Nonlocal Collision Research Articles

The dynamics of particle disks: III. Dense and spinning particle disks

Thermal steady states of differentially rotating axisymmetric disks composed of identical hard-sphere particles which have both spin and translational degrees of freedom are investigated when there are substantial effects due to the finite size of disk particles: nonlocal collisions and finite filling factors. In order to take these effects into account, a kinetic theory of dense gases with Enskog's collision term is employed. Major results are: (i) When the finite particle size effects are included, a thermal steady state becomes possible at any point in the (τ, ε n, ε t) space lying below the thermal balance surface obtained by neglecting these effects. (ii) At finite optical depths the nonlocal collision effect tends to vanish as the filling factor FF decreases. However, if the optical depth is low, the effect can remain substantial even at low filling factors. (iii) A non-Gaussian vertical density profile has been determined by solving the momentum equation. Unlike the particle systems in thermodynamic equilibrium which undergo a phase transition into the zero-shear phase above FF ∼ 0.50, the particle disks under Keplerian shear develop a peculiar layered structure at high filling factors. (iv) It is necessary to introduce the finite particle size effects once the particle spin is taken into consideration. Then the mean spin is found to have the same sense as the mean orbital angular velocity and about 30% of its magnitude at all optical depths regardless of the choice of other model parameters. (v) The thermal balance surface for spinning particle disks determined in Araki (1988) must be shifted when the finite particle size effects are included. (vi) Addition of the overall self-gravity also tends to shift the stability boundary upward. (vii) Viscous instability is not present in any models considered. The present numerical analysis will serve to better understand the structure and stability of the low as well as moderately high optical depth regions in planetary rings where the finite particle size effects are not negligible, including Saturn's B ring.

Comment on the residual rf surface resistance of superconductors

The effect of acoustic generation on the residual rf surface resistance Rs of superconductors has recently been discussed with the use of nonlocal theory. The results obtained are higher than the lowest values of Rs found experimentally. Taking proper account of the nonlocal collision drag force reduces the theoretical values well below the experimental results.

Theory of light scattering from dense plasmas

Projection operator techniques have been applied to derive a coupled set of exact kinetic equations describing microscopic density fluctuations in an infinite, fully-ionized, classical plasma in thermal equilibrium. The time dependence of the nonlocal collision terms in these equations is then approximated in such a way as to yield the correct short and long time behavior of density fluctuations, while allowing the explicit calculation of the dynamic structure factor S (k ,ω) characterizing electron density fluctuations in classical plasmas of arbitrary density. This theory is then applied to analyze light scattering from dense, collision-dominated plasmas, and the results of these calculations are found to compare favorably with both experimental data as well as with earlier theories (at least in the regimes in which these earlier theories are valid).

Verallgemeinerte Boltzmann-Gleichung für mehratomige Gase

A generalized quantum mechanical Boltzmann equation is derived for the one particle distribution operator of a dilute gas consisting of molecules with arbitrary internal degrees of freedom. The effect of an external, time-independent potential on the scattering process is taken into account. The collision term of the transport equation contains the two-particle scattering operator T and its adjoint in a bilinear way and is non-local. The conservation equations for number of particles, energy, momentum and angular momentum as well as the H-theorem are deduced from the transport equation. One obtains the correct equilibrium distribution operator even in the presence of an external field (e. g. for particles with spin in a homogeneous magnetic field). Some special cases of the generalized Boltzmann equation are discussed treating position and momentum of a particle as classical variables but characterizing the internal state of a molecule by quantum mechanical observables. Using the local part of the collision term only and considering molecules with degenerate, but sufficiently separated internal energy levels one arrives at the Waldmann-Snider equation, which in turn comprises the Waldmann equation for particles with spin and the Wang Chang-Uhlenbeck equation. Special attention is drawn to the case of particles with spin in a magnetic field. Finally, for particles with spin, the local conservation equation for angular momentum, i.e. the Barnett effect (magnetization by rotation) and the antisymmetric part of the pressure tensor are derived from the generalized Boltzmann equation with non-local collision term.