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At least 163 records · Page 9

A Potential Function Derivation of a Constitutive Equation for Inelastic Material Response

Physical and thermodynamic concepts are used to develop a potential function for application to high temperature polycrystalline material response. Inherent in the formulation is a differential relationship between the potential function and constitutive equation in terms of the state variables. Integration of the differential relationship produces a state variable evolution equation that requires specification of the initial value of the state variable and its time derivative. It is shown that the initial loading rate, which is directly related to the initial hardening rate, can significantly influence subsequent material response. This effect is consistent with observed material behavior on the macroscopic and microscopic levels, and may explain the wide scatter in response often found in creep testing.

Stouffer, D. C.

A numerical scheme for the identification of hybrid systems describing the vibration of flexible beams with tip bodies

A cubic spline based Galerkin-like method is developed for the identification of a class of hybrid systems which describe the transverse vibration to flexible beams with attached tip bodies. The identification problem is formulated as a least squares fit to data subject to the system dynamics given by a coupled system of ordnary and partial differential equations recast as an abstract evolution equation (AEE) in an appropriate infinite dimensional Hilbert space. Projecting the AEE into spline-based subspaces leads naturally to a sequence of approximating finite dimensional identification problems. The solutions to these problems are shown to exist, are relatively easily computed, and are shown to, in some sense, converge to solutions to the original identification problem. Numerical results for a variety of examples are discussed.

Rosen, I. G.

Thermal evolution of the earth

The earth's heat budget and models of the earth's thermal evolution are discussed. Sources of the planetary heat are considered and modes of heat transport are addressed, including conduction, convection, and chemical convection. Thermal and convectional models of the earth are covered, and models of thermal evolution are discussed in detail, including changes in the core, the influence of layered mantle convection on the thermal evolution, and the effect of chemical differentiation on the continents.

Spohn, T.

A Factorization Approach to the Linear Regulator Quadratic Cost Problem

A factorization approach to the linear regulator quadratic cost problem is developed. This approach makes some new connections between optimal control, factorization, Riccati equations and certain Wiener-Hopf operator equations. Applications of the theory to systems describable by evolution equations in Hilbert space and differential delay equations in Euclidean space are presented.

Milman, M. H.

Highly evolved and ultramafic lithologies from Apollo 14 soils

Eighteen 2-4-mm fragments were extracted from several Apollo 14 soil samples and examined by instrumental neutron activation analysis, and were studied petrographically. Results indicate that these rock fragments span almost the whole range of magma evolution, from ultramafic cumulates to extreme differentiates that were apparently produced by silicate liquid immiscibility. Three of the fragments are dimict granitic breccias composed of granitic clasts intruded by a ferropyroxenitic glass, and may represent an immmiscible melt pair that has been remixed by impact. Two fragments are ultramafic rocks, including a dunite with very low REE abundances and a peridotite/impact melt breccia.

Morris, R. W.

On the receptivity and non-parallel stability of travelling disturbances in rotating disk flow

The generation and evolution of small amplitude wavelength traveling disturbances in rotating disk flow is discussed. The steady rotational speed of the disk is perturbed so as to introduce high frequency oscillations in the flow field. Secondly, surface imperfections are introduced on the disk such as roughness elements. The interaction of these two disturbances will generate the instability waves whose evolution is governed by parabolic partial differential equations that are solved numerically. For the class of disturbances considered (wavelength on the order of Reynolds number), it is found that eigensolutions exist which decay or grow algebraically in the radial direction. However, these solutions grow only for frequencies larger than 4.58 times the steady rotational speed of the disk. The computed receptivity coefficient shows that there is an optimum size of roughness for which these modes are excited the most. The width of these roughness elements in the radial direction is about .1 r(sub 0) where r(sub 0) is the radial location of the roughness. It is also found that the receptivity coefficient is larger for a negative spanwise wavenumber than for a positive one. Typical wave angles found for these disturbances are about -26 degrees.

Balakumar, P.

Statistical mechanics models for motion and force planning

The models of statistical mechanics provide an alternative to the methods of classical mechanics more traditionally used in robotics. They have a potential to: improve analysis of object collisions; handle kinematic and dynamic contact interactions within the same frmework; and reduce the need for perfect deterministic world model information. The statistical mechanics models characterize the state of the system as a probability density function (p.d.f.) whose time evolution is governed by a partial differential equation subject to boundary and initial conditions. The boundary conditions when rigid objects collide reflect the conservation of momentum. The models are being developed to embedd in remote semi-autonomous systems with a need to reason and interact with a multiobject environment.

Rodriguez, G.

On the receptivity and nonparallel stability of traveling disturbances in rotating-disk flow

The generation and evolution of small amplitude long wavelength traveling disturbances in rotating-disk flow are discussed. The steady rotational speed of the disk is perturbed so as to introduce high-frequency oscillations in the flow field. Secondly, surface imperfections on the disk such as roughness elements are introduced. The interaction of these two disturbances will generate the instability waves whose evolution is governed by parabolic partial differential equations which are solved numerically. It is found that, for the class of disturbances considered here (wavelength on the order of Reynolds number), eigensolutions exist which decay or grow algebraically in the radial direction. However, these solutions grow only for frequencies larger than 4.58 times the steady rotational speed of the disk. The computed receptivity coefficient shows that there is an optimum size of roughness for which these modes are preferentially excited.

Balakumar, P.

Radial alignment simulation of solar wind streams observed by Pioneers 10 and 11 in 1974

A particularly favorable radial lineup between spacecraft in Earth orbit and Pioneers 10 and 11 (near the ecliptic plane at approximately 5.5 AU and approximately 4.5 AU, respectively) occurred in mid-1974, when the solar corona was in a stable and well-defined warped-dipole configuration. The radial alignment study reported here differs from previous applications of the technique in two respects: (1) It is the first time a two-dimensional (2-D) MHD model has been tested over such a lengthy propagation interval; the 2-D capability is crucial for treatment of the nonradial shearing motions occurring across the stream interface. (2) The three-dimensional (3-D) structure observed in the white light corona at that time is related to the systematic patterns of nonradial flow deflections appearing at the Pioneer corotating interaction region (CIR) fronts. Comparison of predicted and observed flows for pairs of streams in two successive rotations reveals that when the parent coronal hole projects far across the solar equator in a predominantly north-south orientation (i.e., nearest the 2-D idealization), the mapping is accurate down to details of the flow structures. But where the spacecraft tracks along a latitudinal boundary of a hole or the associated stream front is inclined at a shallow angle to the equator, the numerical projections deviate systematically from the observations. Among the sources of error are 3-D dynamical interactions neglected in the model, differential rotation effects, and slow temporal evolution of the coronal structures. A characteristic pattern of north-south and east-west deflections indicative of the 3-D geometry appears across the CIRs, but these patterns evidently reflect primarily the local, as opposed to global, orientation of the 3-D stream fronts. Such patterns appear common in CIRs observed by Pioneer during this period. These findings thus hold special relevance for the analysis of Ulysses observations, since the present coronal configuration is similar to that of 1974.

Pizzo, V. J.

Algorithm for Stabilizing a POD-Based Dynamical System

This algorithm provides a new way to improve the accuracy and asymptotic behavior of a low-dimensional system based on the proper orthogonal decomposition (POD). Given a data set representing the evolution of a system of partial differential equations (PDEs), such as the Navier-Stokes equations for incompressible flow, one may obtain a low-dimensional model in the form of ordinary differential equations (ODEs) that should model the dynamics of the flow. Temporal sampling of the direct numerical simulation of the PDEs produces a spatial time series. The POD extracts the temporal and spatial eigenfunctions of this data set. Truncated to retain only the most energetic modes followed by Galerkin projection of these modes onto the PDEs obtains a dynamical system of ordinary differential equations for the time-dependent behavior of the flow. In practice, the steps leading to this system of ODEs entail numerically computing first-order derivatives of the mean data field and the eigenfunctions, and the computation of many inner products. This is far from a perfect process, and often results in the lack of long-term stability of the system and incorrect asymptotic behavior of the model. This algorithm describes a new stabilization method that utilizes the temporal eigenfunctions to derive correction terms for the coefficients of the dynamical system to significantly reduce these errors.

Kalb, Virginia L.

Evolution of planetesimals. I - Dynamics: Relaxation in a thin disk. II - Numerical simulations

The study examines the effects of density inhomogeneity and differential rotation as well as inelastic collisions on the dynamical evolution of planetesimals. Consideration is given to a three-step analysis: the dynamical evolution of the planetesimals, collisions and mass accumulation, and interaction with gas. It is shown that the velocity dispersion of a cold system of planetesimals increases rapidly due to elastic gravitational scattering. When the dispersion in the epicycle amplitude becomes comparable to the planetesimals' Roche radius, energy is transferred from the systematic Keplerian shear to the dispersive motion. With a numerical N-body scheme, gravitational scattering and physical collisions among a system of planetesimals is simulated. It is shown that dynamical equilibrium is attained with a velocity dispersion comparable to the surface escape velocity of those planetesimals which contribute most of the system mass.

Palmer, P. L.

Chromospheric activity and stellar evolution

A study of stellar chromospheres based on the internal structure of particular stars is presented. Used are complex flow diagrams of the linkage paths between mass loss, angular momentum loss, magnetic field from the turbulent dynamo and its relations to differential rotations and the convection zone, and stellar evolution.

Kippenhahn, R.

Depth and Differentiation of the Orientale Melt Lake

Impact melt emplacement and evolution in lunar multi-ring basins is poorly understood since impact melt deposits in basins are generally buried by mare basalt fill and obscured by subsequent impact cratering. The relatively young Orientale basin, which is only partially flooded with mare basalt, opens a rare window into basin-scale impact melts. We describe the geology of impact melt-related facies in Orientale and suggest that the central depression of Orientale may represent a solidified impact melt lake that vertically subsided shortly after basin formation due to solidification and cooling. We use Lunar Orbiter Laser Altimeter (LOLA) data to measure the depth (approx. 1.75 km) and diameter (approx 350 km) of this central depression. If all the observed subsidence of the central depression is due to solidification and cooling, the melt lake should be approx 12.5-16 km deep, far more voluminous (approx 106 km3) than the largest known differentiated igneous intrusions on Earth. We investigate the possibility that the Orientale melt lake has differentiated and model 1) the bulk composition of the melt lake, 2) the operation of melt mixing in the melt lake, and 3) the chemical evolution of the resulting liquids on the An-Fo-Qz ternary in order to predict the lithologies that might be present in the solidified Orientale melt lake. Finally, we consider the possible significance of these lithologies.

Vaughan, W. M.

A tale of two planets: Disparate evolutionary models for Mars inferred from radiogenic isotope compositions of Martian meteorites

The radiogenic isotopic compositions of basaltic Martian meteorites (shergottites) and clinopyroxene/olivine cumulate meteorites (nakhlite/chassignites) are used to define the global evolution of Mars. However, the two main groups of meteorites demonstrate that their sources underwent divergent styles of magmatic evolution. The shergottites portray a planet that differentiated ~4.52 billion years ago via solidification of a magma ocean, producing incompatible element-depleted and -enriched reservoirs that remained isolated until melt production. In contrast, the reservoir from which the nakhlite/chassignites derive may have formed earlier, produced melts that fractionated Sm/Nd and Hf/W differently, was compositionally less variable, and experienced a significantly more complex history following primordial differentiation than the shergottite sources. The disparate histories recorded by these two groups of meteorites elucidate important questions that could be addressed by acquiring additional samples. Obtaining samples that shared the isotopic systematics of the shergottites would provide confidence that extrapolating the primordial differentiation history of Mars from shergottite radiogenic isotope systematics is reasonable. Returned samples from Mars will also constrain the physical locations of the meteorite source regions, providing insights into the general structure of the Martian mantle. In addition, they will help constrain the phases present in the martian mantle during melting and the conditions under which they are stable. Finally, identifying an evolved lithology that satisfies the geochemical and isotopic constraints placed on the incompatible element-enriched endmember observed in the shergottites would define the nature of magmatic evolution on Mars and whether it is more akin to processes on the Earth or the Moon.

Mars

Coronal mass ejections and the evolution of the large-scale corona

Coronal mass ejections (CMEs) are dynamic, large-scale events in the solar corona that expel plasma and magnetic fields into the solar wind. The structure of the large-scale corona influences CME occurrence; for example, CMEs are most frequently observed to be disruptions of coronal or helmet streamer configurations on the Sun. We have investigated the evolution of the large-scale corona in the presence of differential rotation, using time-dependent magnetohydrodynamic (MHD) simulations in two and three dimensions. An equilibrium coronal configuration is first computed by superimposing a Parker solar wind flow on an initial potential field, the equations are integrated in time until a steady-state is reached. When differential rotation is introduced, we find that the configuration does not reach a steady state; the closed field regions (helmet streamers) disrupt recurrently, ejecting plasmoids into the solar wind. Our results suggest that differential rotation may be one of the mechanisms by which mass ejections are initiated. We will describe the evolution of the polarization brightness (pB) for the resulting configurations, as well as the propagation of the ejected plasmoids in the solar wind, and we will compare the effects of differential rotation with other possible initiation mechanisms, such as the emergence of new magnetic flux.

Linker, J. A.

The relationship between crustal tectonics and internal evolution in the moon and Mercury

The relationship between crustal tectonics and thermal evolution is discussed in terms of the moon and Mercury. Finite strain theory and depth and temperature-dependent thermal expansion are used to evaluate previous conclusions about early lunar history. Factors bringing about core differentiation in the first 0.6 b.y. of Mercurian evolution are described. The influence of concentrating radioactive heat sources located in Mercury's crust on the predicted contraction is outlined. The predicted planetary volume change is explored with regard to quantitative limits on the extent of Mercurian core solidification. Lunar and Mercurian thermal stresses involved in thermal evolution are reviewed, noting the history of surface volcanism. It is concluded that surface faulting and volcanism are closely associated with the thermal evolution of the whole planetary volume. As the planet cools or is heated, several types of tectonic and volcanic effects may be produced by thermal stress occurring in the lithosphere.

Solomon, S. C.

Three-dimensional stability of growing boundary layers

A theory is developed for the linear stability of three-dimensional growing boundary layers. The method of multiple scales is used to derive partial-differential equations describing the temporal and spatial evolution of the complex amplitudes and wavenumbers of the disturbances. In general, these equations are elliptic unless certain conditions are satisfied. For a monochromatic disturbance, these conditions demand that the ratio of the components of the complex group velocity be real and thereby relate the direction of growth of the disturbance to the disturbance wave angle. For a nongrowing boundary layer, this condition reduces to d-alpha/d-beta being real, in agreement with the result obtained by using the saddle-point method. For a wavepacket, these conditions demand that the components of the group velocity be real.

Nayfeh, A. H.