Necessary conditions for continuous parameter stochastic optimization problems
Continuous parameter stochastic optimization principle using abstract variational theory
Kushner, H. J.↗
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Applications of laser speckles in a holographic nondestructive test system
The grainy or speckle phenomenon of laser light is caused by two inherent characteristics of the laser - the coherence and monochromaticity of the radiation. Recent development have shown that this phenomenon can be used to measure minute surface displacements, surface strains, or vibrations of a body. The present paper deals with two techniques employing the speckle effect. One is called speckle beam holographic interferometry, and the other speckle photographic interferometry. A major advantage of the first technique is the elimination of the stringent vibration isolation requirement in existing holographic nondestructive test systems. The advantage of the second technique is that the resulting photographic data are sensitive only to the in-plane components of the surface variations. The basic principles and practical limitations of these techniques are discussed.
Liu, H.-K.↗
Computing with high-resolution upwind schemes for hyperbolic equations
Computational aspects of modern high-resolution upwind finite-difference schemes for hyperbolic systems of conservation laws are examined. An operational unification is demonstrated for constructing a wide class of flux-difference-split and flux-split schemes based on the design principles underlying total variation diminishing (TVD) schemes. Consideration is also given to TVD scheme design by preprocessing, the extension of preprocessing and postprocessing approaches to general control volumes, the removal of expansion shocks and 'glitches', relaxation methods for implicit TVD schemes, and a new family of high-accuracy TVD schemes.
Chakravarthy, S. R.↗
Kinetic theory based new upwind methods for inviscid compressible flows
Two new upwind methods called the Kinetic Numerical Method (KNM) and the Kinetic Flux Vector Splitting (KFVS) method for the solution of the Euler equations have been presented. Both of these methods can be regarded as some suitable moments of an upwind scheme for the solution of the Boltzmann equation provided the distribution function is Maxwellian. This moment-method strategy leads to a unification of the Riemann approach and the pseudo-particle approach used earlier in the development of upwind methods for the Euler equations. A very important aspect of the moment-method strategy is that the new upwind methods satisfy the entropy condition because of the Boltzmann H-Theorem and suggest a possible way of extending the Total Variation Diminishing (TVD) principle within the framework of the H-Theorem. The ability of these methods in obtaining accurate wiggle-free solution is demonstrated by applying them to two test problems.
Deshpande, S. M.↗
Synergistic Effects of Physical Aging and Damage on Long-Term Behavior of Polymer Matrix Composites
The research consisted of two major parts, first modeling and simulation of the combined effects of aging and damage on polymer composites and secondly an experimental phase examining composite response at elevated temperatures, again activating both aging and damage. For the simulation, a damage model for polymeric composite laminates operating at elevated temperatures was developed. Viscoelastic behavior of the material is accounted for via the correspondence principle and a variational approach is adopted to compute the temporal stresses within the laminate. Also, the effect of physical aging on ply level stress and on overall laminate behavior is included. An important feature of the model is that damage evolution predictions for viscoelastic laminates can be made. This allows us to track the mechanical response of the laminate up to large load levels though within the confines of linear viscoelastic constitutive behavior. An experimental investigation of microcracking and physical aging effects in polymer matrix composites was also pursued. The goal of the study was to assess the impact of aging on damage accumulation, in ten-ns of microcracking, and the impact of damage on aging and viscoelastic behavior. The testing was performed both at room and elevated temperatures on [+/- 45/903](sub s) and [02/903](sub s) laminates, both containing a set of 90 deg plies centrally located to facilitate investigation of microcracking. Edge replication and X-ray-radiography were utilized to quantify damage. Sequenced creep tests were performed to characterize viscoelastic and aging parameters. Results indicate that while the aging times studied have limited ]Influence on damage evolution, elevated temperature and viscoelastic effects have a profound effect on the damage mode seen. Some results are counterintuitive, including the lower strain to failure for elevated temperature tests and the catastrophic failure mode observed for the [+/- 45/9O3](sub s), specimens. The fracture toughness for transverse cracks increases with increasing temperature for both systems: transverse cracking was completely absent prior to failure in [+/- 45/903](sub s), and was suppressed for [02/903](sub s). No significant effect of damage on aging or viscoelastic parameters was observed.
Brinson, L. Cate↗
Electrochemical etching of the semiconductor lead tin telluride
Convective currents during the Bridgman growth of a compound semiconductor lead to temperature fluctuations at the solid-liquid interface. These temperature fluctuations in turn lead to microscopic compositional variations in the solid. Electrochemical principles have been applied to develop three etches which delineate the variations in the compound semiconductor, lead tin telluride, and allow optical studies of the growth kinetics of this material. Use of these etches has shown periodic lines during the initial growth, with indications of oscillatory instabilities developing in later stages of growth, and, finally, complete breakdown of the interface.
Barber, P. G.↗
Precision Clocks in Space and alpha-Variations
Important developments of both in theoretical and observational cosmology have fueled considerable interest in searches for variations of the fine structure constant. Experimentally, Webb et. al. have found evidence for a cosmological variation of the fine structure constant through an analysis of the absorption lines in galactic halos from quasar-emitted light. Recently developed small ion atomic clocks enable Solar System tests for equivalence principle (EP) violating (alpha)-variations by way of rate-comparisons of three ultra-stable atomic clocks near-to and far-from the sun where gravitational red-shift changes are more than 10(exp 4) larger than in low Earth orbit. No space tests of the EP have been made in nearly 30 years, since the GP-A hydrogen maser reached a 10,000 km apogee confirming EP red-shift predictions ~1 part in 10(exp 4). Today's small ion clocks, nearly 100x more stable and 100x smaller then the GP-A H-maser, could probe for EP violating scalar fields near the sun for mission costs comparable to low Earth orbiters and improve the GP-A sensitivity by 5 to 6 orders of magnitude.
(alpha)-variation↗
Partial spline models for the inclusion of tropopause and frontal boundary information in otherwise smooth two- and three-dimensional objective analysis
A new method, based on partial spline models, is developed for including specified discontinuities in otherwise smooth two- and three-dimensional objective analyses. The method is appropriate for including tropopause height information in two- and three-dimensinal temperature analyses, using the O'Sullivan-Wahba physical variational method for analysis of satellite radiance data, and may in principle be used in a combined variational analysis of observed, forecast, and climate information. A numerical method for its implementation is described and a prototype two-dimensional analysis based on simulated radiosonde and tropopause height data is shown. The method may also be appropriate for other geophysical problems, such as modeling the ocean thermocline, fronts, discontinuities, etc.
Shiau, Jyh-Jen↗
Guidance, flight mechanics and trajectory optimization. Volume 7 - The Pontryagin maximum principle
Maxima-minima theory, Pontryagin principle, and calculus of variations for optimal trajectory and control analysis
Mc Intyre, J. E.↗
Optimal control surface locations for aircraft flexure controllers
Optimal control surface location for flexible aircraft determined by matrix minimum principle and calculus of variations
Athans, M.↗
Optimal control-surface locations for flexible aircraft
Aerodynamic control surfaces optimal location for flexible aircraft disturbed by random wind gusts, using matrix minimum principle and calculus of variations
Athans, M.↗
Dynamics of disconnectable microdrives of mine hoisting units
A model study is presented of drives for the electromagnetic clutches used in hoists. Equations are set up and solved, describing the principles of the slip variation during the transient period of the plate engagement.
Pampura, D. P.↗
Optimal trajectories in atmospheric flight
Aspects of optimization theory and switching theory are discussed, taking into account the necessary conditions for extrema, a solution subject to constraints, the calculus of variations, the Pontryagin maximum principle, the canonical transformation, Contensou's domain of maneuverability, optimal switching, a junction with singular arc, and linearized singular control. Equations of motion are considered along with aerodynamic and propulsive forces, the general properties of optimal trajectories, flight in a horizontal plane, optimal coasting flight, supersonic cruise, the supersonic turn, supersonic maneuvers in a vertical plane, energy state approximation, a modified Chapman's formulation for optimal reentry trajectories, optimal planar reentry trajectories, and an optimal glide of reentry vehicles. Orbital aerodynamic maneuvers are examined, giving attention to aerodynamic capture, a change in the apogee, a change in the eccentricity, a change in the perigee, an orbital maneuver, an aerodynamic maneuver, and a combined maneuver.
Vinh, N. X.↗
An X-Ray Reprocessing Model of Disk Thermal Emission in Type 1 Seyfert Galaxies
Using a geometry consisting of a hot central Comptonizing plasma surrounded by a thin accretion disk, we model the optical through hard X-ray spectral energy distributions of the type 1 Seyfert. galaxies NGC 3516 and NGC 7469. As in the model proposed by Poutanen, Krolik, and Ryde for the X-ray binary Cygnus X-1 and later applied to Seyfert galaxies by Zdziarski, Lubifiski, and Smith, feedback between the radiation reprocessed by the disk and the thermal Comptonization emission from the hot central plasma plays a pivotal role in determining the X-ray spectrum, and as we show, the optical and ultraviolet spectra as well. Seemingly uncorrelated optical/UV and X-ray light curves, similar to those which have been observed from these objects can, in principle, be explained by variations in the size, shape, and temperature of the Comptonizing plasma. Furthermore, by positing a disk mass accretion rate which satisfies a condition for global energy balance between the thermal Comptonization luminosity and the power available from accretion, one can predict the spectral properties of the heretofore poorly measured hard X-ray continuum above approximately 50 keV in type 1 Seyfert galaxies. Conversely, forthcoming measurements of the hard X-ray continuum by more sensitive hard X-ray and soft gamma-ray telescopes, such as those aboard the International Gamma-Ray Astrophysics Laboratory (INTEGRAL) in conjunction with simultaneous optical, UV, and soft X-ray monitoring, will allow the mass accretion rates to be directly constrained for these sources in the context of this model.
Chiang, James↗
Tests of gravity Using Lunar Laser Ranging
Lunar laser ranging (LLR) has been a workhorse for testing general relativity over the pa~t four decades. The three retrorefiector arrays put on the Moon by the Apollo astronauts and the French built array on the second Soviet Lunokhod rover continue to be useful targets, and have provided the most stringent tests of the Strong Equivalence Principle and the time variation of Newton's gravitational constant. The relatively new ranging system at the Apache Point :3.5 meter telescope now routinely makes millimeter level range measurements. Incredibly. it has taken 40 years for ground station technology to advance to the point where characteristics of the lunar retrorefiectors are limiting the precision of the range measurements. In this article. we review the gravitational science and technology of lunar laser ranging and discuss prospects for the future.
Merkowitz, Stephen M.↗
Can Vertical Profiles of Tropospheric Methane on Titan Be Derived from Radio-Occultation Soundings?
The intensity of the received signal at Earth in the radio occultations of Titan is attenuated both by refractive defocusing and pressure-induced absorption from N2-N2 and CH4-N2 pairs. Because the absorption strength is different for the two sets of pairs, matching the retrieved absorptivity profile can in principle yield the vertical variation in gaseous methane in the troposphere. There are two factors that make this difficult. The first is the propagation of noise in the phase and amplitude of the received signal in the absorption retrieval. The phase data is first inverted to retrieve vertical profiles of refractivity, from which the refractive defocusing is calculated. This is then subtracted from the observed. intensity attenuation of the received signal to generate a profile of atmospheric absorption. The second problem is the uncertainty in the pressure-induced absorption coefficients. Laboratory data at radio wavelengths is only available near room temperature (see, e.g., [1] for N2-N2), and the extrapolation to the low temperatures in Titan's troposphere is not well established. Ab initio calculations by Borysow et al. [2, 3] provide absorption coefficients at low temperatures and long wavelengths, but their accuracy has come into question. We present examples from Cassini radio occultations of Titan to illustrate the difficulties. For methane mole fractions in the lower troposphere comparable to that inferred from the Huygens probe (approximately 0.05), it will be difficult to separate the contributions of N2-N2 collisions from those of N2-CH4, collisions to the retrieved absorption. However, higher concentrations of CH4 and/or a higher signal-to-noise ratio from a future uplink experiment could result in a successful separation of the two components. However, key to this are highly accurate estimates of the absorption from a combination of laboratory measurements at love temperatures and long wavelengths, and possibly improved theoretical calculations.
Flasar, F. Michael↗
Application of Variational Methods to the Thermal Entrance Region of Ducts
A variational method is presented for solving eigenvalue problems which arise in connection with the analysis of convective heat transfer in the thermal entrance region of ducts. Consideration is given, to both situations where the temperature profile depends upon one cross-sectional coordinate (e.g. circular tube) or upon two cross-sectional coordinates (e.g. rectangular duct). The variational method is illustrated and verified by application to laminar heat transfer in a circular tube and a parallel-plate channel, and good agreement with existing numerical solutions is attained. Then, application is made to laminar heat transfer in a square duct as a check, an alternate computation for the square duct is made using a method indicated by Misaps and Pohihausen. The variational method can, in principle, also be applied to problems in turbulent heat transfer.
Sparrow, E. M.↗
Aeroacoustic and aerodynamic applications of the theory of nonequilibrium thermodynamics
Recent developments in the field of nonequilibrium thermodynamics associated with viscous flows are examined and related to developments to the understanding of specific phenomena in aerodynamics and aeroacoustics. A key element of the nonequilibrium theory is the principle of minimum entropy production rate for steady dissipative processes near equilibrium, and variational calculus is used to apply this principle to several examples of viscous flow. A review of nonequilibrium thermodynamics and its role in fluid motion are presented. Several formulations are presented of the local entropy production rate and the local energy dissipation rate, two quantities that are of central importance to the theory. These expressions and the principle of minimum entropy production rate for steady viscous flows are used to identify parallel-wall channel flow and irrotational flow as having minimally dissipative velocity distributions. Features of irrotational, steady, viscous flow near an airfoil, such as the effect of trailing-edge radius on circulation, are also found to be compatible with the minimum principle. Finally, the minimum principle is used to interpret the stability of infinitesimal and finite amplitude disturbances in an initially laminar, parallel shear flow, with results that are consistent with experiment and linearized hydrodynamic stability theory. These results suggest that a thermodynamic approach may be useful in unifying the understanding of many diverse phenomena in aerodynamics and aeroacoustics.
Horne, W. Clifton↗