Showing papers on "Momentum published in 1979"
TL;DR: In this paper, the authors studied the dynamics of lift and thrust generation by flying animals by considering the distribution of vorticity in the wake of flying animals, and derived the induced power as the rate of increase of wake kinetic energy.
Abstract: The mechanics of lift and thrust generation by flying animals are studied by considering the distribution of vorticity in the wake As wake generation is not continuous, the momentum jet theory, which has previously been used, is not satisfactory, and the vortex theory is a more realistic model The vorticity shed by the wings in the course of each powered stroke deforms into a small-cored vortex ring; the wake is a chain of such rings The momentum of each ring sustains and propels the animal; induced power is calculated as the rate of increase of wake kinetic energy A further advantage of the vortex theory is that lift and induced drag coefficients are not required; estimated instantaneous values of these coefficients are generally too large for steady state aerodynamic theory to be appropriate to natural flapping flight The vortex theory is applied to hovering of insects and to avian forward flight A simple expression for induced power in hovering is found Induced power is always greater than simple momentum jet estimates, and the discrepancy becomes substantial as body mass increases In hovering the wake is composed of a stack of horizontal, coaxial, circular vortex rings In forward flight of birds the rings are elliptic; they are neither horizontal nor coaxial because the momentum of each ring balances the vector sum of parasite and profile drag and the bird9s weight Total power consumption as a function of flight velocity is calculated and compared for several species Power reduction is one of the major factors influencing the choice of flight style A large body of data is used to obtain an approximate scaling between stroke period and the body mass for birds Together with relations between other morphological parameters, this is used to estimate the variation of flight speed and power with body mass for birds, and on this basis deviations from allometric scaling can be related to flight proficiency and to the use of such strategies as the bounding flight of small passerines Note: Present address: Department of Zoology, University of Bristol, Woodland Road, Bristol BS8 IUG, UK
332 citations
TL;DR: In this article, the authors model the wake of a hovering bird or insect as a chain of coaxial small-cored circular vortex rings stacked one upon another; each member of the chain is generated by a single wingstroke.
Abstract: The distribution of vorticity in the wake of a hovering bird or insect is considered. The wake is modelled by a chain of coaxial small-cored circular vortex rings stacked one upon another; each member of the chain is generated by a single wing-stroke. Circulation is determined by the animal's weight and the time for which a single ring must provide lift; ring size is calculated from the circulation distribution on the animal's wing. The theory is equally applicable to birds and insects, although the mechanism of ring formation differs. This approach avoids the use of lift and drag coefficients and is not bound by the constraints of steady-state aerodynamics; it gives a wake configuration in agreement with experimental observations. The classical momentum jet approach has steady momentum flux in the wake, and is difficult to relate to the wing motions of a hovering bird or insect; the vortex wake can be related to the momentum jet, but adjacent vortex elements are disjoint and momentum flux is periodic.The evolution of the wake starting from rest is considered by releasing vortex rings at appropriate time intervals and allowing them to interact in their own velocity fields. The resulting configuration depends on the feathering parameter f (which depends on the animal's morphology); f increases with body size. At the lower end of the wake rings coalesce to form a single large vortex, which breaks away from the rest of the wake at intervals. Wake contraction depends on f; the minimum areal contraction of one-half (as in momentum-jet theory) occurs only in the limit f → 0, but values calculated for smaller insects of just over one-half suggest that the momentum jet may be a good approximation to the wake when f is small.Induced power in hovering is calculated as the limit of the mean rate of increase of wake kinetic energy as time progresses. It can be related to the classical momentum-jet induced power by a simple conversion factor. For an insect or hummingbird the usual momentum-jet estimate may be between 10 and 15% too low, but for a bird it may be as much as 50% too low. This suggests that few, if any, birds are able to sustain aerobic hovering, and that as small a value of f as possible would be necessary if the bird were to hover.Tip losses (energy cost of the vortex-ring wake compared with the equivalent momentum jet) are negligible for insects, but can be in the range 15–20% for birds.
212 citations
TL;DR: In this article, absolute differential cross sections have been obtained using the split-field magnet detector facility (SFM) at the five standard energies for integrated luminosities ranging from 0.3 to 4.9 (pb) −1.
122 citations
TL;DR: In this paper, a projected self-scattering formulation was proposed for describing transport in submicron semiconducting devices in the finite collision duration regime, which is nonlocal in time and momentum.
Abstract: Quantum kinetic equations for describing transport in submicron semiconducting devices in the finite collision duration regime are developed which are nonlocal in time and momentum. Utilizing a projected self-scattering formulation, a retarded path-integral equation is obtained. Quantum kinetic equations are usually exceedingly difficult to solve. The formulation found here presents a powerful technique to achieve these solutions even in the case where nonlocal effects are important.
116 citations
15 Aug 1979
TL;DR: In this paper, the Fourier transform of the electron momentum density (B(r) is examined and a number of theoretical results relating to this new observable are given, and a wave-mechanical representation with (natural) orbitals is employed for the subsequent analysis of B(r).
Abstract: Recent work has shown that the one-dimensional projection of the electron momentum density, the Compton profile, can be usefully interpreted as a position space quantity. This has led to an examination of B(r), the Fourier transform of the momentum density. A number of theoretical results relating to this new observable are given. The wave-mechanical representation with (natural) orbitals is employed, and this forms the basis for the subsequent analysis of B(r). The relationship of B(r) to overlap integrals and more generally to other electron density functions is considered. Atomic wavefunctions for krypton are used to illustrate the potential of this new approach to the analysis of momentum density data. General expressions are derived for atoms and molecules, and the radial and angular dependence of B(r) for various orbitals is displayed. The possibility of extracting accurate bond lengths from B(r) is assessed, and an example is given using some recent theoretical data for the fluorine molecule.
113 citations
TL;DR: In this article, a study of large amplitude, progressive interfacial waves moving between two infinite fluids of different densities was carried out and it was shown that the maximum height of a Boussinesq wave, which has the density almost the same above and below the interface, is 2·5 times higher than a surface wave of the same wavelength.
Abstract: This paper contains a study of large amplitude, progressive interfacial waves moving between two infinite fluids of different densities. The highest wave has been calculated using the criterion that it has zero horizontal fluid velocity at the interface in a frame moving at the phase speed of the waves. For free surface waves this criterion is identical to the criterion due to Stokes, namely that there is a stagnation point at the crest of each wave. I t is found that as the density of the upper fluid increases relative to the density of the lower fluid the maximum height of the wave, for fixed wavelength, increases. The maximum height of a Boussinesq wave, which has the density almost the same above and below the interface, is 2·5 times the maximum height of a surface wave of the same wavelength. A wave with air over the top of it can be about 2% higher than the highest free surface wave. The point at which the limiting criterion is first satisfied moves from the crest for free surface waves to the point half-way between the crest and the trough for Boussinesq waves. The phase speed, momentum, energy and other wave properties are calculated for waves up to the highest using Pade approximants. For free surface waves and waves with air above the interface the maximum value of these properties occurs for waves which are lower than the highest. For Boussinesq waves and waves with the density of the upper fluid onetenth of the density of the lower fluid these properties each increase monotonically with the wave height.
99 citations
TL;DR: In this paper, a finite-difference form of two-dimensional equations for the conservation of mass, momentum, energy, turbulence energy, and dissipation rate with algebraic expressions for the turbulent viscosity and heat diffusivity is presented.
Abstract: Calculations of velocity and temperature distributions in rooms with ventilation arrangements are reported. The method involves the solution, in finite-difference form, of two-dimensional equations for the conservation of mass, momentum, energy, turbulence energy, and dissipation rate, with algebraic expressions for the turbulent viscosity and heat diffusivity. The results are shown to be in reasonable agreement with available experimental data and the method is then applied to provide additional information useful for design purposes.
93 citations
01 Aug 1979
TL;DR: In this paper, the authors reviewed the Kelvin-Helmholtz instability as it applies to the dayside magnetopause and showed that the boundary should generally be unstable to waves moving at a large angle to the Earth's field.
Abstract: The Kelvin-Helmholtz instability as it applies to the dayside magnetopause is reviewed. Simple theory suggests the boundary should generally be unstable to waves moving at a large angle to the Earth's field. Nonlinear effects, how amplitudes might be limited, and what dynamic role the instability could have in boundary regions in stimulating mass and momentum transfer are discussed. Examination of data from a particular ISEE spacecraft pass shows relatively small amplitude (750 km) waves present on the boundary. Corresponding wavelength estimates show wave momentum is not significant at the time of the pass.
83 citations
TL;DR: In this article, a mathematical model for the prediction of spreading and rising of submerged round buoyant jets discharged into a stratified, flowing ambient fluid is presented, based on the differential equations for the conservation of mass, momentum, concentration and thermal energy.
83 citations
15 Jan 1979
TL;DR: In this article, a computer model for an arbitrary array of turbines is described, where the turbine wake expands downstream due to ambient turbulence and mechanically generated turbulence and entrains momentum and mass.
Abstract: Determination of power degradation due to interference between wind turbines in an array is of importance in the engineering and economic planning of wind farms. A computer model for an arbitrary array of turbines is described. The basic fluid mechanics are treated in a simple but rational way. The turbine wake expands downstream due to ambient turbulence and mechanically generated turbulence (caused by momentum gradients) and entrains momentum and mass. Drag or momentum deficit, though, is conserved. Ground effect is handled by imaging. The effect of ambient turbulence is shown to be much greater than of that due to the momentum deficit generated by the turbine. The basic equations use fundamental fluid mechanical expressions related to drag conservation and wake growth due to turbulent entrainment and a family of self-similar wake profiles derived from experiment. This approach fully defines the wake velocity field. The wake of each turbine is then determined, subject to all upstream interferences. Power outputs of selected arrays as functions of wind direction are presented. The model is very well supported by the limited data available, and has proven effective and easy to implement. Advanced models incorporating nonuniformities in wind and turbulence and tower shadow are also described.
79 citations
TL;DR: The electron momentum distribution for molecular hydrogen is calculated from an explicitly correlated Gaussian wave function corresponding to the total energy of -1.174 42 a.u. and accounting for 99.9% of the correlation energy as discussed by the authors.
Abstract: The electron momentum distribution for molecular hydrogen is calculated from an explicitly correlated Gaussian wave function corresponding to the total energy of -1.174 42 a.u. and accounting for 99.9% of the correlation energy. The high-accuracy Compton profile obtained confirms the results of recent high-energy electron-impact spectroscopy measurements of Lee, but disagrees in the region of very small momentum with earlier x-ray Compton-scattering data.
TL;DR: In this paper, the dependence of the Pomeron term on the momentum transfer is taken from a modified version of the relation between matter distribution and charge distribution, and a simple nontrivial form is used for the hadronic-matter current in the proton.
Abstract: We improve significantly the impact picture that was used several years ago to predict the increase of total and integrated differential cross sections at high energies. The major improvements consist of the following: (1) The dependence of the Pomeron term on the momentum transfer is taken from a modified version of the relation between matter distribution and charge distribution, (2) Regge backgrounds are properly taken into account, and (3) a simple nontrivial form is used for the hadronic-matter current in the proton. For proton-proton elastic scattering, the phenomenological differential cross section is in good agreement with the experimental data in the laboratory momentum range of 14 to 2000 GeV/c, and is predicted for ISABELLE energy. Because of the third improvement, predictions are obtained for both polarization and $R$ parameters for proton-proton elastic scattering.
TL;DR: In this article, a comparison between four spectroscopies of solids revealing the range of energies and wave vectors accessible to each of them is presented. But it is impossible to independently vary the energy and momentum of a photon, as Maxwell's equations fix one once the other is known.
Abstract: Publisher Summary Spectroscopy, in one form or another, plays a key role in the evolution of modern physics-optical spectroscopy and atomic physics being the canonical example. One studies the energy dependence of the emission or absorption of some kind of particle or field by a selected sample material. This energy dependence reveals dynamical information about the sample. The most successful kinds of spectroscopy are those in which the particle and sample interact only weakly, because then the dynamical information is characteristic of the unperturbed sample. The chapter provides a comparison between four spectroscopies of solids revealing the range of energies and wave vectors accessible to each. The diagonal line represents optical absorption. It is impossible to independently vary the energy and momentum of a photon, as Maxwell's equations fix one once the other is known. Therefore, any excitation in a solid that is created by absorption of a photon must lie on the line shown. A beam of particles is incident on the sample and scatters through some angle, losing certain energy. If multiple scattering is not a problem, then the energy lost and momentum transferred in the sample are ascribed to the creation of a single excitation. By varying the scattering angle and the energy loss, an entire region in energy-momentum space is studied.
TL;DR: In this article, states of 12 Λ C formed in the (K −, π − ) reaction have been studied for momentum transfers up to 260 MeV/c, using an incident K − beam of 800 MeV /c momentum.
TL;DR: In this paper, the Navier-Stokes equations are generalized over the usual two-dimensional and axisymmetric formulation by allowing nonzero velocity components in the invariant direction.
Abstract: NUMERICAL solutions have been obtained for a twodimensional azimuthal- (or circumferentially) invariant form of the thin-layer Navier-Stokes equations. The governing equations which have been developed are generalized over the usual two-dimensional and axisymmetric formulation by allowing nonzero velocity components in the invariant direction. The equation formulation along with the solution method is described, and results for spinning and nonspinning bodies are presented. Contents The three-dimensional flow field equations are frequently simplified for flowfields which are invariant in one coordinate direction. In the usual axisymmetric approximation, the azimuthal velocity is assumed to be zero, and the momentum equation in that direction can be eliminated. Thus, only four equations are required to be solved for four unknowns. However, for a variety of interesting flowfields, the velocity component in the invariant direction (here taken as TJ) is not zero although the governing equations are still twodimensional. Examples include viscous flow about an infinitely swept wing, the viscous flow about a spinning axisymmetric body at 0-deg angle of attack, and axisymmetric swirl flows. Each of these flows can be solved as a twodimensional problem although all three momentum equations have to be retained, and source terms replace the derivative of the flux terms in the rj-direction. Azimuthal-invariant equations are obtained from the threedimensional equations1 by making use of two restrictions: 1) all body geometries are of axisymmetric types and 2) the state variables and the contravariant velocities do not vary in the azimuthal direction. Here, TJ is used for the azimuthal coordinate, and the terms azimuthal and rj-invariant will be used interchangeably. A sketch of a typical axisymmetric body is shown in Fig. la. In order to determine the circumferential variation of typical flow and geometric parameters, we first establish correspondence between the
TL;DR: In this paper, a Lagrangian type of MHD code was developed by treating elements of the fluid as finite-sized particles, i.e., position, mass, momentum and temperature, while the magnetic fields are advanced in an Eulerian manner.
TL;DR: In this article, the authors report a theroetical prediction of a new feature in the spectrum of light scattered from a fluid in a nonequilibrium stationary state with a temperature gradient.
Abstract: We report a theroetical prediction of a new feature in the spectrum of light scattered from a fluid in a nonequilibrium stationary state with a temperature gradient. The spectrum is not symmetric in the frequency shift and the Brillouin components have different intensities. The phenomenon is linked to the breaking of time-reversal symmetry and to the appearance of a static correlation function between momentum and number densities which is zero in equilibrium, but has a $\frac{1}{{k}^{2}}$ dependence in the stationary state. We suggest a light scattering experiment by means of which these predictions can be verified.
TL;DR: In this paper, pressure drop and choking were calculated for dense-phase vertical pneumatic conveying of solids using a model employing two continuity and two momentum equations, and the calculated pressure drops and choking velocities were found to be in good agreement with IGT high-pressure lift-line experiments.
TL;DR: In this paper, a new economical finite-difference method is described for the calculation of three-dimensional heated surface jets discharging into stagnant water, where the equations solved are for continuity, lateral and longitudinal momentum, and thermal energy.
Abstract: A new economical finite-difference method is described for the calculation of three-dimensional heated surface jets discharging into stagnant water. The equations solved are for continuity, lateral and longitudinal momentum, and thermal energy. The turbulent shear stresses and heat fluxes in these equations are determined with a turbulence model involving simplified forms of the transport equations for these stresses and fluxes and the solution of differential transport equations for the turbulent kinetic energy κ and the rate of its dissipation e. The experimentally observed entrainment reduction due to buoyancy is reproduced by this model. The predictions are compared in detail with the recent measurements of Pande & Rajaratnam, which are judged to be superior to those of other investigators. The agreement is generally satisfactory.
TL;DR: In this article, the current and voltage profiles of electron flows from their momentum distributions were derived and the potential difference across the flow can usually be found from the line-current measurements.
Abstract: Equations are derived for finding the current and voltage profiles of electron flows from their momentum distributions It is found that many of the features of the flow are independent or quasi‐independent of the distribution functions For this reason, it is concluded that the potential difference across the flow can usually be found from the line‐current measurements
TL;DR: In this paper, a consistent approach to the problem of axial meson exchange currents (MEC) was developed, which incorporates the current algebra and PCAC together with the vector dominance and allows one to study the pion as well as heavy meson exchanges on an equal footing.
TL;DR: In this paper, a relativistic Uehling-Uhlenbeck equation, free of convective terms, is derived for the temporal evolution of the hadronic momentum distributions and a statistical solution method is developed.
TL;DR: In this paper, a hard-scattering mechanism was proposed to describe proton and pion spectra from high-energy nuclear collisions, using free nucleon-nucleon cross sections and the empirical momentum distribution for nucleons within the nuclei.
TL;DR: In this paper, the authors compared the electric field gauge with the radiation gauge and other "simple" gauges for problems where intense-field and/or relativistic effects are significant.
Abstract: The properties of the electric field gauge are compared with the radiation gauge and other "simple" gauges for problems where intense-field and/or relativistic effects are significant. Electromagnetic shifts in free-electron mass and momentum, which can be of major importance in both kinematics and dynamics when the field is intense, and which are clearly in evidence in second-order radiation-gauge formulations, do not appear in the electric field gauge in any finite order of perturbation theory. Intense-field expressions like the closed-form Volkov solution, and mass and momentum intensity parameters, are shown to be invariant in form in "simple" gauges, but find no natural expression in the electric field gauge. It is also shown that intensity effects introduce strongly spin-coupled terms even in nonrelativistic problems. For both charged and neutral bound-state systems, "crossed" vector-potential terms occur in electric field gauge which prevent separation of the Schr\"odinger equation into center-of-mass and relative-coordinate equations when the field intensity is high. This difficulty does not arise in the radiation gauge. These considerations inhibit the use of electric field gauge in intense-field problems.
TL;DR: In this article, the response of axisymmetric toroidal tokamak plasma to first-order particle and momentum sources is investigated, and a generalized Ohm's law is obtained and used to determine how particle sources drive parallel currents and alter the evolution of the q profile.
Abstract: The response of an axisymmetric toroidal tokamak plasma to first‐order particle and momentum sources is investigated. The momentum sources drive coupled poloidal and toroidal mass flows and electrostatic field evolution which relax to asymptotic values on a time scale characteristic of the dominant viscous or external drag mechanism. The asymptotic steady‐state momentum balance provides the necessary condition to completely determine the ambipolar potential, the particle fluxes, and currents in the flux surfaces and, hence, to determine transport fluxes across flux surfaces. Transport fluxes are driven across flux surfaces both by interspecies collisional momentum exchange, the usual case, and by momentum exchange between the plasma and external sources and/or drags. A generalized Ohm’s law is obtained and used to determine how particle and momentum sources drive parallel currents and alter the evolution of the q profile. The theory is formulated for arbitrary plasma cross sections, beta, and collision regimes.
TL;DR: In this paper, the authors obtained the acceleration, momentum and angular momentum for two gravitating particles to the first order in G. As "criterial" conditions for the determination of the acceleration they used the Lorentz invariant equations obtained by Havas and Goldberg, (1962).
Abstract: Following the method developed by Bel, Salas and Sanchez Ron (1973) to solve the equations of predictive mechanics, and the method by Bel and Martin (1975) to obtain the momentum and angular momentum of a system of particles, the author obtains the accelerations, momentum and angular momentum for two gravitating particles to the first order in G. As 'criterial' conditions for the determination of the acceleration he has used the Lorentz invariant equations obtained by Havas and Goldberg, (1962).
TL;DR: In this article, the authors derived a unified way from a generalization of Kotchine's theorem which includes explicitly surface sources for momentum and energy, and other boundary conditions required to obtain the full solution to a liquid-vapour flow problem.
Abstract: The principles of conservation of mass, momentum, and energy require that certain relationships between the flow fields be satisfied at a liquid-vapor interface. These relationships are derived in a unified way from a generalization of Kotchine's theorem which includes explicitly surface sources for momentum and energy. The case of a multi-component mixture is also considered. Finally, other boundary conditions required to obtain the full solution to a liquid-vapour flow problem are outlined and discussed. Our results are applicable to other fluid-fluid interfaces as well.
TL;DR: In this article, a quantum-mechanical description of the double-scattering mechanism for charge transfer is given, showing that at asymptotically high collision velocities, the total cross-section of charge transfer via this double scattering mechanism exhibits the same nu -11 decrease as the classical cross section of Thomas.
Abstract: In 1927 Thomas suggested a classical mechanism of charge transfer whereby the attachment of a target electron to an incident ion is facilitated by the recoil of a second target electron. This second electron recoils with the speed of the incident ion in a direction perpendicular to the ion direction. A quantum-mechanical description of this process is given. The cross section for charge transfer, differential in the electron recoil momentum, is shown to peak when the classical Thomas scattering conditions are satisfied. At asymptotically high collision velocities nu , the total cross section for charge transfer via this double-scattering mechanism exhibits the same nu -11 decrease as the classical cross section of Thomas.
TL;DR: In this paper, the suprathermal drag force and motion of electrons in momentum space are analyzed for a multi-component plasma. And the acceleration and slowing-down of runaways are also briefly discussed.
Abstract: The suprathermal drag force and the motion of suprathermal electrons in momentum space are analysed for a multi-component plasma. The calculations of the particle motion are based on the suprathermal Fokker-Planck equation and include relativistic effects. It is found that, owing to pitch angle scattering, the flow patterns in momentum space are more complicated than previously assumed. Simple expressions for the runaway threshold and the perpendicular momentum of relativistic runaways are derived. The acceleration and slowing-down of runaways are also briefly discussed.
TL;DR: In this paper, it was shown that the electron propagator in the first approximation of the Johnson-Baker-Willey scheme has complex branch-points in the momentum variable, instead of the real branch-point that physics requires.