We continue our study of the nonlinear Boltzmann equation for “diffuse” binary scattering between subsystems in a microcanonical ensemble. Exact similarity solutions of Bobylev-Krook-Wu type are found for systems of arbitrary dimensionality and in both continuous and discrete state...

The “p-q” model earlier introduced by the authors to describe persistent scattering under a scalar Boltzmann equation is here examined in detail. After deriving the scattering kernel and exhibiting its properties we obtain moment and similarity solutions and show how the model effectively...

We consider a class of scalar nonlinear Boltzmann equations describing the evolution of a microcanonical ensemble in which sub-systems exchange internal energy ‘randomly’ in binary interactions.

When a medium energy neutron hits a free atom there is a finite probability that as a consequence of the recoil the atom becomes excited or ionised. For the simple case of a hydrogen atom exact calculations are reported of the transition probabilities for various initial and final states as a...

We present detailed tabulations of the first few eigenfunctions of the hard-sphere energy scattering kernel for a test-particle in a background heat-bath. Calculations, for a range of heat bath/test particle mass-ratios between 18 and 11024, were carried out by a Rayleigh-Ritz method using the...