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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

The solution of the relaxation problem for the Boltzmann equation by the integral iteration method

The Boltzmann equation is considered in terms of the problem of relaxation of some initial distribution function which depends only on velocities, to Maxwell's distribution function. The Boltzmann equation is given for the relaxation problem in which the distribution function f(t, u, v) is time dependent and is also dependent on two other variables u and v (the velocities of rigid spherical molecules). An iteration process is discussed in which the velocity space u, v is subdivided into squares, the distribution function in each square being approximated by the second-order surface from the values of the distribution function at nine points. The set of all of these points forms a network of u, v values at the nodes of which the distribution function can be found.

Limar, Y. F.↗
NASA NTRS1972

Stress relaxation of high strength A-286 bolts in simulated storage at room temperature

It was concluded that thermally activated relaxation of the type customarily encountered at high temperatures was not expected to occur at the low temperatures where long time NERVA storage conditions will prevail. Instances where relaxation occurred by a different mechanism at such moderate temperatures were also reported. Twelve simulated bolted flange test specimens were prepared. Parameters that were varied among the twelve specimens were the flange material, the bolt shank diameter, and the bolt loading in terms of percent of yield strength.

Sampson, R. C.↗
NASA NTRS1973

Auroral ion velocity distributions using a relaxation model.

Calculation of ion velocity distributions for a weakly-ionized plasma subjected to crossed electric and magnetic fields for application to the auroral ionosphere. By replacing the Boltzmann collision integral with a simple relaxation model, an exact solution to Boltzmann's equation could be obtained. This solution has the advantage over a series expansion in that all the higher-order velocity moments are inherent in it. The exact solution is particularly advantageous when studying large departures of the distribution from its Maxwellian form, because these departures are caused by the higher velocity moments. In general, however, a simple relaxation model can only be used to obtain qualitative information on the distribution function. Consequently, it is possible to determine when the higher-order velocity moments affect the ion velocity distribution and the nature of their effect, but it is not possible to obtain accurate quantitative results.

St-Maurice, J.-P.↗
NASA NTRS1973

Interrelated structures of the transport shock and collisional relaxation layer in a multitemperature, multilevel ionized gas

The gas dynamic structures of the transport shock and the downstream collisional relaxation layer are evaluated for partially ionized monatomic gases. Elastic and inelastic collisional nonequilibrium effects are taken into consideration. In the microscopic model of the atom, three electronic levels are accounted for. By using an asymptotic technique, the shock morphology is found on a continuum flow basis. This procedure gives two distinct layers in which the nonequilibrium effects to be considered are different. A transport shock appears as the inner solution to an outer collisional relaxation layer. The results show four main interesting points: (1) on structuring the transport shock, ionization and excitation rates must be included in the formulation, since the flow is not frozen with respect to the population of the different electronic levels; (2) an electron temperature precursor appears at the beginning of the transport shock; (3) the collisional layer is rationally reduced to quadrature for special initial conditions, which (4) are obtained from new Rankine-Hugoniot relations for the inner shock.

Vinolo, A. R.↗
NASA NTRS1973

Theoretical models for electron energy relaxation in the lower ionosphere

Elastic collisions and rotation inelastic collisions involving quadrupole molecular transitions are important in energy relaxation of electrons in molecular gases. It has been customary in studying the cooling of electrons in a plasma heated by high-frequency waves to characterize this relaxation by the ionospheric G factor. The G factor is first defined in a fundamental way by use of kinetic theory. Then present models for theoretical cross sections for electron collision with O2 and N2 are used to derive expressions for the G factor in the lower ionosphere. Two models are considered: one uses Gerjuoy-Stein models for both N2 and O2; the other uses a Gerjuoy-Stein model for N2 and a Geltman-Takayanaki model for O2. Neither O2 model has been definitely established experimentally. It is found that temperature dependence of G is critically dependent on the O2 model.

Hagenbuch, K. M.↗
NASA NTRS1973

Radiative relaxation behind strong shock waves in hydrogen-helium mixtures

Radiative relaxation rates have been investigated in a series of hydrogen-helium mixtures over a range of temperatures encountered during outer planet atmospheric entry. Using a conical electric arc shock tube, shock waves with velocities between 10 and 36 km/sec were studied in mixtures of 10% to 85% hydrogen in helium diluent. Intensities for several hydrogen continuum wavelengths and the H-alpha and H-beta lines of hydrogen were measured as a function of time. The nonequilibrium relaxation times were longer than expected for shock velocities greater than 18 km/sec and reached a plateau at higher shock velocities. Data from all mixtures were found to correlate with shock wave temperature.

Leibowitz, L. P.↗
NASA NTRS1974

Electron-ion relaxation in a dense plasma

The microscopic physics of the thermonuclear runaway in highly degenerate carbon-oxygen cores is investigated to determine if and how a detonation wave is generated. An expression for the electron-ion relaxation time is derived under the assumption of large degeneracy and extreme relativity of the electrons in a two-temperature plasma. Since the nuclear burning time proves to be several orders of magnitude shorter than the relaxation time, it is concluded that in studying the structure of the detonation wave the electrons and ions must be treated as separate fluids.

Littleton, J. E.↗
NASA NTRS1974

Thermal relaxation of a two-dimensional plasma in a d.c. magnetic field. I - Theory. II - Numerical simulation

Theoretical considerations relevant to the rate of thermal relaxation of a two-dimensional plasma in a strong uniform dc magnetic field are developed. The Vahala-Montgomery (1971) kinetic description is completed by providing a cut-off time for the time of interaction of two particles contributing to the collision term. The kinetic equation is shown to predict that thermal relaxation varies as a function of defined dimensionless time.

Hsu, J.-Y.↗
NASA NTRS1974

The spin-temperature theory of dynamic nuclear polarization and nuclear spin-lattice relaxation

A detailed derivation of the equations governing dynamic nuclear polarization (DNP) and nuclear spin lattice relaxation by use of the spin temperature theory has been carried to second order in a perturbation expansion of the density matrix. Nuclear spin diffusion in the rapid diffusion limit and the effects of the coupling of the electron dipole-dipole reservoir (EDDR) with the nuclear spins are incorporated. The complete expression for the dynamic nuclear polarization has been derived and then examined in detail for the limit of well resolved solid effect transitions. Exactly at the solid effect transition peaks, the conventional solid-effect DNP results are obtained, but with EDDR effects on the nuclear relaxation and DNP leakage factor included. Explicit EDDR contributions to DNP are discussed, and a new DNP effect is predicted.

Byvik, C. E.↗
NASA NTRS1974

Effect of crosslinking density on biaxial relaxation of SBR by using reduced variables

The use of reduced variables to account for the effect of crosslinking density in a styrene-butadiene rubber (SBR) system is demonstrated for general biaxial stress states. Recently published results from stress relaxation tests on five SBR vulcanizates crosslinked to different degrees by tetramethylthiuram disulfide were superposed by using the crosslinking density as a reduction variable. The equilibrium shear modulus calculated from the master relaxation curve at long reduced times was in satisfactory agreement with other results for SBR. The time-axis shifts were related in a linear logarithmic manner to the crosslinking density but had a slope slightly less than values previously reported for elastomer systems.

Arenz, R. J.↗
NASA NTRS1975

Aerosol size spectrum analysis using relaxation time measurement

An experimental method has been developed to measure the dynamic relaxation times of aerosol particles. The particle relaxation time (tau-p) is determined from the ratio of the velocity amplitude of an aerosol particle (v-p) to the velocity amplitude of the medium (u-g) while the aerosol is subjected to acoustic excitation of a known frequency. A differential laser Doppler velocimeter is used to measure v-p, while a microphone is used to measure u-g. From the value of tau-p, the aerodynamic diameter of the particle can be determined if the particle density is known. The method can be applied to real-time in situ measurement of size distribution of an aerosol containing both solid particles and liquid droplets in the range of 0.1-10.0-micron diameters.

Kirsch, K. J.↗
NASA NTRS1976

Proton magnetic relaxation and internal rotations in tetramethylammonium cadmium chloride

Nuclear magnetic resonance (NMR) and relaxation studies of the proton spin-lattice relaxation time (PSLRT) and proton second moment (PSM) are reported. Tetramethylammonium cadmium chloride (TMCC) was selected as a diamagnetic member of the isomorphic series, and hence proton data relate directly to the motion of the tetramethylammonium ion in the absence of paramagnetic ions. In the model adopted, the correlation time for hindered motion of one of the methyl groups differs from that of the other three groups in the low-temperature phase below 104 K. PSLRT and PSM values agree closely with experimental data with this model. Crystallographic phase transitions in TMCC occur at 104 K and 119 K according to the PSLRT measurements. Dipolar interactions between adjacent protons account for the PSLR rates below 104 K.

Tsang, T.↗
NASA NTRS1977

Effects of control laws and relaxed static stability on vertical ride quality of flexible aircraft

State variable techniques are utilized to generate the RMS vertical load factors for the B-52H and B-1 bombers at low level, mission critical, cruise conditions. A ride quality index is proposed to provide meaningful comparisons between different controls or conditions. Ride quality is shown to be relatively invariant under various popular control laws. Handling quality variations are shown to be major contributors to ride quality variations on both vehicles. Relaxed static stability is artificially implemented on the study vehicles to investigate its effects on ride quality. The B-52H ride quality is generally degraded when handling characteristics are automatically restored by a feedback control to the original values from relaxed stability conditions. The B-1 airplane shows little ride quality sensitivity to the same analysis due to the small rigid body contribution to load factors at the flight condition investigated.

Roberts, P. A.↗
NASA NTRS1976

Neutral-atom electron binding energies from relaxed-orbital relativistic Hartree-Fock-Slater calculations for Z between 2 and 106

Electron binding energies in neutral atoms have been calculated relativistically, with the requirement of complete relaxation. Hartree-Fock-Slater wave functions served as zeroth-order eigenfunctions to compute the expectation of the total Hamiltonian. A first-order correction to the local approximation was thus included. Quantum-electrodynamic corrections were made. For all elements with atomic numbers ranging from 2 to 106, the following quantities are listed: total energies, electron kinetic energies, electron-nucleus potential energies, electron-electron potential energies consisting of electrostatic and Breit interaction (magnetic and retardation) terms, and vacuum polarization energies. Binding energies including relaxation are listed for all electrons in all atoms over the indicated range of atomic numbers. A self-energy correction is included for the 1s, 2s, and 2p(1/2) levels. Results for selected atoms are compared with energies calculated by other methods and with experimental values.

Huang, K.-N.↗
NASA NTRS1978

Exchange and relaxation effects in low-energy radiationless transitions

The effect on low-energy atomic inner-shell Coster-Kronig and super Coster-Kronig transitions that is produced by relaxation and by exchange between the continuum electron and bound electrons was examined and illustrated by specific calculations for transitions that deexcite the 3p vacancy state of Zn. Taking exchange and relaxation into account is found to reduce, but not to eliminate, the discrepancies between theoretical rates and measurements.

Chen, M. H.↗
NASA NTRS1978

Calculation of spin-lattice relaxation during pulsed spin locking in solids

The spin-lattice relaxation time has been calculated for dipolar solids in the case where the spins are locked by an RF pulse sequence with pulses of arbitrary angle and finite width. Expressions are given for the homonuclear case in general and for the heteronuclear case in the delta-function limit. The results for the homonuclear case are experimentally confirmed using solid C6F12. The analysis shows that for small pulse angles, at which the direct spin heating effect is known to be small, the relaxation behavior will be identical to the CW irradiation case.

Rhim, W.-K.↗
NASA NTRS1978

NMR relaxation rate and the libron energy of solid hydrogen

By taking the rotational relaxation of orthohydrogen (o-H2) in solid hydrogen into account, the authors have theoretically investigated the longitudinal NMR spin lattice relaxation rate of o-H2. The rate is characterized by an anomalous maximum, as a function of temperature, at temperatures close to the mean libron energy of o-H2. Application of the theory for o-H2 concentrations between 42% and 75% reveals a nearly concentration-independent mean libron energy equivalent to about 1 K. This qualitatively and quantitatively contradicts the conclusions of other theories, but agrees with recent experiments.

Sugawara, K.↗
NASA NTRS1979

Collapse and relaxation of rotating stellar systems

The evolution of initially spherical, uniform-density, and uniform-velocity-dispersion stellar systems is investigated by means of a three-dimensional N-body computer model. Some 100,000 simulation stars are used to follow the collapse and relaxation of the system for various amounts of angular momentum in solid-body rotation. For initially low values of the angular momentum satisfying the Ostriker-Pebbles stability criterion the systems quickly relax to an axisymmetric shape and resemble elliptical galaxies in appearance. The maximum flattening for these systems is equivalent only to an E2 system. For larger values of the initial angular momentum bars develop, and the systems undergo a much more drastic evolution. The apparent rotational and random velocities of the barred systems are very sensitive to the viewing direction. An additional complication is the frequent misalignment of the apparent major axis with the direction that reflects the maximum rotation.

Hohl, F.↗