Instantaneous Collisions Research Articles

Scales and kinetics of granular flows.

When a granular material experiences strong forcing, as may be the case, e.g., for coal or gravel flowing down a chute or snow (or rocks) avalanching down a mountain slope, the individual grains interact by nearly instantaneous collisions, much like in the classical model of a gas. The dissipative nature of the particle collisions renders this analogy incomplete and is the source of a number of phenomena which are peculiar to "granular gases," such as clustering and collapse. In addition, the inelasticity of the collisions is the reason that granular gases, unlike atomic ones, lack temporal and spatial scale separation, a fact manifested by macroscopic mean free paths, scale dependent stresses, "macroscopic measurability" of "microscopic fluctuations" and observability of the effects of the Burnett and super-Burnett "corrections." The latter features may also exist in atomic fluids but they are observable there only under extreme conditions. Clustering, collapse and a kinetic theory for rapid flows of dilute granular systems, including a derivation of boundary conditions, are described alongside the mesoscopic properties of these systems with emphasis on the effects, theoretical conclusions and restrictions imposed by the lack of scale separation. (c) 1999 American Institute of Physics.

Noninstantaneous collisions and two concepts of quasiparticles

The kinetic theory recently implemented in heavy ion reactions combines a nonlocal and noninstantaneous picture of binary collisions with quasiparticle features. We show that the noninstantaneous description is compatible with the spectral concept of quasiparticles while the commonly used variational concept is consistent only with instantaneous collisions. The rearrangement energy, by which the variational concept surpasses the spectral one, is shown to be covered by a medium effect on noninstantaneous collisions.

MEMORY-DEPENDENT CONSTITUTIVE EQUATIONS IN INFORMATIONAL STATISTICAL THERMODYNAMICS

The nonequilibrium Statistical Operator Method, seemingly contained within the scope of Jaynes’ Predictive Statistical Mechanics, provides a foundation for irreversible thermodynamics in what is called Informational Statistical Thermodynamics, and within it a way of deriving generalized constitutive equations which contain non-localities on space. Here we present a derivation of these equations of evolution describing how memory effects are incorporated into the theory. We show that the memory kernels in the kinetic coefficients and relaxation times can be expressed in terms of an infinite series of instantaneous collisions integrals, of ever increasing order in the interaction strengths that are related to the slow relaxation processes that develop in the system. The kinetic coefficients are derived on the basis of the Hamiltonian dynamics of the system accompanied by appropriate averages over the nonequilibrium informational statistical ensemble.

On the Brownian motion of a massive sphere suspended in a hard-sphere fluid. II. Molecular dynamics estimates of the friction coefficient

The friction coefficient ψ exerted by a hard-sphere fluid on an infinitely massive Brownian sphere is calculated for several size ratios Σσ, where Σ and σ are the diameters of the Brownian and fluid spheres, respectively. The exact microscopic expression derived in part I of this work from kinetic theory is transformed and shown to be proportional to the time integral of the autocorrelation function of the momentum transferred from the fluid to the Brownian sphere during instantaneous collisions. Three different methods are described to extract the friction coefficient from molecular dynamics simulations carried out onfinite systems. The three independent methods lead to estimates of ψ which agree within statisticalerrors (typically 5%). The results are compared to the predictions of Enskog theory and of the hydrodynamic Stokes law. The former breaks down as the size ratio and/or the packing fraction of the fluid increase. Somewhat surprisingly, Stokes' law is found to hold withstick boundary conditions, in the range 1≤Σ/σ≤4.5 explored in the present simulations, with a hydrodynamic diameterd=Σ. The analysis of the moleuclar dynamics data on the basis of Stokes' law withslip boundary conditions is less conclusive, although the right trend is found as Σ/σ increases.

Energy relaxation and dephasing of photoexcited carriers: memory effects and cross terms between different interactions

On short time-scales two fundamental assumptions made in the derivation of the semiclassical Boltzmann equation become questionable: first, the concept of instantaneous collisions described by scattering rates due to Fermi's golden rule and, second, the neglect of interference terms between different interactions. We present a full quantum-kinetic description of a photoexcited carrier-phonon system and discuss the various types of approximations leading to the semiclassical case. Numerical results for the relaxation and dephasing process on different levels of approximations are given.

Mean square torques and correlation functions of the ν3 vibration of N2O mixed in argon at variable temperature

The second and fourth spectral moments of the ν3 vibration of N2O mixed in compressed argon are reported for five temperatures. The ratio of the mean square torque to the density is deduced and it is found to increase with the temperature, thus showing the major role of the repulsive potential in the formation of the torque. Comparison of experimental correlation functions with models shows that the assumption of instantaneous collisions is too crude. The Steele memory function theory yields instead a satisfactory agreement with the experimental data.

Random walks with sign reversals and the intrinsic angular momentum behaviour on lattices

Classical uniaxial rotators on lattices are considered. The assumption is made that the rotators exchange angular momentum only in a certain sector of relative orientations (collision sector) because of the finite range of the anisotropic interaction potential; the latter may in particular be a hard core potential (instantaneous collisions). Since the axes of the rotators are supposed to be parallel but not collinear, during each collision the exchange of angular momentum occurs with sign reversal, i.e. is of the cog-wheel type. In a first approximation all correlations between successive collisions are neglected. This amounts to considering a random walk on a lattice in which the walker carries with him a variable whose sign is changed at each step. Then, one is led to distinguish two types of lattices, depending upon the possibility for returning to the initial site after an odd number of steps. For two-dimensional lattices, the asymptotic solution of the autocorrelation function of the angular momentum is analytically given, and its behaviour at shorter times is obtained by a numerical method. For the odd lattices, the asymptotic behaviour is generally exponential, whereas there exist algebraic long tails for the even lattices. Finally, coming back to the problem where the successive collisions are not independent, some simulation results for two-dimensional lattices of soft core diatomics are described.

Model interpretations of the far infrared absorptions in compressed gaseous and liquid bromotrifluoromethane, CBrF3

The far infrared (2–100 cm–1) absorption of the symmetric top molecule bromotrifluoromethane (CBrF3) has been measured for the gas phase in pressure range 1.2–46.2 bar and for the liquid. Whereas the peak of the broad bands observed moves only slightly from 9.8 cm–1 at 1.2 bar to 11.0 cm–1 in the liquid at the same temperature (295 K), there are pronounced differences in the bandshape which are reflected in considerable damping of the time functions obtained by Fourier transformation of the frequency data. A simple model of bimolecular collision induced dipolar absorption accounts fairly well for the high frequency shoulders which appear in the spectra of the compressed gas. Using this model, preliminary values of the quadrupole (Q) and octopole moment (Ω) of the molecule have been obtained. A mechanism of collision disturbed torsional oscillation of the permanent dipole (µ) within potential wells accounts more satisfactorily for the absorption in the liquid than the J-diffusion model, which assumes free rotation between instantaneous collisions.

Forced oscillations with a sliding regime range of a two-mass system interacting with a fixed stop: PMM vol. 37, n≗6, 1973, pp. 999–1006

We investigate, by the method developed in [1]. the forced oscillations with a sliding regime range of a two-mass system with elastic connection between the elements, impacting a fixed stop. The system being considered is a dynamic model for a number of vibrational mechanisms. Forced oscillations with a sliding regime range of a system with shock interactions are periodic motions accompanied by a period of an infinite succession of instantaneous collisions of two fixed elements of the model [2]. Within the framework of conditions of roughness of the parameter space [3], in this paper we study by the method of [1] periodic motions with a sliding regime range of a two-mass system with a stop. This problem was posed because in real systems the velocity recovery factor R changes from shock to shock, mainly taking small values (0, 0.2). At the same time, the regions of realizability of one-impact oscillations, in practice the most essential ones among motions with a finite number of interactions over a period, narrow down sharply as R decreases and becomes very small even for R < 0.6 [4]. Thus, the stability of the given operation can be ensured by a law of motion which is independent or weakly dependent on R ( ∗ ∗ An analogous conclusion has been made on the basis of an experimental study of the dynamics of a vibrating hammer in [5]. ) (see footnote on the next page). By virtue of what has been said above, finite-impact periodic modes are little suitable for this purpose. Regions, delineated in the parameter space of the model being considered, of existence of stable periodic motions with a sliding regime range have proved to be sufficiently broad. By virtue of the adopted approximation of the sliding regime, the dynamic characteristics of these motions do not depend upon R. The circumstances mentioned confirm the practical value of motions with a sliding regime range in dynamic systems with impact interactions.

Hard-sphere dynamics and binary-collision operators

Abstract The dynamics of a classical hard-sphere system has as peculiarities that the particles suffer instantaneous collisions and that certain (“overlapping”) areas in phase space are not accessible to the particles. It is mainly the latter feature that prevents a straightforward application of the usual binary collision expansion, generating the particle trajectories. Depending on how the relevant streaming operators are extended to the overlapping areas binary collision expansions can be developed. The different expressions so far proposed are critically examined and the restrictions to their applicability are determined. The binary-collision expansion for potentials consisting of a hard core and a soft tail is also discussed.