Showing papers on "Momentum published in 1976"
TL;DR: In this paper, a fluid dynamical treatment of an ultra-relativistic spherical blast wave enclosed by a strong shock is presented, and a simple similarity solution describing the explosion of a fixed amount of energy in a uniform medium is derived, and generalized to include cases in which power is supplied by a central source and the density of the external medium varies with radius.
Abstract: A fluid dynamical treatment of an ultra‐relativistic spherical blast wave enclosed by a strong shock is presented. A simple similarity solution describing the explosion of a fixed amount of energy in a uniform medium is derived, and this is generalized to include cases in which power is supplied by a central source and the density of the external medium varies with radius. Radiative shocks, in which the escaping photons carry away momentum as well as energy, are also discussed. Formulas that interpolate between the non‐ and ultra‐relativistic limits are proposed.
1,164 citations
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01 May 1976
TL;DR: Momentum, energy, and mass transfer in continua, Momentum and energy, mass transfer and energy transfer in continuous continua, this paper,...,.
Abstract: Momentum, energy, and mass transfer in continua , Momentum, energy, and mass transfer in continua , دانشگاه تهران
611 citations
TL;DR: In this article, the Schwinger-Dyson equation of the fermion propagator in the massless vector theory is discussed and it is found that the Baker-Johnson-Willey solution in lowest approximation is in fact a confining solution.
164 citations
TL;DR: In this paper, a technique of local averaging is applied to obtain general equations which describe mass and momentum transport in porous media, without significantly idealizing either the porous medium or the pertinent fluid mechanical relations.
Abstract: A technique of local averaging is applied to obtain general equations which describe mass and momentum transport in porous media. The averaging is performed without significantly idealizing either the porous medium or the pertinent fluid mechanical relations. The resulting general flow equation is simplified to treat flow of a Newtonian fluid in a slowly deforming solid matrix for two special cases. For flow in an isotropic medium where convective and inertial terms are important, an equation is developed which is dependent only on five medium parameters which could be evaluated by experiment. Flow in an anisotropic medium is also analyzed, and the general equation is reduced to Darcy's law when the convective and inertial terms are neglected.
159 citations
TL;DR: In this paper, a numerical model for the flow in a deep turbulent boundary layer over water waves is proposed, where the momentum equations are closed by the use of an isotropic eddy viscosity and the turbulent energy equation.
Abstract: A numerical model is proposed for the flow in a deep turbulent boundary layer over water waves. The momentum equations are closed by the use of an isotropic eddy viscosity and the turbulent energy equation. For small amplitudes the results are similar to those of Townsend's (1972) linear model, but nonlinear effects become important as the ratio of wave height to wavelength increases. With uniform surface roughness zo, the predicted fractional rate of energy input per radian advance in phase, ζ, decreases slightly with increasing amplitude and is of the same order of magnitude as in Miles’ (1957, 1959) and Townsend's linear theories. If zo is allowed to vary with position along the wave, however, the fractional rate of energy input can be significantly increased for small amplitude waves. If the variation in zo is half the mean value and the maximum wave slope zak is 0.01, we find ζ ≈ 60 (ρair/ρwater) (uo/c)2, where uo is the friction velocity and c the wave phase speed. Comparison is also made with recent laboratory and field data.
154 citations
TL;DR: In this paper, the conservation equations for one-dimensional two-phase flow are derived from first principles and the effects of the radial distributions of velocities, enthalpies, and void fraction are taken into account through the use of correlation coefficients.
118 citations
TL;DR: In this paper, a phenomenological model with "planar spin" and "antiferromagnetic" dynamics is introduced, and their critical behavior is analyzed using renomalization-group methods.
Abstract: Phenomenological models with "planar-spin" and "antiferromagnetic" dynamics are introduced, and their critical behavior is analyzed using renomalization-group methods. Dynamic scaling is shown to hold for these models to all orders in $\ensuremath{\epsilon}=4\ensuremath{-}d$, and the dynamic exponents are expressed entirely in terms of static exponents, in agreement with earlier phenomenological and mode-coupling theories. The magnitudes of the diverging transport and kinetic coefficients are expressed purely in terms of static properties and of universal constants which are calculated to second order in $\ensuremath{\epsilon}$. Matching conditions are proved between the characteristic frequencies above and below ${T}_{c}$, and the corresponding universal amplitude ratios are calculated to second order in $\ensuremath{\epsilon}$. The principal applications are to liquid helium and the Heisenberg antiferromagnet RbMn${\mathrm{F}}_{3}$, where the experimental exponents and amplitudes both agree reasonably well with theory. In the case of liquid helium ("asymmetric" case with $\ensuremath{\alpha}l0$) the asymptotic critical behavior is somewhat masked by correction terms, due to the slow approach of the spectific heat to its finite value at ${T}_{\ensuremath{\lambda}}$. These correction terms are analyzed in detail, and a proposal is made for extracting the true asymptotic behavior from the data. The effects of other conserved fields such as the mass density and momentum in helium, and the energy density in the magnet, are considered, and shown to be irrelevant for the critical behavior of the order parameter.
111 citations
TL;DR: In this article, the interaction between short internal gravity waves and a larger-scale mean flow in the ocean is analyzed in the Wkbj approximation, and the vertical viscosity coefficient is found to be vv [ape ] 4 x 103cm2/s and exceeds values typically used in models of general circulation by at least two orders of magnitude.
Abstract: The interaction between short internal gravity waves and a larger-scale mean flow in the ocean is analysed in the Wkbj approximation. The wave field determines the radiation-stress term in the momentum equation of the mean flow and a similar term in the buoyancy equation. The mean flow affects the propagation characteristics of the wave field. This cross-coupling is treated as a small perturbation. When relaxation effects within the wave field are considered, the mean flow induces a modulation of the wave field which is a linear functional of the spatial gradients of the mean current velocity. The effect that this modulation itself has on the mean flow can be reduced to the addition of diffusion terms to the equations for the mass and momentum balance of the mean flow. However, there is no vertical diffusion of mass and other passive properties. The diffusion coefficients depend on the frequency spectrum and the relaxation time of the internal-wave field and can be evaluated analytically. The vertical viscosity coefficient is found to be vv [ape ] 4 x 103cm2/s and exceeds values typically used in models of the general circulation by at least two orders of magnitude.
103 citations
CERN1
TL;DR: In this article, the authors study subasymptotic hadron target and quark-parton mass corrections to scaling in deep inelastic scattering, ignoring interactions, using a modified scaling variable common to parton, light-cone and short-distance operator product expansion formalisms, with model-dependent spectral conditions.
102 citations
TL;DR: In this article, the effect of toroidal geometry on the slowing-down of fast ions in a tokamak plasma is considered, and an appropriate bounce-averaged Fokker-Planck equation which includes particle trapping in the toroidal field gradient is derived.
Abstract: The effect of toroidal geometry upon the slowing-down of fast ions in a tokamak plasma is considered. An appropriate bounce-averaged Fokker-Planck equation which includes particle trapping in the toroidal field gradient is derived. The equation is solved by expressing the solution in terms of a series of 'finite-geometry' eigenfunctions. This solution is then used to show that the trapping of the fast ions in the toroidal field gradient reduces the fast-ion current by terms of order (r/R)½. The radial transport of the fast ions as they slow down is calculated, and it is found that for counter-injection (co-injection) the ions diffuse outwards (inwards) by approximately a fast-ion banana width. The diffusion is accompanied by a loss of fast-ion toroidal momentum and a consequent reduction in the momentum transferred to the background plasma.
100 citations
TL;DR: In this article, a numerical method is presented for calculating the transient flow of a homogeneous two-phase (gas-liquid) fluid at small Mach numbers and is applicable in one, two, or three space dimensions.
TL;DR: In this paper, it was shown that neither Minkowski's result, according to which the ratio of momentum to energy for a light wave in a medium of refractive index n is n/c, nor that of Abraham, who found 1/nc, is correct.
Abstract: It is shown that neither Minkowski's result, according to which the ratio of momentum to energy for a light wave in a medium of refractive index n is n/c, nor that of Abraham, who found 1/nc, is correct. For a broad wave in a uniform medium, the correct answer is given by (2.12) with $\sigma =\frac{1}{5}$. For weak refraction it is approximately equal to the average of the Abraham and Minkowski results. Abraham's formula gives correctly the part of the momentum which resides in the electromagnetic field, but not the mechanical momentum of the medium which travels with the light pulse. Minkowski's formula gives the pseudo-momentum, a quantity of physical interest. The momentum change upon reflexion or transmission usually involves also acoustic transients, these are discussed for some simple cases.
TL;DR: In this article, the production of π and η mesons at 90° from proton-proton collisions has been measured at the CERN ISR at centre-of-mass energies between 23.5 and 62.4 GeV.
TL;DR: In this article, the invariant differential cross-section of charged pions produced at x = 0 in proton-proton collisions at the CERN ISR was investigated and the range covered is 40 to 400 MeV/c in transverse momentum and 23 to 63 GeV in collision energy.
TL;DR: In this article, the commutator of the position operator and the momentum operator of a particle when the dimension of the space on which they act is finite with a discrete spectrum was shown to reduce to the usual relation of Heisenberg.
Abstract: We explicitly compute, following the method of Weyl, the commutator [Q, P] of the position operatorQ and the momentum operatorP of a particle when the dimension of the space on which they act is finite with a discrete spectrum; and we show that in the limit of a continuous spectrum with the dimension going to infinity this reduces to the usual relation of Heisenberg.
TL;DR: In this paper, the general equations of a flexible spacecraft in a gravitational field are derived, where the motion of a generic point of the body is described as the superposition of a rigid motion plus a combination of structural modes.
TL;DR: In this paper, a computer program for the calculation of ion trajectory is described, which is applicable to any ion optical system consisting of drift spaces, cylindrical or toroidal electric sector fields, homogeneous or inhomogeneous magnetic sector field, magnetic and electrostatic Q-lenses.
Abstract: A computer program for the calculation of ion trajectory is described. This program“TRIO”(Third Order Ion Optics)is applicable to any ion optical system consisting of drift spaces, cylindrical or toroidal electric sector fields, homogeneous or inhomogeneous magnetic sector fields, magnetic and electrostatic Q-lenses. The influence of the fringing field is taken into consideration. A special device is introduced to the method of matrix multiplication to shorten the calculation time and the required time proves to be about 40 times shorter than the ordinary method as a result. The trajectory calculation is possible to execute with accuracy up to third order. Any one of three dispersion bases, momentum, energy, mass and energy, is possible to be selected. Full LIST of the computer program and an example are given
TL;DR: In this article, the valence shell electronic structure of NH 3 was studied in an (e,2e) experiment with symmetric non-coplanar geometry. But the results of the experiment were limited to the 3a 1 distribution, which is sensitive to the form of the wave function.
TL;DR: In this article, the poles and residues of the complete outgoing Green function in the complex momentum plane are used to obtain, in the case of finite range potentials, an eigenfunction expansion of the continuum wave solution.
TL;DR: In this paper, a Doppler-broadening apparatus was used to study positron-annihilation lineshapes in Ag, Cd, In, Sn and Be with an improved peak-to-background ratio.
TL;DR: In this article, the axial vector form factor of the nucleon GA(k2) was deduced using PCAC and current algebra-based models, and it was found that the dipole parametrisation is favored over the monopole.
TL;DR: In this paper, a general theory of two-body reaction rates in a relativistic plasma is developed, and exact expressions for total rates involving only a single integral over the cross section for the usual case of the Bose-Einstein momentum distribution are derived.
Abstract: A general theory of two-body reaction rates in a relativistic plasma is developed. The most notable results of this theory are exact expressions for total rates involving only a single integral over the cross section for the usual case of relativistic Maxwell-Boltzmann or Bose-Einstein momentum distributions. This simplification arises from the fact that in the relativistic as well as the nonrelativistic case, an effective combined-particle distribution function can be found analytically. These results are applied to calculate the rates for radiative Compton scattering, photon-photon pair creation, and pion production in proton-proton collisions.
TL;DR: In this article, it was suggested that quasi-free processes dominate the hypernuclear spectra for (K −, π − ) strangeness exchange reactions on nuclei at 0° for momentum 900 MeV/c.
TL;DR: In this paper, the authors show how a magnetic field minimum at the point of minmum potential can remove the difficulty of electron energy analysis in a strong magnetic field using conventional retarding field methods.
Abstract: Electrostatic electron energy analysis in a strong magnetic field using conventional retarding‐field methods may be inaccurate, because these devices discriminate against parallel momentum and not total energy. We show how a magnetic‐field minimum at the point of minmum potential can remove this difficulty. Examples of elastic and inelastic electron–atom scattering, and of electron energy loss in a plasma, are given.
TL;DR: In this article, an analytical method based on Boltzmann's equation is developed to obtain the electron momentum distribution in zero temperature and low electron concentration, where the only important effect limiting the electric conductivity in a perfect polar semiconductor is the emission of real longitudinal optical phonons.
Abstract: At zero temperature and low electron concentration the only important effect limiting the electric conductivity in a perfect polar semiconductor is the emission of real longitudinal optical phonons. An analytical method based on Boltzmann's equation is developed to obtain the electron momentum distribution in this situation. Resulting plots of the distribution function with parameters corresponding to InSb and E = 12 and 120 V/cm are given.
Am Temperaturnullpunkt und bei niedrigen Elektronenkonzentrationen ist der einzige bedeutsame Effekt, der die elektrische Leitfahigkeit in einem perfekten polaren Halbleiter begrenzt, die Emission von realen, longitudinalen optischen Phononen. Es wird auf der Grundlage der Boltzmann-Gleichung eine analytische Methode entwickelt, um die Elektronenimpulsverteilung in dieser Situation zu erhalten. Die Kurven der Verteilungsfunktion mit Parametern fur InSb und E = 12 bzw. 120 V/cm werden angegeben.
TL;DR: In this paper, the optical matrix elements of the momentum operator were found independent of polarity, as in studies by Lawaetz and by Cohen, consistent with the expectations of the Penn model of the dielectric constant and with linear-combination-of-atomic-orbitals models.
Abstract: Values of the optical matrix elements are estimated from experimental values of the dielectric constant and the energy of the optical reflectivity peak. The matrix elements of the momentum operator are found independent of polarity, as in studies by Lawaetz and by Cohen. This is found to be consistent with the expectations of the Penn model of the dielectric constant and with linear-combination-of-atomic-orbitals models. It is also found to differ from but not nullify the assumptions of the Phillips-Van Vechten ionicity model. The matrix elements of momentum also vary significantly with bond length (or metallicity), but in such a way that both the bond-orbital and the pseudopotential descriptions simultaneously retain essential validity. Significant corrections to the $\ensuremath{\gamma}$ values of the bond-orbital model for the heavier elements are suggested by the study.
01 Oct 1976
TL;DR: In this article, a set of multiphase field equations based on multi-phase mechanics is developed for mixtures of phases which are separated by interfaces and are mutually exclusive, which is in contrast to the field equations of mixtures based on continuum mechanics which directly applies to molecular mixtures.
Abstract: A set of multiphase field equations—conservation of mass, momentum and energy-based on multiphase mechanics is developed. Multiphase mechanics applies to mixtures of phases which are separated by interfaces and are mutually exclusive. This is in contrast to the field equations of mixtures based on continuum mechanics which directly applies to molecular mixtures where the phases coexist at the same points in space. Based on the multiphase mechanics formulation, additional terms appear in the field equations when the physical size of the dispersed phase (bubble or droplet) is many times larger than the inter-molecular spacing:These terms are the' inertial coupling due to virtual mass and the additional viscous coupling due to unsteadiness of the flow field. These physical effects as well as the continuum inertia! coupling terms were neglected in many other two-phase calculations. By including this inertial coupling term, the onedimensional multiphase equations are found to give real characteristics. Furthermore, the sum of momentum equations of all phases reduces to the momentum equations of the mixture as should be expected.