Showing papers on "Momentum published in 1975"

Energy Cascade in Large-Eddy Simulations of Turbulent Fluid Flows

Abstract: The derivation of smoothed or filtered momentum and continuity equations for large-scale, energy-containing eddies is considered. Questions regarding the energy loss of large-scale turbulence are discussed along with aspects of turbulent diffusion of a passive scalar. It is found that the large-scale fluctuations satisfy filtered or averaged momentum and continuity equations. An averaging of the nonlinear advection term yields two terms.

On the effects of a gravitational field on the turbulent transport of heat and momentum

Abstract: This paper suggests a simple way of including gravitational effects in the pres-sure-containing correlations that appear in the equations for the transport of Reynolds stress and heat flux. The predicted changes in structure due to the gravitational field are shown to agree closely with Webster's (1964) measurements in a stably stratified shear flow.

Momentum distributions of isotopes produced by fragmentation of relativistic C-12 and O-16 projectiles

Abstract: The fragment momentum distributions in the projectile rest frame are, typically, Gaussian shaped, narrow, consistent with isotropy, depend on fragment and projectile, and have no significant correlation with target mass or beam energy. The nuclear temperature is inferred from the momentum distributions of the fragments and is approximately equal to the projectile nuclear binding energy, indicative of small energy transfer between target and fragment.

Liquid‐crystal twist cell dynamics with backflow

Abstract: We describe and present results of a numerical method we have used to solve the hydrodynamic equations with negligible rates of change of momentum and angular momentum, but without other approximations, in a liquid‐crystal twist cell. We verify that the ’’bounce’’ in transmission of normally incident light that is observed when the electric potential across the cell is turned off is an effect of shear flow (backflow) which causes temporary reverse rotation of directors in the middle of the cell. It is not an inertial effect. Inertial effects would have transient times much shorter than the times associated with the optical bounce. When fluid flow is omitted, as in our previous papers, molecules do not tilt backward and the ’’optical bounce’’ occurs only for light that is obliquely incident in one quadrant. A qualitative explanation of the optics of the bounce is given, in addition to numerical results.

Study of mass transfer at the air-water interface by an isotopic method

Abstract: The calculation of the evaporation flux is based on certain assumptions concerning processes in the vicinity of the air-water interface. Most of the recently proposed evaporation theories differ mainly in the estimated contributions of molecular and turbulent mass transfer in the vapor phase just above the liquid surface. This paper will show that, by analyzing the hydrogen and oxygen stable isotope distribution in liquid and water vapor, the processes taking place on a very small scale near the liquid can be investigated. The effect of molecular mass transfer is directly obtained without having to perform difficult measurements in the air in the immediate vicinity of the water surface. Experiments are carried out in the Institut de Mecanique Statistique de la Turbulence air-water tunnel specially designed for the simulation of ocean-atmosphere energy exchanges. The wind velocities vary from 0.7 to 7 m/s. The experimental results obtained do not support the classical Reynolds analogy between momentum and mass transfer down to the interface and the theory proposed by Sheppard, but they are in agreement with Sverdrup's, Kitaigorodskiy and Volkov's, and Brutsaert's theories, all of which involve a layer just above the air-water interface through which mass transfer is dominated by molecular diffusion. The thickness of this layer in the two first theories is shown to decrease with increasing wind velocity. Direct application of Brutsaert's theory for roughness Reynolds numbers smaller than 1 is in good agreement with our experimental data.

Short-range correlations and the structure factor and momentum distribution of electrons

Abstract: It is shown that for any system of non-relativistic electrons and nuclei the large-wavevector limit of the probability of finding an electron with momentum h(cross)k is proportional to 1/k8, and the electronic structure factor is proportional to 1/k4 Furthermore, the coefficient of the 1/k4 term in the structure factor is proportional to the zero separation electron-electron correlation The coefficient of the 1/k8 term in the momentum distribution is proportional to the sum of zero-range electron-electron and electron-nuclear correlations

Deep Inelastic Structure Functions in an Approximation to the Bag Theory

Abstract: A cavity approximation to the bag theory developed earlier is extended to the treatment of forward virtual Compton scattering. In the Bjorken limit and for small values of ω (ω=|2p·qq2|) it is argued that the operator nature of the bag boundaries might be ignored. Structure functions are calculated in one and three dimensions. Bjorken scaling is obtained. The model provides a realization of light-cone current algebra and possesses a parton interpretation. The structure functions show a quasielastic peak. The spreading of the structure functions about the peak is associated with confinement. As expected, Regge behavior is not obtained for large ω. The "momentum sum rule" is saturated, indicating that the hadron's charged constituents carry all the momentum in this model. νWL is found to scale and is calculable. Application of the model to the calculation of spin-dependent and chiral-symmetry-violating structure functions is proposed. The nature of the intermediate states in this approximation is discussed. Problems associated with the cavity approximation are also discussed.

Exciton dispersion in degenerate bands

Abstract: The dispersion relations of band-gap excitons in covalent cubic crystals are investigated. For low momentum a perturbation method is used following Baldereschi and Lipari. At very low momentum the dispersion is strongly affected by a splitting of the fourfold $K=0$ degeneracy for those materials with nonspherical conduction-band energy surfaces. In silicon and germanium this splitting leads to strong nonparabolic effects at energies in the 0.1-meV range. For large momentum a band decoupling scheme which generalizes the center-of-mass transformation method is derived and the concept of "light-mass" and "heavy-mass" excitons naturally results. Numerical values are given for germanium, silicon, and gallium arsenide.

(e, 2e) Probe for Hydrogen-Molecule Wave Functions

Abstract: The ($e, 2e$) reaction promises to be an extremely sensitive probe for molecular wave functions. As an initial test we have applied it to the ${\mathrm{H}}_{2}$ and ${\mathrm{D}}_{2}$ molecules in order to investigate its sensitivity to electronic and vibrational details. A detailed configuration-interaction wave function fits the data, whereas simpler functions do not. The simple Born-Oppenheimer approximation is confirmed to the accuracy of the experiment. The probe is compared with the Compton profile as a means of investigating the electron momentum distribution in ${\mathrm{H}}_{2}$.

Momentum density measurements by positron annihilation in metals and alloys. Recent experiments with a multicounter two-dimensional angular correlation apparatus

Abstract: The technique of positron annihilation as applied to the study of momentum densities and Fermi surfaces is reviewed. The angular correlation of the two annihilation photons is directly related to the momentum distribution of the positron-electron system; breaks in this distribution reveal the size and shape of the Fermi surface. After a general introduction to the theory and the experimental techniques used, the results yielding various features of the fermi surface in high concentration disordered alloys are reviewed, and are compared with theoretical predictions. A new multicounter two-dimensional correlation apparatus is described and results in several solids are presented.

Non-linear plasma transport equations for high flow velocity

Abstract: Collision terms for plasma transport equations are derived from the Fokker-Planck equation without the usual linearization in U=flow velocity/thermal velocity. A 13-moment ansatz for the distribution functions includes the linearized dependence of the collision terms on viscous pressure and heat flow in the transport equations for momentum, energy, viscous pressure and heat flow. The masses and temperatures of the species are arbitrary. An expansion in U is made and the lowest non-vanishing terms are retained. The resulting system is discussed. The nonlinear terms in U may be important even for moderate U. All analytic results were obtained with the symbolic computer language REDUCE.

Positron annihilation in germanium

Abstract: High precision long-slit and cross-slit geometry angular distributions of annihilation radiation from oriented germanium are presented The momentum distributions from the long-slit measurements are compared with recent Compton profile data to test the importance of the positron wavefunction and positron-electron correlations Evidence for Umklapp annihilation is discussed No observable differences are found between distributions from heavily doped and intrinsic germanium samples Differences in the angular distributions between 5 K and 300 K are attributed to positron thermal motion, and the results are analyzed by a new method to obtain an estimate of the positron effective mass

Theories and Principles of Viscosity

Abstract: Viscosity is a transport phenomenon. Viscosity is the transport of momentum due to a velocity gradient. The beginning of the phenomenological studies of viscosity goes back to the ancient Greeks and later the Romans characteristically applied what they had learned in practical ingenious ways [1]. Modern theories of viscosity of liquids are based on continuum mechanics and molecular theory.

An Experimental Study on Confluence of Two Two-Dimensional Jets

Abstract: An experimental study on the confluence of two two-dimensional incompressible turbulent jets, issuing from nozzles with angle θ0 against the nozzle exit plane, has been presented. The axial momentum and the energy flux of the jets along the z-axis perpendicular to the exit plane are calculated by using the measured values of velocity and pressure distributions. It has been shown that the axial momentum flux along the z-axis decreases owing to the confluence, that the energy flux also decreases remarkably owing to the confluence, that the energy flux also decreases remarkably owing to the confluence, and that the decreased values are approximately 40% of the efflux energy of the jet, independent of the ratio of a distance between two nozzles to the nozzle width and θ0. A method of predicting the velocity distribution also has been proposed. The predicted values agreed well with the experimental results.

Particle‐gas dispersion effects in confined coaxial jets

Abstract: The objective of this study was to determine the mixing characteristics of two-phase, confined, coaxial jets. Gas composition, gas velocity, and particle mass flux radial profiles were obtained at different axial stations using 20% by weight of 6 or 30 μm spherical aluminum particles in the primary stream. Additional tests were conducted without particles. Radial profiles for gas composition, velocity, and particle flux were correlated using the principle of similarity. In the gas phase, mass mixed more rapidly than momentum, and the 6 μm particles mixed less rapidly than mass or momentum. Systems with low primary density and low secondary velocity mixed most rapidly. An implicit numerical model was developed to predict the rate of mixing of the gas/particle mixture. The model included coupled dynamic and thermal nonequilibrium effects between the gas and solid phases. Comparisons of model predictions and experimental results were good.

Momentum deposition by heavy-ion bombardment and an application to sputtering

Abstract: The depth distribution of momentum deposited by heavy-ion bombardment of random targets has been calculated. A brief report is given on the transport equation governing deposited momentum and its solution via moment expansion, as well as the problem of constructing the momentum profiles from given moments. Two representative examples are shown, and from the results the mean velocities of sputtered atoms have been calculated. These are compared with experimental data from the literature. Momentum distributions are relevant to recoil implantation.

Addendum. Low-energy electron scattering by atomic oxygen

Abstract: Recently computed differential cross sections for elastic electron scattering from the ground state of oxygen have been used to compute momentum- transfer cross sections for energies 0.136less than or equal toE (eV) less than or equal to11.02. Leading terms from the threshold laws have been used to estimate the zero-temperature limits of the rate constants for deactivation by electron impact.

Pion inclusive momentum distribution at 90° in a hydrodynamical model

Abstract: We show that pion inclusive momentum distributions in pp collisions at 90$sup 0$ up to Fermilab and CERN-ISR energies can be accounted for by a hydrodynamical model which has frame-independence symmetry and incorporates the evaporation phenomena. Within our solution, during its space--time development, the matter system possesses only a local thermal equilibrium but not a global equilibrium. The proper time interval needed to achieve this equilibrium comes out to be comparable (with c = 1) to the longitudinal dimension estimated previously based on considerations of quantum statistical fluctuation. (AIP)

Use of the momentum approximation in classical scattering calculations

Abstract: The validity range of the momentum approximation in binary collisions : s investigated. It is shown that at high energies, E ≳ 10 · Z 1 Z 2 e 2/a TF, the approximation is even applicable to scattering angles ϑ as large as 60 degrees. An empirical formula for the evaluation of the momentum approximation employing the Thomas-Fermi-Moliere potential is given. It reduces the computer time to calculate ϑ to ∼⊥10 of the time consumed in using the standard algebraic functions appearing in the momentum approximation.

The influence of momentum advections on a well-mixed layer

Abstract: This study examines the influence of weak horizontal advections of momentum on a well-mixed planetary boundary layer. In the simple flow system examined, the direction and magnitude of flow modifications depend on the Rossby number, the nondimensional surface drag coefficient and the orientation of the geostrophic wind gradient field. It is found that advective modification of the boundary layer vertical motion field involves dependencies on the square of the local vorticity and dependencies on vorticity gradients. The mixed-layer assumptions are relaxed for a special flow case to show that these results do not depend crucially on the mixed-layer condition.