S. Simons

Is the solution of the Boltzmann equation positive

Abstract A proof is given that the solution of the general non-linear space- and time-dependent Boltzmann equation, combined with suitable boundary conditions, in non-negative. For the spatially homogeneous situation the proof is extended to show that the solution is always positive.

On the solution of the time independent equation for the diffusion of coagulating clusters

Abstract A solution is obtained of the time independent equation describing steady state diffusion and coagulation of an assembly of particles for the case where both diffusion coefficient and coagulation kernel are constants. Explicit results are derived for the dependence of cluster number density on position and cluster size.

Aerosol growth by condensation of “small” particles

Abstract It is shown that the growth of a “large” particle aerosol due to its coagulation with “small” particles may be represented by a condensation-type term subject to a certain condition on the particle sizes. Formulae are derived to estimate the error when this condition is not satisfied.

On the stability of thermal conduction

Abstract It is shown that previous treatments of the stability of thermal conduction will break down when very rapid changes in the physical parameters can occur. A new approach is developed which remedies this.

On the passage to equilibrium

Abstract It is pointed out that for various systems, quantities equal or closely related to successive time derivatives of the entropy alternate in sign during the passage to equilibrium.

On the thermal conductivity of paramagnetic salts

Abstract It is pointed out that the existence of phonon-phonon N-processes may prevent measurements of the magnetic field dependence of the thermal conductivity of paramagnetic salts from yielding information about other types of phonon interactions.

An extension of the proof of stability of thermal conduction

Abstract A previous proof of the stability of thermal conduction is extended to cover the situation where the variation in the temperature distribution in the steady state can be arbitrarily large.

On the entropy variation during the passage to radiative equilibrium

Abstract It is shown that for a simple isolated system attaining equilibrium through the emission and absorption of radiation, the second time derivative of the entropy is always negative. For the situation close to equilibrium the proof is extended to show that for a general system of radiators, all succssive derivatives of the entropy alternate in sign.

On the diffusion of dust through a gas in a force field

Abstract It is shown that the standard theory for diffusion of dust in a turbulent gas in the presence of a force field can lead to a paradox. The resolution of this paradox is discussed and a modification to the theory is developed which, under certain conditions, yields significantly different results.