2-D Langmuir waves self-consistently with the electron distribution function. Progress was also made in developing 2-D Particle in Cell (PIC) codes.

Goldman, Martin↗

Parallel Implementation of a High Order Implicit Collocation Method for the Heat Equation

We combine a high order compact finite difference approximation and collocation techniques to numerically solve the two dimensional heat equation. The resulting method is implicit arid can be parallelized with a strategy that allows parallelization across both time and space. We compare the parallel implementation of the new method with a classical implicit method, namely the Crank-Nicolson method, where the parallelization is done across space only. Numerical experiments are carried out on the SGI Origin 2000.

Kouatchou, Jules↗

Recent Progress in Parallel Schur Complement Preconditioning for Computational Fluid

We consider preconditioning methods for nonself-adjoint advective-diffusive systems based on a nonoverlapping Schur complement procedure for arbitrary triangulated domains. The triangulation is first partitioned using the METIS multi-level $k$-way partitioning code. This partitioning of the triangulation induces a natural 2x2 partitioning of the demoralization matrix. By considering various inverse approximations of the 2x2 system we have developed a family of robust preconditioning techniques. The performance of these approximations will be discussed and numerous examples shown to illustrate the efficiency of the technique.

Barth, Tim↗

Elemental Abundances in NGC 3516

We present Reflection Grating Spectrometer data from an XMM-Newton observation of the Seyfert 1 galaxy NGC 3516, taken while the continuum source was in an extremely low flux state. This observation offers a rare opportunity for a detailed study of emission from a Seyfert 1 galaxy as these are usually dominated by high nuclear continuum levels and heavy absorption. The spectrum shows numerous narrow emission lines (FWHM approximately less than 1300 kilometers per second) in the 0.3 - 2 keV range, including the H-like lines of C, N, and O and the He-like lines of N, O and Ne. The emission-line ratios and the narrow width of the radiative recombination continuum of CVI indicate that the gas is photoionized and of fairly low temperature (kT approximately less than 0.01 keV). The availability of emission lines from different elements for two iso-electronic sequences allows us to constrain the element abundances. These data show that the N lines are far stronger than would be expected from gas of solar abundances. Based on our photoionization models we find that nitrogen is overabundant in the central regions of the galaxy, compared to carbon, oxygen and neon by at least a factor of 2.5. We suggest that this is the result of secondary production of nitrogen in intermediate mass stars, and indicative of the history of star formation in NGC 3516.

Turner, T. J.↗

A Hybrid SBR/MoM Technique for Analysis of Scattering from Small Protrusions on a Large Conducting Body

For analysis of large-scale electromagnetic scattering problems, high-frequency asymptotic methods are fast but approximate, whereas low-frequency numerical methods are accurate but slow. Neither can produce an efficient and accurate solution to scattering by large bodies containing small structures. A promising approach is to combine the best features of both types of methods to produce a hybrid technique that is sufficiently fast, reasonably accurate, and applicable to a class of unsolvable problems such as the scatterers mentioned above. There are two extremes for this type of hybridization. One is simply to superimpose solutions from asymptotic and numerical methods. While this approach is most widely used in practical applications, it neglects the interactions between the two solutions, which can be significant in many problems. The other extreme is to combine an asymptotic and a numerical method in an exact manner. In this approach, the effect of a large body is included by incorporating its diffraction into the Green's function in the integral equation for the small structures, which accounts for all interactions. While this approach is accurate, it is difficult to be implemented in a general-purpose computer code because of its complex nature. A more practical approach is to develop a technique that can include all significant interactions and neglect all trivial interactions. The resulting hybrid technique can produce sufficient accuracy and can be implemented in a general-purpose computer code. In this paper, we develop a technique that combines the shooting and- bouncing-ray (SBR) method and the method of moments (MoM) to solve for the scattering by large conducting bodies with small structures mounted on their surfaces.

Jin, J. M.↗

Development and Validation of Passive Yaw in the Open-Source WEC-Sim Code: Preprint

A passive yaw implementation is developed, validated, and explored for the Wave Energy Converter Simulator (WEC-Sim), an open-source wave energy converter modeling tool that works within MATLAB/Simulink. The Reference Model 5 (RM5) is selected for this investigation, and a WEC-Sim model of the device is modified to allow yaw motion. A boundary element method (BEM) code was used to calculate the excitation force coefficients for a range of wave headings. An algorithm was implemented in WEC-Sim to determine the equivalent wave heading from a body’s instantaneous yaw angle and interpolate the appropriate excitation coefficients to ensure the correct time-domain excitation force. This approach is able to determine excitation force for a body undergoing large yaw displacement. For the mathematically simple case of regular wave excitation, the dynamic equation was integrated numerically and found to closely approximate the results from this implementation in WEC-Sim. A case study is presented for the same device in irregular waves. In this case, computation time is increased by 32x when this interpolation is performed at every time step. To reduce this expense, a threshold yaw displacement can be set to reduce the number of interpolations performed. A threshold of 0.01 was found to increase computation time by only 22x without significantly affecting time domain results. Similar amplitude spectra for yaw force and displacements are observed for all threshold values less than or equal to 1, for which computation time is only increased by 2.2x.

50 EE - Wind and Water Power Program - Water (EE-4↗