Finite Collision Time Research Articles

How Fast are Elastic Domino Waves?

The paper is concerned with the problem of toppling propagation velocity in elastic, domino-like mechanical systems. We build on the work of Efthimiou and Johnson, who developed the theory of perfectly elastic collisions of thin rigid dominoes on a frictional foundation. This theory has been criticised for the lack of correspondence with the experimental observations, in particular, prediction of infinite propagation velocity for zero spacing between dominoes, as well as the inability to represent the collective nature of collisions in real domino systems. In our work we consider a more realistic scenario of dominoes of finite stiffness and obtain a theory of fast elastic domino waves, taking into account a limit velocity of the perturbation propagation in the system of dominoes. Moreover, finite collision time allows to extract dynamic quantities of collisions and establish upper and lower borders for domino separations where the theory could still be applied. Our discrete element simulations support our theoretical findings and shed light on the nature of collective interactions in the nearly-elastic domino chains.Graphical abstract

Generalized Fokker-Planck equation, Brownian motion, and ergodicity

Microscopic theory of Brownian motion of a particle of mass M in a bath of molecules of mass m<<M is considered beyond lowest order in the mass ratio mM . The corresponding Langevin equation contains nonlinear corrections to the dissipative force, and the generalized Fokker-Planck equation involves derivatives of order higher than 2. These equations are derived from first principles with coefficients expressed in terms of correlation functions of microscopic force on the particle. The coefficients are evaluated explicitly for a generalized Rayleigh model with a finite time of molecule-particle collisions. In the limit of a low-density bath, we recover the results obtained previously for a model with instantaneous binary collisions. In the general case, the equations contain additional corrections, quadratic in bath density, originating from a finite collision time. These corrections survive to order (m/M)2 and are found to make the stationary distribution non-Maxwellian. Some relevant numerical simulations are also presented.

Line-mixing and collision-time asymmetry of spectral line shapes

The quantum-mechanical Baranger-Kolb-Griem theory of pressure broadening is reexamined in order to include both the effects due to overlapping lines and finite duration of collision. A general line-shape formula is derived which for near wings can be presented as a linear combination of the Lorentzian and dispersion profiles. The asymmetry parameter is expressed by means of evolution operators for the initial and final states. It is shown that in the weak-coupling case only the resultant asymmetry parameter can be approximately given as the sum of parameters describing the asymmetry due to line mixing and finite collision time.

Semiclassical theory of atom-crystal scattering diffraction and interaction with phonons

This paper deals with the problem of phonon-inelastic atom-surface scattering on the base of the path integral expression for the 5-matrix in the momentum representation. The Faddeev-Popov method is used to fix classical paths with respect to the symmetry of the system. The semiclassical evaluation of the path integral over projectile variables with the help of the generalized eikonal method, which allows us to take into consideration the recoil effect, results in an integral representation for the scattering probability of Van Hove type. This representation, taking into account a finite collision time and improving the semiclassical perturbation theory and the sudden approximation, is employed to describe phonon-inelastic scattering from an ideal crystal surface in the thermal and diffractive regimes. Two limiting cases of single-phonon and multi-phonon scattering are considered. The probabilities of single-phonon scattering in the diffractive regime are expressed through the Bessel functions as well as the diffractive intensities. Possible resonances during the inelastic scattering from a corrugated surface, which may simplify the expression for the relevant probability, are discussed. We also suggest a new approximation to the dynamic structure factor (i.e. energy and tangential momentum transfer probability) for multi-phonon scattering. It has the Gaussian form and, being a generalization of the well-known Brako-Newns formula, accounts for the average transfer of the tangential momentum, satisfies the principle of detailed balance, and is valid for arbitrary collision times and surface temperatures. An approximate expression for the average momentum transfer is proposed.

Grazing reactions in collisions between heavy nuclei

A microscopic model of grazing collisions based on well-known form factors for single-particle transfer gives a comprehensive description of the distribution of mass and charge, and of the energy- and angular momentum loss for grazing collisions of heavy nuclei at low bombarding energies. The overall agreement between the predictions and experimental results of collisions with a major loss of kinetic energy supports the picture of the reaction, where deep inelastic reactions are a part of the regime of grazing collisions, a regime distinct from reactions where the nuclear surfaces merge to form a fused system which may later disintegrate. These deep inelastic grazing reactions are to a large extent governed by the quantal energy width associated with the finite collision time and the description is thus rather different from the classical picture of a friction mechanism.

Monte Carlo Code ODIN and Energy Density Analysis in Relativistic Heavy Ion Collisions11The project partially supported by National Natural Science Foundation of China and U.S. Department of Energy

The energy density reached in relativistic heavy ion collisions is analyzed based on the Monte Carlo code ODIN. The effect of different parameters in ODIN code on the energy density is investigated. The results show that the actually reached energy density is lower than Bjorken's estimation due to the finite collision time.

Analysis of the single-particle scattering spectra for spin-density fluctuations of electrons in n-GaAs at T=300 K

The line shapes of single-particle scattering spectra for spin-density fluctuations of electrons in n-GaAs with carrier concentrations ranging from 5×1015 to 7×1017 cm−3 have been analyzed. We have found that the Raman line shapes can be very well explained by a theory developed by Hamilton and McWhorter which takes into account both the band-structure effects in semiconductors and the effects of carrier collision in a relaxation time approximation. For carrier concentration n≥2×1016 cm−3, the effects of finite collision time has been demonstrated to be very important and these effects must be properly taken into account in order to satisfactorily interpret the line shapes of single-particle scattering spectra for spin-density fluctuations in n-GaAs at T=300 K. We show that although Lindhard–Mermin’s expression for dielectric constant as well as Hamilton and McWhorter’s theory fit the Raman line shapes equally well for carrier density n=7×1017 cm−3, neglect of band-structure effects of the former tends to underestimate the carrier collision time. An interpretation of the deduced collision time in terms of electron-electron, electron-impurity, and electron-phonon scattering is also given.

Theoretical study of time-resolved Raman scattering profiles of hot electrons in semiconductors

A comprehensive time-resolved electronic Raman scattering theory for nonequilibrium carrier excitations in semiconductors is presented. The following are simultaneously taken into account: (i) the effects of the ultrashort laser pulse for probing the excited carrier distribution function; (ii) the fact that the fluctuation-dissipation theorem is not valid under conditions of nonequilibrium carrier distributions; (iii) the effects of quasiparticle life time via a finite collision time in the Raman scattering cross section; and (iv) the effect of the time-dependent resonant enhancement factor due to the band structure. The single-particle scattering spectra for spin-density fluctuation contribution is found to be significantly broadened by an ultrashort laser pulse, but is substantially narrowed by the finite collision time. The effect of the time-dependent resonant enhancement factor has been demonstrated to broaden the line shape of single-particle scattering spectra for the spin-density fluctuation contribution as the probe photon energy increases.

Measurement of the broadening and asymmetry of the calcium resonance line (422.7 nm)

The broadening parameters of the calcium resonance line (422.7 nm) perturbed by rare gases have been obtained by laser fluorescence so as to be free of instrumental broadening. The data have been fitted directly to a more sophisticated lineshape which was found to describe the data to a much higher degree of accuracy than the usual Voigt profile. This modified lineshape (the asymmetric speed-dependent Voigt profile ASDVP) includes the effect of finite collision time and of correlations between pressure broadening and emitter speed. The values obtained for broadening by the rare gases He, Ne, Ar, Kr and Xe are as follows: 24.4, 14.9, 27.8, 28.9 and 33.7*10-24 mK m3 (full Lorentzian widths). The collision time asymmetry parameter, b, has also been measured for each of these gases, and the following values obtained: +1.04, +0.3, -0.7, -1.35 and -2.24*10-4 mK-1. A negative value indicates greater intensity in the red wing.

Spectral features in solar hard X-ray and radio events and particle acceleration

view Abstract Citations (79) References (34) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Spectral features in solar hard X-ray and radio events and particle acceleration. Benz, A. O. Abstract Hard X-ray and radio intensities of two major solar outbursts are found to anticorrelate in time with their spectral indices, which, furthermore, are in satisfactory correlation with each other. The radio emission must be synchrotron radiation from the same electron population that causes the X-ray bremsstrahlung. A delay of temporal features, increasing with energy, is clearly observed in one of the X-ray events. The observations are interpreted with a simple model, which assumes ion-acoustic instability in a current sheet, transformation of turbulence energy into Langmuir waves, and their escape into the ambient plasma where they accelerate particles. A power-law index of the electron energy distribution is derived for acceleration being balanced by escape of particles. Anticorrelation of intensity and spectral index then follows naturally from variations of the spectral wave energy density or the dimension of the acceleration region. The finite collision time in the acceleration region and its increase with energy introduce a perturbation which can explain the observed drift of temporal features. Publication: The Astrophysical Journal Pub Date: January 1977 DOI: 10.1086/154928 Bibcode: 1977ApJ...211..270B Keywords: Particle Acceleration; Solar Radio Emission; Solar Wind; Solar X-Rays; X Ray Spectra; Bremsstrahlung; Electron Energy; Ion Acoustic Waves; Solar Electrons; Synchrotron Radiation; Solar Physics full text sources ADS |

On the structure of the three-particle operator in generalized kinetic equations for inhomogeneous gases

It is shown that the three-particle kinetic operator for inhomogeneous gases obtained using Prigogine's method and the matrix representation of the Liouville equation introduced by Balescu is equivalent to the corresponding expression derived by Choh and Uhlenbeck using Bogolubov's method. Both theories take into account the space and time delocalization associated with finite collision time, and the resulting corrections to the asymptotic collision operator are equivalent.