Within a granular material stress is transmitted by forces exerted at points of mutual contact between particles. When the particles are close together and deformation of the assembly is slow, contacts are sustained for long times, and these forces consist of normal reactions and the associated tangential forces due to friction. When the particles are widely spaced and deformation is rapid, on the other hand, contacts are brief and may be regarded as collisions, during which momentum is transferred. While constitutive relations are available which model both these situations, in many cases the average contact times lie between the two extremes. The purpose of the present work is to propose constitutive relations and boundary conditions for this intermediate case and to solve the corresponding equations of motion for plane shear of a cohesionless granular material between infinite horizontal plates. It is shown that, in general, not all the material between the plates participates in shearing, and the solutions for the shearing material are coupled to a yield condition for the non-shearing material to give a complete solution of the problem.

Measurements of the relation between mass hold-up and flow rate have been made for glass beads in fully developed flow down an inclined chute, over the whole range of inclinations for which such flows are possible. Velocity profiles in the flowing material have also been measured. For a given inclination it is found that two different flow regimes may exist for each value of the flow rate in a certain interval. One is an ‘energetic’ flow, and is produced when the particles are dropped into the chute from a height, while the other is relatively quiescent and occurs when entry to the chute is regulated by a gate. At some values of the inclination jumps in the flow pattern occur between these branches, and it is even possible for both branches to coexist in the same chute, separated by a shock. A theoretical treatment of chute flow has been based on a rheological model of the material which takes into account both collisional and fractional mechanisms for generating stress. Its predictions include most aspects of the observed behaviour, but quantitative comparison of theory and experiment is difficult because of the uncertain values of some parameters appearing in the theory.

The plasma equation for a warm collisionless plasma with a Maxwellian particle source is solved in plane parallel geometry. The generalized Bohm criterion is used to identify the plasma–sheath boundary. This kinetic treatment, in common with fluid and cold-ion kinetic models, results in an infinite electric field at the sheath edge. This is in sharp contrast to results from a previous warm-ion kinetic model, by Emmert et al. [Phys. Fluids 23, 803 (1980)], which gave a finite electric field at the sheath edge. Also, the presheath potential given by the present model is greater than that given by Emmert and is in better agreement with fluid results.

Accurate values of the relative transition probabilities Aupsilon ' upsilon '' for 41 bands in the N2 second positive system have been measured using single-photon counting techniques on a repetitive pulsed source. A computer code simulating the band structure, including multiplet splitting, and intensity distribution enables any band intensity to be deduced from the fractional intensity seen at the peak in the P branch (band-head). The variation of the electronic transition moment with internuclear separation Re(r) is obtained from the measured Aupsilon ' upsilon '' by means of a weighted least-squares curve-fitting procedure based on nth moment r centroids. It is best represented by a polynomial of degree 2, (1-1.336r+0.487r2) whose curvature is in the opposite sense to previously derived fits.

Four models of collisionless one-dimensional plasma flow to a boundary are compared with regard to their predictions of particle and heat fluxes to the boundary for a given plasma density and temperature far from the boundary. The models include two kinetic treatments, that of Emmert et al. [Phys. Fluids 23, 803 (1980)], and that of Bissell and Johnson [Phys. Fluids 30, 779 (1987)], an isothermal fluid model, Self and Ewald [Phys. Fluids 9, 2486 (1966) and Stangeby, [Phys. Fluids 27, 2699 (1984)], and an adiabatic fluid model, Zawaideh, Najmabadi, and Conn [Phys. Fluids 29, 463 (1986)]. The fluid models do not explicitly include collisions; however, the adiabatic closure condition employed, namely, neglect of ion heat conduction, implies a degree of ion self-collisionality. It is found that the particle and heat fluxes to the boundary differ very little among the four models—spanning a range of about ±10%. It is therefore concluded that, with regard to modeling of such important practical quantities as outfluxes, a simple and convenient formulation, such as the isothermal fluid model, is adequate. Substantial differences among the models are found for certain other predicted quantities, namely, the spatial variation of ion temperature along the flow and the magnitude of the electric field near the boundary.