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NASA NTRS1996

Controlled Quantum Packets

We look at time evolution of a physical system from the point of view of dynamical control theory. Normally we solve motion equation with a given external potential and we obtain time evolution. Standard examples are the trajectories in classical mechanics or the wave functions in Quantum Mechanics. In the control theory, we have the configurational variables of a physical system, we choose a velocity field and with a suited strategy we force the physical system to have a well defined evolution. The evolution of the system is the 'premium' that the controller receives if he has adopted the right strategy. The strategy is given by well suited laboratory devices. The control mechanisms are in many cases non linear; it is necessary, namely, a feedback mechanism to retain in time the selected evolution. Our aim is to introduce a scheme to obtain Quantum wave packets by control theory. The program is to choose the characteristics of a packet, that is, the equation of evolution for its centre and a controlled dispersion, and to give a building scheme from some initial state (for example a solution of stationary Schroedinger equation). It seems natural in this view to use stochastic approach to Quantum Mechanics, that is, Stochastic Mechanics [S.M.]. It is a quantization scheme different from ordinary ones only formally. This approach introduces in quantum theory the whole mathematical apparatus of stochastic control theory. Stochastic Mechanics, in our view, is more intuitive when we want to study all the classical-like problems. We apply our scheme to build two classes of quantum packets both derived generalizing some properties of coherent states.

DeMartino, Salvatore↗

NASA NTRS2008

The Hertz/VPM Polarimeter: Design and First Light Observations

We present first results of Hertz/VPM, the first submillimeter polarimeter employing the dual Variable-delay Polarization Modulator (dual-VPM). This device differs from previously used polarization modulators in that it, operates in translation rather than mechanical rotation. We discuss the basic theory behind this device, and its potential advantages over the commonly used half wave plate (HFVP). The dual-VPM was tested both at the Submillimeter Telescope Observatory (SMTO) and in the lab. In each case we present a detailed description of the setup. We discovered nonideal behavior in the system. This is at least in part due to properties of the VPM wire grids (diameter, spacing) employed in our experiment. Despite this, we found that the dual-VPM system is robust, operating with high efficiency and low instrumental polarization. This device is well suited for air and space-borne applications.

Krejny, Megan↗

NASA NTRS1999

Recent Development on O(+) - O Collision Frequency and Ionosphere-Thermosphere Coupling

The collision frequency between an oxygen atom and its singly charged ion controls the momentum transfer between the ionosphere and the thermosphere. There has been a long standing discrepancy, extending over a decade, between the theoretical and empirical determination of this frequency: the empirical value of this frequency exceeded the theoretical value by a factor of 1.7. Recent improvements in theory were obtained by using accurate oxygen ion-oxygen atom potential energy curves, and partial wave quantum mechanical calculations. We now have applied three independent statistical methods to the observational data, obtained at the MIT/Millstone Hill Observatory, consisting of two sets A and B. These methods give results consistent with each other, and together with the recent theoretical improvements, bring the ratio close to unity, as it should be. The three statistical methods lead to an average for the ratio of the empirical to the theoretical values equal to 0.98, with an uncertainty of +/-8%, resolving the old discrepancy between theory and observation. The Hines statistics, and the lognormal distribution statistics, both give lower and upper bounds for the Set A equal to 0.89 and 1.02, respectively. The related bounds for the Set B are 1.06 and 1.17. The average values of these bounds thus bracket the ideal value of the ratio which should be equal to unity. The main source of uncertainties are errors in the profile of the oxygen atom density, which is of the order of 11%. An alternative method to find the oxygen atom density is being suggested.

Omidvar, K.↗

NASA NTRS1973

Turbulence in electrostatic ion acoustic shocks

Three types of collisionless electrostatic ion acoustic shocks are investigated using a double plasma (DP) device: (1) laminar shocks; (2) small amplitude turbulent shocks in which the turbulence is confined to be upstream of the shock potential jump; and (3) large amplitude turbulent shocks in which the wave turbulence occurs throughout the shock transition. The wave turbulence is generated by ions which are reflected from the shock potential; linear theory spatial growth increments agree with experimental values. The experimental relationship between the shock Mach number and the shock potential is shown to be inconsistent with theoretical shock models which assume that the electrons are isothermal. Theoretical calculations which assume a trapped electron equation of a state and a turbulently flattened velocity distrubution function for the reflected ions yields a Mach number vs potential relationship in agreement with experiment.

Means, R. W.↗

NASA NTRS1973

Turbulence in electrostatic ion-acoustic shocks

Three types of collisionless electrostatic ion-acoustic shocks are investigated using the University of California, Los Angeles, double plasma device: (1) laminar shocks; (2) small amplitude turbulent shocks in which the turbulence is confined to be upstream of the shock potential jump; and (3) large amplitude turbulent shocks in which the wave turbulence occurs throughout the shock transition. The wave turbulence is generated by ions which are reflected from the shock potential; linear theory spatial growth increments agree with experimental values. The experimental relationship between the shock Mach number and the shock potential is shown to be inconsistent with theoretical shock models which assume that the electrons are isothermal. Theoretical calculations which assume a trapped electron equation of a state and a turbulently flattened velocity distribution function for the reflected ions yields a Mach number vs potential relationship in agreement with experiment.

Means, R. W.↗

NASA NTRS1999

Recent Development on O(+)-O Collision Frequency and Ionosphere-Middle Atmosphere Coupling

The collision frequency between an oxygen atom and its singly charged ion controls the transfer of energy between the solar radiation and the thermosphere. There were a long standing discrepancy, extending over a decade, between the theoretical and empirical determination of this frequency, and the empirical value of this frequency exceeded the theoretical value by a factor of 1.7. Recent improvements in theory were obtained by using accurate oxygen ion-oxygen atom potential energy curves, and partial wave quantum mechanical calculations. Similarly, recently three independent statistical methods were applied to the empirical determination of this frequency. These methods give results consistent with each other, and together with the recent theoretical improvements, bring the ratio close to unity, as it should be. It will be shown that the old statistical method for this determination contained accumulative errors, leading to a larger value for this ratio. The recent improvements lead to an average value of the empirical to the theoretical ratio equal to 0.98, with an uncertainty of +/- 8%, resolving the old discrepancy between theory and observations. The main source of uncertainties are errors in the profile of the oxygen atom density, which is of the order of 11 %. An alternative method to find the oxygen atom density is being suggested.

Omidvar, K.↗

NASA NTRS1994

Gravity waves in Titan's atmosphere

Scintillations (high frequency variations) observed in the radio signal during the occultation of Voyager 1 by Titan (Hinson and Tyler, 1983) provide information concerning neutral atmospheric density fluctuations on scales on hundreds of meters to a few kilometers. Those seen at altitudes higher than 25 km above the surface were interpreted by Hinson and Tyler as being caused by linear, freely propagating (energy-conserving) gravity waves, but this interpretation was found to be inconsistent with the scintillation data below the 25-km altitude level. Here an attempt is made to interpret the entire scintillation profile between the surface and the 90-km altitude level in terms of gravity waves generated at the surface. Numerical calculations of the density fluctuations caused by two-dimensional, nonhydrostatic, finite-amplitude gravity waves propagating vertically through Titan's atmosphere are performed to produce synthetic scintillation profiles for comparison with the observations. The numerical model accurately treats the effects of wave transience, nonlinearity, and breakdown due to convective instability in the overturned part of the wave. The high-altitude scintillation data were accurately recovered with a freely propagating wave solution, confirming the analytic model of Hinson and Tyler. It is found that the low-altitude scintillation data can be fit by a model where a component of the gravity waves becomes convectively unstable and breaks near the 15 km level. The large-scale structure of the observed scintillation profile in the entire altitude range between 5 and 85 km can be simulated by a model where the freely propagating and breaking waves are forced at the surface simultaneously. Further analysis of the Voyager 1 Titan low-altitude scintillation data, using inversion theory appropriate for strong scattering, could potentially remove some of the ambiguities remaining in this analysis and allow a better determination of the strength and source of the waves.

Friedson, A. James↗

NASA NTRS1984

Wave-particle transport from density drift instabilities - A comparison of local and nonlocal theories

Second-order Vlasov theory is used to compute the dissipation rates of plasma irregularities with a variety of shapes. A derivation of the nonlocal dispersion equation using linearized Vlasov theory is presented. Expressions for the normalized amplitudes of the first-order plasma density and electrostatic potential fluctuations are derived. Expressions are given for the saturation amplitudes of the electrostatic eigenmodes. The wave-particle transport and irregularity dissipation rate are computed by using formulas whose derivation is presented. Computational results for specific density variations are shown, and conclusions on the validity of the local theory as opposed to the nonlocal theory are given.

Bernhardt, P. A.↗

NASA NTRS1989

Application of a full potential method to AGARD standard airfoils

One of the most important uses of method that calculate unsteady aerodynamic loads is to predict and analyze the aeroelastic responses of flight vehicles. Currently, methods based on transonic small disturbance potential aerodynamics are the primary tools for aeroelastic analysis. Flow solutions obtained using isentropic potential theory can be highly inaccurate and even multivalued, because they do not model the effects of entropy that is produced when shock waves are in the flow field. From the results that are presented, it is concluded that nonisentropic potential methods more accurately model Euler solutions than do isentropic methods. The primary effects of modeling shock generated entropy are: (1) to eliminate mulitple flow solutions when strong shock waves are in the flow field; and (2) to bring the strengths and locations of computed shock waves into better agreement with those calculated using Euler method and those measured during experiments.

Whitlow, Woodrow, Jr.↗

NASA NTRS1994

General analytic results for nonlinear waves and solitons in molecular clouds

We study nonlinear wave phenomena in self-gravitating fluid systems, with a particular emphasis on applications to molecular clouds. This paper presents analytical results for one spatial dimension. We show that a large class of physical systems can be described by theories with a 'charge density' q(rho); this quantity replaces the density on the right-hand side of the Poisson equation for the gravitational potential. We use this formulation to prove general results about nonlinear wave motions in self-gravitating systems. We show that in order for stationary waves to exist, the total charge (the integral of the charge density over the wave profile) must vanish. This 'no-charge' property for solitary waves is related to the capability of a system to be stable to gravitational perturbations for arbitrarily long wavelengths. We find necessary and sufficient conditions on the charge density for the existence of solitary waves and stationary waves. We study nonlinear wave motions for Jeans-type theories (where q(rho) = rho-rho(sub 0)) and find that nonlinear waves of large amplitude are confined to a rather narrow range of wavelengths. We also study wave motions for molecular clouds threaded by magnetic fields and show how the allowed range of wavelengths is affected by the field strength. Since the gravitational force in one spatial dimension does not fall off with distance, we consider two classes of models with more realistic gravity: Yukawa potentials and a pseudo two-dimensional treatment. We study the allowed types of wave behavior for these models. Finally, we discuss the implications of this work for molecular cloud structure. We argue that molecular clouds can support a wide variety of wave motions and suggest that stationary waves (such as those considered in this paper) may have already been observed.

Adams, Fred C.↗

NASA NTRS1981

Adaptation of the TH Epsilon Mu formalism for the analysis of the equivalence principle in the presence of the weak and electroweak interaction

The TH epsilon mu formalism, used in analyzing equivalence principle experiments of metric and nonmetric gravity theories, is adapted to the description of the electroweak interaction using the Weinberg-Salam unified SU(2) x U(1) model. The use of the TH epsilon mu formalism is thereby extended to the weak interactions, showing how the gravitational field affects W sub mu (+ or -1) and Z sub mu (0) boson propagation and the rates of interactions mediated by them. The possibility of a similar extension to the strong interactions via SU(5) grand unified theories is briefly discussed. Also, using the effects of the potentials on the baryon and lepton wave functions, the effects of gravity on transition mediated in high-A atoms which are electromagnetically forbidden. Three possible experiments to test the equivalence principle in the presence of the weak interactions, which are technologically feasible, are then briefly outline: (1) K-capture by the FE nucleus (counting the emitted X-ray); (2) forbidden absorption transitions in high-A atoms' vapor; and (3) counting the relative Beta-decay rates in a suitable alpha-beta decay chain, assuming the strong interactions obey the equivalence principle.

Fennelly, A. J.↗

NASA NTRS2010

Ten-Year Climatology of Summertime Diurnal Rainfall Rate Over the Conterminous U.S.

Diurnal cycles of summertime rainfall rates are examined over the conterminous United States, using radar-gauge assimilated hourly rainfall data. As in earlier studies, rainfall diurnal composites show a well-defined region of rainfall propagation over the Great Plains and an afternoon maximum area over the south and eastern portion of the United States. Zonal phase speeds of rainfall in three different small domains are estimated, and rainfall propagation speeds are compared with background zonal wind speeds. Unique rainfall propagation speeds in three different regions can be explained by the evolution of latent-heat theory linked to the convective available potential energy, than by gust-front induced or gravity wave propagation mechanisms.

Matsui, Toshihisa↗

NASA NTRS1999

On the Linearly-Balanced Kinetic Energy Spectrum

It is well known that the earth's atmospheric motion can generally be characterized by the two dimensional quasi-geostrophic approximation, in which the constraints on global integrals of kinetic energy, entrophy and potential vorticity play very important roles in redistributing the wave energy among different scales of motion. Assuming the hypothesis of Kolmogrov's local isotropy, derived a -3 power law of the equilibrium two-dimensional kinetic energy spectrum that entails constant vorticity and zero energy flows from the energy-containing wave number up to the viscous cutoff. In his three dimensional quasi-geostrophic theory, showed that the spectrum function of the vertical scale turbulence - expressible in terms of the available potential energy - possesses the same power law as the two dimensional kinetic energy spectrum. As the slope of kinetic energy spectrum in the inertial range is theoretically related to the predictability of the synoptic scales (Lorenz, 1969), many general circulation models includes a horizontal diffusion to provide reasonable kinetic energy spectra, although the actual power law exhibited in the atmospheric general circulation is controversial. Note that in either the atmospheric modeling or the observational analyses, the proper choice of wave number Index to represent the turbulence scale Is the degree of the Legendre polynomial.

Lu, Huei,-Iin↗

NASA NTRS2016

Exploring the Use of Alfven Waves in Magnetometer Calibration at Geosynchronous Orbit

An Alfven wave is a type magnetohydrodynamicwave that travels through a conducting fluid under the influence of a magnetic field. Researchers have successfully calculated offset vectors of magnetometers in interplanetary space by optimizing the offset to maximize certain Alfvenic properties of observed waves (Leinweber, Belcher). If suitable Alfven waves can be found in the magnetosphere at geosynchronous altitude then these techniques could be used to augment the overall calibration plan for magnetometers in this region such as on the GOES spacecraft, possibly increasing the time between regular maneuvers. Calibration maneuvers may be undesirable because they disrupt the activities of other instruments. Various algorithms to calculate an offset using Alfven waves were considered. A new variation of the Davis-Smith method was derived because it can be mathematically shown that the Davis-Smith method tolerates filtered data, which expands potential applications. The variant developed was designed to find only the offset in the plane normal to the main field because the overall direction of Earth's magnetic field rarely changes, and theory suggests the Alfvenic disturbances occur transverse to the main field. Other variations of the Davis-Smith method encounter problems with data containing waves that propagate in mostly the same direction. A searching algorithm was then designed to look for periods of time with potential Alfven waves in GOES 15 data based on parameters requiring that disturbances be normal to the main field and not change field magnitude. Final waves for calculation were hand-selected. These waves produced credible two-dimensional offset vectors when input to the Davis-Smith method. Multiple two-dimensional solutions in different planes can be combined to get a measurement of the complete offset. The resulting three dimensional offset did not show sufficient precision over several years to be used as a primary calibration method, but reflected changes in the offset fairly well, suggesting that the method could be helpful in monitoring trends of the offset vector when maneuvers cannot be used.

calibration↗

NASA NTRS1982

Finite element-integral simulation of static and flight fan noise radiation from the JT15D turbofan engine

An iterative finite element integral technique is used to predict the sound field radiated from the JT15D turbofan inlet. The sound field is divided into two regions: the sound field within and near the inlet which is computed using the finite element method and the radiation field beyond the inlet which is calculated using an integral solution technique. The velocity potential formulation of the acoustic wave equation was employed in the program. For some single mode JT15D data, the theory and experiment are in good agreement for the far field radiation pattern as well as suppressor attenuation. Also, the computer program is used to simulate flight effects that cannot be performed on a ground static test stand.

Baumeister, K. J.↗

NASA NTRS1984

Finite element-integral acoustic simulation of JT15D turbofan engine

Baumeister, K. J.↗

NASA NTRS1989

Rototranslational absorption spectra of H2-H2 pairs in the far infrared

On the basis of ab initio induced dipole components and a well-tested isotropic potential, the collision-induced absorption rototranslational profiles of hydrogen have been determined using an exact wave-mechanical theory. The main induction mechanisms, particularly the quadrupole-induced 0223,2023 components, are found to be consistent with observations. It is demonstrated that the present theory can be used to predict spectra at temperatures where no measurements exist, as is needed for the modeling of planetary and stellar atmospheres.

Meyer, Wilfried↗

NASA NTRS2015

In-Flight Aeroelastic Stability of the Thermal Protection System on the NASA HIAD, Part II: Nonlinear Theory and Extended Aerodynamics

Conical shell theory and a supersonic potential flow aerodynamic theory are used to study the nonlinear pressure buckling and aeroelastic limit cycle behavior of the thermal protection system for NASA's Hypersonic Inflatable Aerodynamic Decelerator. The structural model of the thermal protection system consists of an orthotropic conical shell of the Donnell type, resting on several circumferential elastic supports. Classical Piston Theory is used initially for the aerodynamic pressure, but was found to be insufficient at low supersonic Mach numbers. Transform methods are applied to the convected wave equation for potential flow, and a time-dependent aerodynamic pressure correction factor is obtained. The Lagrangian of the shell system is formulated in terms of the generalized coordinates for all displacements and the Rayleigh-Ritz method is used to derive the governing differential-algebraic equations of motion. Aeroelastic limit cycle oscillations and buckling deformations are calculated in the time domain using a Runge-Kutta method in MATLAB. Three conical shell geometries were considered in the present analysis: a 3-meter diameter 70 deg. cone, a 3.7-meter 70 deg. cone, and a 6-meter diameter 70 deg. cone. The 6-meter configuration was loaded statically and the results were compared with an experimental load test of a 6-meter HIAD. Though agreement between theoretical and experimental strains was poor, the circumferential wrinkling phenomena observed during the experiments was captured by the theory and axial deformations were qualitatively similar in shape. With Piston Theory aerodynamics, the nonlinear flutter dynamic pressures of the 3-meter configuration were in agreement with the values calculated using linear theory, and the limit cycle amplitudes were generally on the order of the shell thickness. The effect of axial tension was studied for this configuration, and increasing tension was found to decrease the limit cycle amplitudes when the circumferential elastic supports were neglected, but resulted in more complex behavior when the supports were included. The nominal flutter dynamic pressure of the 3.7-meter configuration was significantly lower than that of the 3-meter, and it was found that two sets of natural modes coalesce to flutter modes near the same dynamic pressure. This resulted in a significant drop in the limit cycle frequencies at higher dynamic pressures, where the flutter mode with the lower frequency becomes more critical. Pre-buckling pressure loads and the aerodynamic pressure correction factor were studied for all geometries, and these effects resulted in significantly lower flutter boundaries compared with Piston Theory alone. The maximum dynamic pressure predicted by aerodynamic simulations of a proposed 3.7-meter HIAD vehicle was still lower than any of the calculated flutter dynamic pressures, suggesting that aeroelastic effects for this vehicle are of little concern.

Goldman, Benjamin D.↗