Showing papers on "Momentum published in 1974"

On the spectral dissipation of ocean waves due to white capping

Abstract: The effect of white capping on the spectral energy balance of surface waves is investigated by expressing the white-cap interactions in terms of an equivalent ensemble of random pressure pulses. It is shown first that the source function for any non-expansible interaction process which is weak-in-the-mean is quasi-linear. In the case of white capping, the damping coefficient is then shown to be proportional to the square of the frequency, provided the wave scales are large compared with the white-cap dimensions. The remaining free factor is determined indirectly from consideration of the spectral energy balance. The proposed white-capping dissipation function is consistent with the structure of the energy balance derived from JONSWAP, and the existence of a δ−5 spectrum governed by a non-local energy balance between the atmospheric input, the nonlinear energy transfer and dissipation. However, closure of the energy balance involves hypotheses regarding the structure of the atmospheric input function which need to be tested by further measurements. The proposed set of source functions may nevertheless be useful for numerical wave-prediction. According to the model, nearly all the momentum transferred across the air-sea interface enters the wave field. For fetchlimited and fully developed spectra in a stationary, uniform wind field, the drag coefficient remains approximately constant. However, for more general wind conditions, this will not be the case and the wave spectrum should be included in an accurate parameterisation of the air-sea momentum transfer.

Dynamics of extended bodies in general relativity. III. Equations of motion

Abstract: A study is made of the motion of an extended body in arbitrary gravitational and electromagnetic fields In a previous paper it was shown how to construct a set of reduced multipole moments of the charge-current vector for such a body This is now extended to a corresponding treatment of the energy-momentum tensor It is shown that, taken together, these two sets of moments have the following three properties First, they provide a full description of the body, in that they determine completely the energy-momentum tensor and charge-current vector from which they are constructed Secondly, they include the total charge, total momentum vector and total angular momentum (spin) tensor of the body Thirdly, the only restrictions on the moments, apart from certain symmetry and orthogonality conditions, are the equations of motion for the total momentum and spin, and the conservation of total charge The time dependence of the higher moments is arbitrary, since the process of reduction used to construct the moments has eliminated those contributions to these moments whose behaviour is determinate The uniqueness of the chosen set of moments is investigated, leading to the discovery of a set of properties which is sufficient to characterize them uniquely The equations of motion are first obtained in an exact form Under certain conditions, the contributions from the moments of sufficiently high order are seen to be negligible It is then convenient to make the multipole approximation, in which these high order terms are omitted When this is done, further simplifications can be made to the equations of motion It is shown that they take an especially simple form if use is made of the extension operator of Veblen & Thomas This is closely related to repeated covariant differentiation, but is more useful than that for present purposes By its use, an explicit form is given for the equations of motion to any desired multipole order It is shown that they agree with the corresponding Newtonian equations in the appropriate limit

On the Mass, Momentum, Energy and Circulation of a Solitary Wave. II

Abstract: By accurate calculation it is found that the speed $F$ of a solitary wave, as well as its mass, momentum and energy, attains a maximum value corresponding to a wave of less than the maximum amplitude. Hence for a given wave speed $F$ there can exist, when $F$ is near its maximum, two quite distinct solitary waves. The calculation is made possible, first, by the proof in an earlier paper ($I$) of some exact relations between the momentum and potential energy, which enable the coefficients in certain series to be checked and extended to a high order; secondly, by the introduction of a new parameter $\omega $ (related to the particle velocity at the wave crest) whose range is exactly known; and thirdly by the discovery that the series for the mass $M$ and potential energy $V$ in powers of $\omega $ can be accurately summed by Pade approximants. From these, the values of $F$ and of the wave height $\epsilon $ are determined accurately through the exact relations $3V=(F^{2}-1)M$ and $2\epsilon =(\omega +F^{2}-1$. The maximum wave height, as determined in this way, is $\epsilon \_{\max}$ = 0.827, in good agreement with the values found by Yamada (1957) and Lenau (1966), using completely different methods. The speed of the limiting wave is $F$ = 1.286. The maximum wave speed, however, is $F\_{\max}$ = 1.294, which corresponds to $\epsilon =0.790$. The relation between $\epsilon $ and $F$ is compared to the laboratory observations made by Daily & Stephan (1952), with reasonable agreement. An important application of our results is to the understanding of how waves break in shallow water. The discovery that the highest solitary wave is not the most energetic helps to explain the qualitative difference between plunging and spilling breakers, and to account for the marked intermittency which is characteristic of spilling breakers.

Computer simulation of transferred electron devices using the displaced Maxwellian approach

Abstract: Computer simulations of GaAs transferred electron devices have been performed by solving the time- and space-dependent Boltzmann equation and assuming displaced Maxwellian distributions for the two conduction band valleys. Since this model includes particle, momentum, and energy relaxation (as distinct from models using instantaneous velocity field dependence) and retains the spatial dependence (as distinct from uniform field models) it is particularly well suited for studying cases that are characterized by a strong x-dependence of electron temperature. Short devices as well as long ones operating at very high frequencies have been studied extensively, since these devices were thought and, in fact, have been found to be strongly affected by nonuniform energy relaxation due to contacts, domains, and other types of space charge. The results have been compared with experimental findings and with theoretical results computed by others.

Two-dimensional turbulence near the viscous limit

Abstract: Two-dimensional incompressible motion is generated by a steady external body force varying sinusoidally with a transverse co-ordinate. Such flow is found to be unstable for Reynolds numbers greater than 2½, and under these conditions evolves towards a new steady state. This ‘steady-eddy’ state is itself unstable in a sense, and its breakdown suggests the catastrophic onset of a cascade of turbulence. The mechanics of this cascade can be represented by a kind of recursion system in which the turbulence dynamics of one scale is repeated in the next, and a law of turbulent stress results. The spectrum of kinetic energy generated by a steady input of momentum at a discrete wavelength shows a rapid decrease (as k−5) towards shorter wavelengths but a much slower decrease (as k) towards longer wavelengths.

Effects of neutral injection heating upon toroidal equilibria

Abstract: Effects of neutral beam injection upon the equilibrium of a toroidal plasma are considered. The distribution function of energetic ions produced by the beam in the plasma is calculated for injection both parallel and perpendicular to the magnetic field taking account of effects due to the toroidal geometry. The effect of trapped particles on the current induced in the plasma by such a beam is calculated, together with the associated cross-field diffusion. Loss mechanisms for the momentum deposited in the plasma by the neutral beam are considered. Ripples in the toroidal magnetic field strength are particularly efficient at destroying toroidal momentum and lead to flow velocities much less than the sound speed for typical injection parameters.

Driving force in electromigration

Abstract: The driving force in electromigration is generally assumed to consist of a "direct force" due to the applied field and an "electron-wind" term due to momentum exchange with the current carriers. In the case of the "direct force" it is uncertain how effectively the charge is screened. In the case of the "electron wind" it is unclear whether the moving atom senses the carrier's change in lattice momentum or real momentum. A method first utilized by Bosvieux and Friedel, and expanded by Sorbello, resolves these problems by calculating driving forces on the unscreened ion resulting from the nonuniformities in spatial carrier distribution. These theories depend, however, on an incomplete picture of the spatial variations in the electric field, which inevitably accompany current flow past localized scatterers. Furthermore, "screening" of the charge of a lattice defect is related to inhomogeneities in carrier density and the resulting spatial inhomogeneity in the rate of current production which a uniform field would provide. Terms of this latter sort have never received explicit consideration.

Total Cross Sections of p and p ¯ on Protons and Deuterons between 50 and 200 GeV/ c

Abstract: Proton and antiproton total cross sections on protons and deuterons have been measured at 50, 100, 150, and 200 GeV/c. The proton cross sections rise with increasing momentum. Antiproton cross sections fall with increasing momentum, but the rate of fall decreases between 50 and 150 GeV/c, and from 150 to 200 GeV/c there is little change in cross section.

Chromospheric Fine Structure

Abstract: The mechanical (nonradiative) energy that is responsible for the solar chromosphere and corona is generated in the subphotospheric layers and propagates into the outer layers where it is dissipated. The propagating energy probably carries momentum as well as energy. Also, because the energy source is mechanical it is expected to be associated with temporal and spatial fluctuations of physical variables. It is logical to assume, therefore, that the transport of mechanical energy and momentum will produce local fluctuations in intensity and velocity and possibly in magnetic field strength. Solar fine structure, at least in part, is the observational manifestation of such processes. The dissipation process, of course, may involve intermediate phenomena that influence the fine structure, and, in turn, the fine structure undoubtedly influences the energy propagation. In any case, the nature of the propagating energy and its dissipation is undoubtedly imprinted in the fine structure.

Generalized oscillator strengths for 7.4 eV excitation of H2O at 300, 400, and 500 eV kinetic energy. Singlet‐triplet energy differences

Abstract: Generalized oscillator strengths f have been determined as a function of scattering angle for the 7.4 eV excitation of H2O vapor by studying the scattering of electrons with kinetic energies of 300, 400, and 500 eV. Over the angle range studied, 2°–7°, f vs (ΔP)2 (ΔP the momentum change) lie approximately on a common curve at all three kinetic energies. Extrapolation to zero momentum change gives the value f0 =0.060±0.006 for the limiting oscillator strength. Singlet‐triplet energy differences are calculated using the generalized oscillator strengths and a recently developed theory by Lassettre and Dillon.

Compton profile and electron momentum distribution of water

Abstract: The Compton profile and electron momentum distribution of water have been calculated using a number of self‐consistent‐field wavefunctions of various types, including a near Hartree‐Fock function. The results are found to be sensitive to the choice of basis functions. Comparison with recent experimental data shows good agreement, with the effects of improved wavefunction quality paralleling those of certain experimental corrections.

Classical-particle description of photons and phonons

Abstract: An $\ensuremath{\hbar}$-free analogy-free synthesis of classical mechanics and geometrical optics (acoustics) is presented which embraces without distinction particles of both zero and finite rest energy. The point-particle Lagrangian and other classical-particle properties of a photon (corpuscle) in gallium phosphide are found explicitly. Further brief applications are given to Newtonian mechanics, relativistic particle dynamics, fluid-immersed-body dynamics, hole-electron recombination in semiconductors, electrostatic and magnetic lenses, standardization of particle-flux units, and the still-controversial question of optical and acoustical radiation pressure and momentum.

Localized molecular orbital studies in momentum space. I. compton profiles of 1s core electrons and hydrocarbons

Abstract: The calculations of momentum space properties for the polyatomic molecules CH 4 , C 2 H 4 and C 2 H 6 using localized molecular orbitals of double zeta quality basis sets are presented. The LMO analysis shows that localized and canonical core electrons have different momentum space properties, and that in agreement with the experimental data of Eisenberger and Marra one can distinguish the momentum properties of the CC single and double bonds. The effect of environment on a bond is seen by comparing the CH bond in these three molecules. The concept of electron pair size is introduced as a quantitative guide for interpreting momentun space properties.

The stopping power of solids for low-velocity channelled heavy ions

Abstract: A model of the stopping of a low-velocity heavy ion moving through an electron gas is used to calculate the stopping power of solids for channelled heavy ions. The heavy ion is considered to lose energy by transferring momentum to target electrons which scatter elastically from it, so that the stopping cross section is proportional to the momentum-transfer cross section. This cross section varies periodically with the Z1 of the incident ion, the periodicity being shown to be connected with the successive filling of atomic sub-shells of electrons. The model is applied to the stopping power of silicon for ions channelled along the (110) and (111) directions and good agreement is obtained with the data of Eisen. A feature of this approach is the reproduction of deep minima in channelled stopping power in certain regions of the periodic table.

Kinetic theory of polyatomic liquids. I. The generalized moment method

Abstract: It is demonstrated that one can successfully generalize the moment method of dilute gas kinetic theory to a dense fluid composed of polyatomic molecules. The basic premise of the theory is Bogoliubov's assumption of the existence of a functional relationship between the pair and singlet distribution functions. The theory is rendered explicit by selecting for this functional the generalization to polyatomic fluids of a relationship first obtained by Severne and subsequently modified and generalized by Prigogine, Nicolis, and Misguich and by Davis. This leads to a closed set of approximate moment equations from which are extracted explicit, computationally tractable formulas for the characteristic relaxation times and frequency dependent transport coefficients associated with the transport of momentum, energy, and molecular internal angular momentum or spin.

Collisional coupling in counterstreaming laser-produced plasmas

Abstract: The collisional processes which transfer momentum between counterstreaming plasmas are reviewed and applied to the example of a laser‐produced plasma expanding into a partially ionized background. Experimental measurements of the dependence of the ion flow field on collisional momentum transfer demonstrate the validity of the simplified treatment of collision processes which have been adopted. A numerical model which simulates the laser‐plasma interaction with the background confirms the importance of collisions in previous experimental studies of momentum coupling, and provides some insight into the distinction between collisional and collisionless flow regimes.

The momentum spectra of nuclear active particles in the cosmic radiation at sea level. I. Experimental data

Abstract: A cosmic ray spectrograph has been used to measure the momentum spectra of cosmic ray protons and pions in the momentum range 1-30 GeV/c in the near vertical direction at sea level. The observed intensities of both protons and pions are greater than those obtained in the previous measurements.