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At least 199 records · Page 11

Control of micromachined deformable mirrors

A micromachined deformable mirror with pixelated electrostatic actuators is proposed. The paper begins with a physical description of the proposed mirror. Then a mathematical model in the form of a nonlinear partial differential equation describing the mirror surface deformations is derived. This model is used to derive the required voltages for the actuators to achieve a specified static deformation of the mirror surface. This is followed by the derivation of a static nonlinear feedback controller for achieving noninteracting actuation. Then the structure for a complete control system for wavefront correction is proposed. The paper concludes with a discussion of the physical implementation of the proposed control system.

Agronin, M. L.↗

Control of Micromachined Deformable Mirrors

A micromachined deformable mirror with pixelated electrostatic actuators is proposed. The paper begins with a physical description of the proposed mirror. Then, a mathematical model in the form of a nonlinear partial differential equation describing the mirror surface deformations is derived. This model is used to derive the required voltages for the actuators to achieve a specified static deformation of the mirror surface. This is followed by the derivation of a static nonlinear feedback controller for achieving noninteracting actuation. Then, the structure for a complete control system for wavefront correction is proposed. The paper concludes with a discussion of the physical implementation of the proposed control system.

mirrors↗

Differential Deposition to Correct Surface Figure Deviations in Astronomical Grazing-Incidence X-Ray Optics

A coating technique is being developed to correct the surface figure deviations in reflective-grazing-incidence X-ray optics. These optics are typically designed to have precise conic profiles, and any deviation in this profile, as a result of fabrication, results in a degradation of the imaging performance. To correct the mirror profiles, physical vapor deposition has been utilized to selectively deposit a filler material inside the mirror shell. The technique, termed differential deposition, has been implemented as a proof of concept on miniature X-ray optics developed at MSFC for medical-imaging applications. The technique is now being transferred to larger grazing-incidence optics suitable for astronomy and progress to date is reported.

Kilaru, Kiranmayee↗

Magnetic Helicity Condensation and the Solar Cycle

Solar filaments exhibit a global chirality pattern where dextral/sinistral filaments, corresponding to negative/ positive magnetic helicity, are dominant in the northern/southern hemisphere. This pattern is opposite to the sign of magnetic helicity injected by differential rotation along east–west oriented polarity inversion lines, posing a major conundrum for solar physics. A resolution of this problem is offered by the magnetic helicity-condensation model of Antiochos. To investigate the global consequences of helicity condensation for the hemispheric chirality pattern, we apply a temporally and spatially averaged statistical approximation of helicity condensation. Realistic magnetic field configurations in both the rising and declining phases of the solar cycle are simulated. For the helicity-condensation process, we assume convective cells consisting of positive/negative vorticities in the northern/southern hemisphere that inject negative/positive helicity. The magnitude of the vorticity is varied as a free parameter, corresponding to different rates of helicity injection. To reproduce the observed percentages of dominant and minority filament chiralities, we find that a vorticity of magnitude 2.5 x 10(exp −6)/s is required. This rate, however, is insufficient to produce the observed unimodal profile of chirality with latitude. To achieve this, a vorticity of at least 5 x 10(exp −6)/s is needed. Our results place a lower limit on the small-scale helicity injection required to dominate differential rotation and reproduce the observed hemispheric pattern. Future studies should aim to establish whether the helicity injection rate due to convective flows and/or flux emergence across all latitudes of the Sun is consistent with our results.

Mackay, Duncan H.↗

An investigation of a mathematical model of an optically pumped Ti(3+):Al2O3 laser system

During the last several years, solid state lasers were developed that have the potential for meeting rigorous performance requirements for space-based remote sensing of the atmosphere. In order to design a stable and efficient laser and to understand the effect on laser output of changes in the physical and design parameters, an understanding of the development of the dynamical processes of the laser is necessary. Typically, the dynamical processes in a laser system are investigated via rate equations describing the evolution of the occupancy in the electronic levels and of the photon density in the laser cavity. There are two approaches to this type of study. Most often, for the sake of simplicity, the spatial variations of the dynamic variables in the laser system are disregarded and the mathematical model consists of a system of first order nonlinear ordinary differential equations (ODE). The second approach is to take into account both spatial and temporal variations in the dynamic variables in the laser cavity. The resulting model consists of a first order semilinear system of partial differential equations (PDE). The model which was studied was studied was generic in the sense that it was a four-level laser system, but the parameters used in the numerical study were specific to Titanium-doped sapphire. For simplicity, a constant, spatially uniform pumping scheme was considered. In addition, a simplification of the model was made so that it treats a single lasing wavelength with a narrow bandwidth. The purpose was to investigate both versions of the mathematical model and to determine whether the numerical solutions are similar both qualitatively and quantitatively. The systems of ordinary differential equations were solved numerically using a Runge-Kutta-Fehlberg algorithm which was very efficient for typical values of the physical parameters. A numerical scheme, based on the Modified Euler method, for computing solutions to the system of partial differential equations was developed and implemented. The PDE model was solved numerically at the expense of greatly increased computer time.

Roberts, Lila F.↗

A theoretical/experimental program to develop active optical pollution sensors

Light detection and ranging (LIDAR) technology was applied to the assessment of air quality, and its usefulness was evaluated by actual field tests. Necessary hardware was successfully constructed and operated in the field. Measurements of necessary physical parameters, such as SO2 absorption coefficients were successfully completed and theoretical predictions of differential absorption performance were reported. Plume modeling improvements were proposed. A full scale field test of equipment, data analysis and auxiliary data support was conducted in Maryland during September 1976.

Mills, F. S.↗

Stellar occultation studies of the solar system

The paper covers the principles, observational procedures, and results relating to occultations of stars by solar system bodies other than the moon. Physical processes involved in occultations are presented including (1) extinction by ring material, (2) differential refraction by a planetary atmosphere, (3) extinction by a planetary atmosphere, and (4) Fresnel diffraction by sharp edges. It is noted that from a sufficient number of immersion and emersion timings of a stellar occultation, the radius and ellipticity of the occulting body can be accurately determined. From an occultation by a planet having an atmosphere, temperature, pressure, and number density profiles can be obtained along with information about the composition of the atmosphere and the extinction.

Elliot, J. L.↗

Solution of Euler's Equations of Motion and Eulerian Angles for near symmetric rigid bodies subject to constant moments

Analytic expressions are found for Euler's Equations of Motion and for the Eulerian Angles for both symmetric and near symmetric rigid bodies under the influence of arbitrary constant body-fixed torques. These solutions provide the body-fixed angular velocities and the attitude of the body, respectively, as functions of time. They are of special interest in applications to spinning spacecraft (such as the Galileo Spacecraft to be launched in 1984) because they include the effect of time-varying spin rate. Thus they can be applied to spin-up and spin-down maneuvers as well as to error analysis for thruster misalignments. The solutions are given for arbitrary initial conditions in terms of Fresnel, Sine and Cosine Integrals. Numerical integration of the governing differential equations has verified that the approximate analytic solutions are very accurate in many physical situations of interest.

Longuski, J. M.↗

A cryogenic multichannel electronically scanned pressure module

Consideration is given to a cryogenic multichannel electronically scanned pressure (ESP) module developed and tested over an extended temperature span from -184 to +50 C and a pressure range of 0 to 5 psig. The ESP module consists of 32 pressure sensor dice, four analog 8 differential-input multiplexers, and an amplifier circuit, all of which are packaged in a physical volume of 2 x 1 x 5/8 in with 32 pressure and two reference ports. Maximum nonrepeatability is measured at 0.21 percent of full-scale output. The ESP modules have performed consistently well over 15 times over the above temperature range and continue to work without any sign of degradation. These sensors are also immune to repeated thermal shock tests over a temperature change of 220 C/sec.

Shams, Qamar A.↗

A brief survey of constrained mechanics and variational problems in terms of differential forms

There has been considerable interest recently in constrained mechanics and variational problems. This is in part due to applied interests (such as 'non-holonomic mechanics in robotics') and in other part due to the fact that several schools of 'pure' mathematics have found that this classical subject is of importance for what they are trying to do. I have made various attempts at developing these subjects since my Lincoln lab days of the late 1950's. In this Chapter, I will sketch a Unified point of view, using Cartan's approach with differential forms. This has the advantage from the C-O-R viewpoint being developed in this Volume that the extension from 'smooth' to 'generalized' data is very systematic and algebraic. (I will only deal with the 'smooth' point of view in this Chapter; I will develop the 'generalized function' material at a later point.) The material presented briefly here about Variational Calculus and Constrained Mechanics can be found in more detail in my books, 'Differential Geometry and the Calculus of Variations', 'Lie Algebras and Quantum Mechanics', and 'Geometry, Physics and Systems'.

Hermann, Robert↗

Modeling for Battery Prognostics

For any battery-powered vehicles (be it unmanned aerial vehicles, small passenger aircraft, or assets in exoplanetary operations) to operate at maximum efficiency and reliability, it is critical to monitor battery health as well performance and to predict end of discharge (EOD) and end of useful life (EOL). To fulfil these needs, it is important to capture the battery's inherent characteristics as well as operational knowledge in the form of models that can be used by monitoring, diagnostic, and prognostic algorithms. Several battery modeling methodologies have been developed in last few years as the understanding of underlying electrochemical mechanics has been advancing. The models can generally be classified as empirical models, electrochemical engineering models, multi-physics models, and molecular/atomist. Empirical models are based on fitting certain functions to past experimental data, without making use of any physicochemical principles. Electrical circuit equivalent models are an example of such empirical models. Electrochemical engineering models are typically continuum models that include electrochemical kinetics and transport phenomena. Each model has its advantages and disadvantages. The former type of model has the advantage of being computationally efficient, but has limited accuracy and robustness, due to the approximations used in developed model, and as a result of such approximations, cannot represent aging well. The latter type of model has the advantage of being very accurate, but is often computationally inefficient, having to solve complex sets of partial differential equations, and thus not suited well for online prognostic applications. In addition both multi-physics and atomist models are computationally expensive hence are even less suited to online application An electrochemistry-based model of Li-ion batteries has been developed, that captures crucial electrochemical processes, captures effects of aging, is computationally efficient, and is of suitable accuracy for reliable EOD prediction in a variety of operational profiles. The model can be considered an electrochemical engineering model, but unlike most such models found in the literature, certain approximations are done that allow to retain computational efficiency for online implementation of the model. Although the focus here is on Li-ion batteries, the model is quite general and can be applied to different chemistries through a change of model parameter values. Progress on model development, providing model validation results and EOD prediction results is being presented.

Prognostics↗

Propulsion Physics Using the Chameleon Density Model

To grow as a space faring race, future spaceflight systems will require a new theory of propulsion. Specifically one that does not require mass ejection without limiting the high thrust necessary to accelerate within or beyond our solar system and return within a normal work period or lifetime. The Chameleon Density Model (CDM) is one such model that could provide new paths in propulsion toward this end. The CDM is based on Chameleon Cosmology a dark matter theory; introduced by Khrouy and Weltman in 2004. Chameleon as it is hidden within known physics, where the Chameleon field represents a scalar field within and about an object; even in the vacuum. The CDM relates to density changes in the Chameleon field, where the density changes are related to matter accelerations within and about an object. These density changes in turn change how an object couples to its environment. Whereby, thrust is achieved by causing a differential in the environmental coupling about an object. As a demonstration to show that the CDM fits within known propulsion physics, this paper uses the model to estimate the thrust from a solid rocket motor. Under the CDM, a solid rocket constitutes a two body system, i.e., the changing density of the rocket and the changing density in the nozzle arising from the accelerated mass. Whereby, the interactions between these systems cause a differential coupling to the local gravity environment of the earth. It is shown that the resulting differential in coupling produces a calculated value for the thrust near equivalent to the conventional thrust model used in Sutton and Ross, Rocket Propulsion Elements. Even though imbedded in the equations are the Universe energy scale factor, the reduced Planck mass and the Planck length, which relates the large Universe scale to the subatomic scale.

Robertson, Glen A.↗

Interaction of surface radiation with convection in crystal growth by physical vapor transport

Growth of single crystals from vapor in closed ampoules is governed by an intricate interplay between mass, momentum and heat transfer processes. The objective of this study is to examine and isolate the effects of surface radiation heat transfer on the vapor transport process using a mathematical model. The model consists of a set of coupled nonlinear partial differential equations for conservation of mass, momentum, energy and species, and the integrodifferential equations which represent radiative exchange. It depends on five important physical parameters. These are Grashof number, Prandtl number, Schmidt number, aspect ratio and the radiation-conduction number. The effects of these dimensionless groupings are systematically investigated. From the cases examined, it is concluded that surface radiation can change the flow structure appreciably. This is especially true in microgravity environment where radiation competes primarily with conduction in modifying the thermal profiles. The numerical results also show that in the presence of radiation, the top heating configuration (source on top) is no longer stable and that near the growing crystal, radiation-induced vortices can introduce significant nonuniformities in the growth flux.

Kassemi, Mohammad↗

Thermal evolution of the moon.

The thermal history and current state of the lunar interior are investigated using constraints imposed by recent geological and physical data. Theoretical temperature models are computed taking into account different initial conditions, heat sources, differentiation and simulated convection. To account for the early formation of the lunar highlands, the time duration of magmatism and present-day temperatures estimated from lunar electrical conductivity profiles, it is necessary to restrict initial temperatures and abundances of radioactive elements. Successful models require that the outer half of the moon initially heated to melting temperatures, probably due to rapid accretion. Differentiation of radioactive heat sources toward the lunar surface occurred during the first 1.6 billion years. Temperatures in the outer 500 km are currently low, while the deep interior (radius less than 700 to 1000 km) is warmer than 1000 C, and is of primordial material.

Toksoz, M. N.↗

Extravehicular mobility unit thermal simulator

The analytical methods, thermal model, and user's instructions for the SIM bay extravehicular mobility unit (EMU) routine are presented. This digital computer program was developed for detailed thermal performance predictions of the crewman performing a command module extravehicular activity during transearth coast. It accounts for conductive, convective, and radiative heat transfer as well as fluid flow and associated flow control components. The program is a derivative of the Apollo lunar surface EMU digital simulator. It has the operational flexibility to accept card or magnetic tape for both the input data and program logic. Output can be tabular and/or plotted and the mission simulation can be stopped and restarted at the discretion of the user. The program was developed for the NASA-JSC Univac 1108 computer system and several of the capabilities represent utilization of unique features of that system. Analytical methods used in the computer routine are based on finite difference approximations to differential heat and mass balance equations which account for temperature or time dependent thermo-physical properties.

Hixon, C. W.↗

AIR Instrument Array

The large number of radiation types composing the atmospheric radiation requires a complicated combination of instrument types to fully characterize the environment. A completely satisfactory combination has not as yet been flown and would require a large capital outlay to develop. In that the funds of the current project were limited to essential integration costs, an international collaboration was formed with partners from six countries and fourteen different institutions with their own financial support for their participation. Instruments were chosen to cover sensitivity to all radiation types with enough differential sensitivity to separate individual components. Some instruments were chosen as important to specify the physical field component and other instruments were chosen on the basis that they could be useful in dosimetric evaluation. In the present paper we will discuss the final experimental flight package for the ER-2 flight campaign.

Jones, I. W.↗

Application of the method of lines for solutions of the Navier-Stokes equations using a nonuniform grid distribution

The feasibility of the method of lines for solutions of physical problems requiring nonuniform grid distributions is investigated. To attain this, it is also necessary to investigate the stiffness characteristics of the pertinent equations. For specific applications, the governing equations considered are those for viscous, incompressible, two dimensional and axisymmetric flows. These equations are transformed from the physical domain having a variable mesh to a computational domain with a uniform mesh. The two governing partial differential equations are the vorticity and stream function equations. The method of lines is used to solve the vorticity equation and the successive over relaxation technique is used to solve the stream function equation. The method is applied to three laminar flow problems: the flow in ducts, curved-wall diffusers, and a driven cavity. Results obtained for different flow conditions are in good agreement with available analytical and numerical solutions. The viability and validity of the method of lines are demonstrated by its application to Navier-Stokes equations in the physical domain having a variable mesh.

Abolhassani, J. S.↗

Atmospheric Pre-Corrected Differential Absorption Techniques to Retrieve Columnar Water Vapor: Theory and Simulations

Two different approaches exist to retrieve columnar water vapor from imaging spectrometer data: (1) Differential absorption techniques based on: (a) Narrow-Wide (N/W) ratio between overlapping spectrally wide and narrow channels; (b) Continuum Interpolated Band Ratio (CIBR) between a measurement channel and the weighted sum of two reference channels. (2) Non-linear fitting techniques which are based on spectral radiative transfer calculations. The advantage of the first approach is computational speed and of the second, improved retrieval accuracy. Our goal was to improve the accuracy of the first technique using physics based on radiative transfer. Using a modified version of the Duntley equation, we derived an "Atmospheric Pre-corrected Differential Absorption" (APDA) technique and described an iterative scheme to retrieve water vapor on a pixel-by-pixel basis. Next we compared both, the CIBR and the APDA using the Duntley equation for MODTRAN3 computed irradiances, transmissions and path radiance (using the DISORT option). This simulation showed that the CIBR is very sensitive to reflectance effects and that the APDA performs much better. An extensive data set was created with the radiative transfer code 6S over 379 different ground reflectance spectra. The calculated relative water vapor error was reduced significantly for the APDA. The APDA technique had about 8% (vs. over 35% for the CIBR) of the 379 spectra with a relative water vapor error of greater than +5%. The APDA has been applied to 1991 and 1995 AVIRIS scenes which visually demonstrate the improvement over the CIBR technique.

Borel, Christoph C.↗