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At least 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Simulations of sonic boom ray tube area fluctuations for propagation through atmospheric turbulence including caustics via a Monte Carlo method

A theory which gives statistical predictions for how often sonic booms propagating through the earth's turbulent boundary layer will encounter caustics, given the spectral properties of the atmospheric turbulence, is outlined. The theory is simple but approximately accounts for the variation of ray tube areas along ray paths. This theory predicts that the variation of ray tube areas is determined by the product of two similar area factors, psi (x) and phi (x), each satisfying a generic harmonic oscillator equation. If an area factor increases the peak acoustic pressure decreases, and if the factor decreases the peak acoustic pressure increases. Additionally, if an area factor decreases to zero and becomes negative, the ray has propagated through a caustic, which contributes a phase change of 90 degrees to the wave. Thus, it is clear that the number of times that a sonic boom wave passes through a caustic should be related to the distorted boom waveform received on the ground. Examples are given based on a characterization of atmospheric turbulence due to the structure function of Tatarski as modified by Crow.

Sparrow, Victor W.↗
NASA NTRS1992

Thermochemical nonequilibrium and radiative interactions in supersonic hydrogen-air combustion

The two-dimensional, elliptic Navier-Stokes equations are used to investigate supersonic flows with nonequilibrium chemistry and thermodynamics, coupled with radiation, for hydrogen-air systems. The chemistry source term in the species equation is treated implicitly to alleviate the stiffness associated with fast reactions. The explicit, unsplit MacCormack finite-difference scheme is used to advance the governing equations in time, until convergence is achieved. The specific problem considered is the premixed, expanding flow in a supersonic nozzle. The reacting flow consists of seven species, one of which is the inert N2 molecule. The thermal state of the gas is modeled with one translational-rotational temperature and five vibrational temperatures. The harmonic oscillator model is used in the formulation for vibrational relaxation. The tangent slab approximation is used in the radiative flux formulation. A pseudo-gray model is used to represent the absorption-emission characteristics of the participating species. Results obtained for specific conditions indicate the presence of nonequilibrium in the expansion region. This reduces the radiative interactions and can have a significant influence on the flowfield.

Chandrasekhar, R.↗
NASA NTRS1992

Fuel optimal propulsive reboost of flexible spacecraft

This paper presents for the first time an exact solution to the fuel optimal propulsive reboost problem for flexible spacecraft. The spacecraft undergoes rigid-body motion and flexible-body motion and reboost is achieved propulsively through the use of reaction control jets. The exact fuel optimal solution to the associated minimization problem is found numerically based on an adaptive grid bisection search. The reboost of the floating harmonic oscillator reveals properties of the fuel optimal solution. Nondimensional plots of minimum fuel versus maneuver time expose the nature of the solution classes depending on the maneuver time. Some very interesting properties are observed, among them, the shifting of impulses to the smaller oscillator mass, and comparisons are made with near fuel optimal solutions obtained by other investigators.

Silverberg, Larry↗
NASA NTRS1992

Distribution of ULF energy (f is less than 80 mHz) in the inner magnetosphere - A statistical analysis of AMPTE CCE magnetic field data

Magnetic field measurements made with the AMPTE CCE spacecraft are used to investigate the distribution of ULF energy in the inner magnetosphere. The data base is employed to examine the spatial distribution of ULF energy. The spatial distribution of wave power and spectral structures are used to identify several pulsation types, including multiharmonic toroidal oscillations; equatorial compressional Pc 3 oscillations; second harmonic poloidal oscillations; and nightside compressional oscillations. The frequencies of the toroidal oscillations are applied to determine the statistical radial profile of the plasma mass density and Alfven velocity. A clear signature of the plasma pause in the profiles of these average parameters is found.

Takahashi, Kazue↗
NASA NTRS1991

Monte Carlo study of vibrational relaxation processes

A new model is proposed for the computation of vibrational nonequilibrium in the direct simulation Monte Carlo method (DSMC). This model permits level to level vibrational transitions for the first time in a Monte Carlo flowfield simulation. The model follows the Landau-Teller theory for a harmonic oscillator in which the rates of transition are related to an experimental correlation for the vibrational relaxation time. The usual method for simulating such processes in the DSMC technique applies a constant exchange probability to each collision and the vibrational energy is treated as a continuum. A comparison of these two methods is made for the flow of nitrogen over a wedge. Significant differences exist for the vibrational temperatures computed. These arise as a consequence of the incorrect application of a constant exchange probability in the old method. It is found that the numerical performances of the two vibrational relaxation models are equal.

Boyd, Iain D.↗
NASA NTRS1992

Computer program for calculating and fitting thermodynamic functions

A computer program is described which (1) calculates thermodynamic functions (heat capacity, enthalpy, entropy, and free energy) for several optional forms of the partition function, (2) fits these functions to empirical equations by means of a least-squares fit, and (3) calculates, as a function of temperture, heats of formation and equilibrium constants. The program provides several methods for calculating ideal gas properties. For monatomic gases, three methods are given which differ in the technique used for truncating the partition function. For diatomic and polyatomic molecules, five methods are given which differ in the corrections to the rigid-rotator harmonic-oscillator approximation. A method for estimating thermodynamic functions for some species is also given.

Mcbride, Bonnie J.↗
NASA NTRS1993

The universal propagator

For a general Hamiltonian appropriate to a single canonical degree of freedom, a universal propagator with the property that it correctly evolves the coherent-state Hilbert space representatives for an arbitrary fiducial vector is characterized and defined. The universal propagator is explicitly constructed for the harmonic oscillator, with a result that differs from the conventional propagators for this system.

Klauder, John R.↗
NASA NTRS1993

The SU(2) action-angle variables

Operator angle-action variables are studied in the frame of the SU(2) algebra, and their eigenstates and coherent states are discussed. The quantum mechanical addition of action-angle variables is shown to lead to a noncommutative Hopf algebra. The group contraction is used to make the connection with the harmonic oscillator.

Ellinas, Demosthenes↗
NASA NTRS1993

Deformation of supersymmetric and conformal quantum mechanics through affine transformations

Affine transformations (dilatations and translations) are used to define a deformation of one-dimensional N = 2 supersymmetric quantum mechanics. Resulting physical systems do not have conserved charges and degeneracies in the spectra. Instead, superpartner Hamiltonians are q-isospectral, i.e. the spectrum of one can be obtained from another (with possible exception of the lowest level) by q(sup 2)-factor scaling. This construction allows easily to rederive a special self-similar potential found by Shabat and to show that for the latter a q-deformed harmonic oscillator algebra of Biedenharn and Macfarlane serves as the spectrum generating algebra. A general class of potentials related to the quantum conformal algebra su(sub q)(1,1) is described. Further possibilities for q-deformation of known solvable potentials are outlined.

Spiridonov, Vyacheslav↗
NASA NTRS1993

Two photon annihilation operators and squeezed vacuum

Inverses of the harmonic oscillator creation and annihilation operators by their actions on the number states are introduced. Three of the two photon annihilation operators, viz., a(sup +/-1)a, aa(sup +/-1), and a(sup 2), have normalizable right eigenstates with nonvanishing eigenvalues. The eigenvalue equation of these operators are discussed and their normalized eigenstates are obtained. The Fock state representation in each case separates into two sets of states, one involving only the even number states while the other involving only the odd number states. It is shown that the even set of eigenstates of the operator a(sup +/-1)a is the customary squeezed vacuum S(sigma) O greater than.

Roy, Anil K.↗
NASA NTRS1993

Decoherence of multimode thermal squeezed coherent states

It is well known that any multimode positive definite quadratic Hamiltonian can be transformed into a Hamiltonian of uncoupled harmonic oscillators. Based on this theorem, the multimode thermal squeezed coherent states are constructed in terms of density operators. Decoherence of multimode thermal squeezed coherent states is investigated via the characteristic function and it is shown that the decohered (reduced) states are still thermal squeezed coherent states in general.

Yeh, Leehwa↗
NASA NTRS1993

Second quantization in bit-string physics

Using a new fundamental theory based on bit-strings, a finite and discrete version of the solutions of the free one particle Dirac equation as segmented trajectories with steps of length h/mc along the forward and backward light cones executed at velocity +/- c are derived. Interpreting the statistical fluctuations which cause the bends in these segmented trajectories as emission and absorption of radiation, these solutions are analogous to a fermion propagator in a second quantized theory. This allows us to interpret the mass parameter in the step length as the physical mass of the free particle. The radiation in interaction with it has the usual harmonic oscillator structure of a second quantized theory. How these free particle masses can be generated gravitationally using the combinatorial hierarchy sequence (3,10,137,2(sup 127) + 136), and some of the predictive consequences are sketched.

Noyes, H. Pierre↗
NASA NTRS1993

Calculation of the nucleon structure function from the nucleon wave function

Harmonic oscillator wave functions have played an historically important role in our understanding of the structure of the nucleon, most notably by providing insight into the mass spectra of the low-lying states. High energy scattering experiments are known to give us a picture of the nucleon wave function at high-momentum transfer and in a frame in which the nucleon is traveling fast. A simple model that crosses the twin bridges of momentum scale and Lorentz frame that separate the pictures of the nucleon wave function provided by the deep inelastic scattering data and by the oscillator model is presented.

Hussar, Paul E.↗
NASA NTRS1993

Impulse damping control of an experimental structure

The characteristics associated with the fuel optimal control of a harmonic oscillator are extended to develop a near minimum fuel control algorithm for the vibration suppression of spacecraft. The operation of single level thrusters is regulated by recursive calculations of the standard deviations of displacement and velocity resulting in a bang-off-bang controller. A vertically suspended 16 ft cantilevered beam was used in the experiment. Results show that the structure's response was easily manipulated by minor alterations in the control law and the control system performance was not seriously degraded in the presence of multiple actuator failures.

Redmond, J.↗
NASA NTRS1992

Fuel optimal control of an experimental multi-mode system

In this paper, the dynamic characteristics associated with the fuel optimal control of a harmonic oscillator are utilized in the development of a near fuel optimal feedback control strategy for spacecraft vibration suppression. In this scheme, single level thrust actuators are governed by recursive computations of the standard deviations of displacement and velocity at the actuator's locations. The algorithm was tested on an experimental structure possessing a significant number of flexible body modes. The structure's response to both single and multiple mode excitation is presented.

Redmond, J.↗
NASA NTRS1992

Theoretical shell-model signatures in heavy-ion, coherent pion production

A comprehensive summary of a many-body, microscopic, particle-hole formalism is presented that describes coherent, subthreshold, pion production in peripheral, heavy-ion collisions. The formalism uses a new separable model transition interaction that produces Delta-hole states in either the projectile or target nucleus. Shell-model states described by harmonic oscillator functions are used in the calculation of Delta formation and decay and Lorentz-contraction effects of the nucleus not at rest are included. An analytical expression to lowest multipole order for the differential cross section is examined. The sensitivity of the theoretical results to the shell-model states is determined with preliminary shape results compared with data. The effects of higher multipoles are examined with attention paid to the second-order multipole value.

Maung, Khin M.↗
NASA NTRS1992

Classical electron mass and fields. II

Continued here is the development of a model of the electron (HYDRA), which includes rotational and magnetic terms. The atomic electron state is discussed and a comparison is made with a simple harmonic oscillator. Experimental data is reviewed that supports the possibility of a new lepton.

Spaniol, Craig↗
NASA NTRS1993

Vibrational nonequilibrium effects on diatomic dissociation rates

The collision-induced dissociation rate of diatomic molecules from a ladder of rotational and anharmonic vibrational states is developed, and the correction for vibrational nonequilibrium is considered. The result is similar to an analytic correction derived by Hammerling et al. (1959) for harmonic oscillators. An empirical correction algorithm suggested by Park (1987, 1990) gives similar results when vibrational temperature is comparable to kinetic temperature but underestimates the dissociation rate when vibrational temperature is small compared with the kinetic temperature. This algorithm uses an effective temperature in the experimentally determined Arrhenius expression for the rate coefficient, which is a weighted average of the vibrational and kinetic temperature, whereas theory indicates that kinetic temperature should appear only in the exponential term of the Arrhenius expression. Nevertheless, an effective temperature can always be found that will numerically duplicate the proper rate coefficient at any given condition, but a constant weighting factor cannot be expected to provide this. However, the algorithm can he adjusted to give reasonable results over a range of conditions if the geometric weighting factor is taken to be a simple linear function of the ratio of vibrational to kinetic temperature in the gas.

Hansen, C. F.↗