The collision branching process

We consider a branching model, which we call the collision branching process (CBP), that accounts for the effect of collisions, or interactions, between particles or individuals. We establish that there is a unique CBP, and derive necessary and sufficient conditions for it to be nonexplosive. We review results on extinction probabilities, and obtain explicit expressions for the probability of explosion and the expected hitting times. The upwardly skip-free case is studied in some detail.

A study of modelling approaches for rail vehicle collision behaviour

A rigid wall model has been used widely in the numerical simulation of rail vehicle impacts. Finite element impact modelling of rail vehicles is generally based on a half-width and full-length or half-length structure, depending on the symmetry. The structure and components of rail vehicles are normally designed to cope with proof loading to ensure adequate ride performance. In this paper, the authors present a study of a rail vehicle with driving cab focused on improving the modelling approach and exploring the intrinsic structural weaknesses to enhance its crashworthiness. The underpinning research used finite element analysis and compared the behaviour of the rail vehicle in different impact scenarios. It was found that the simulation of a rigid wall impact can mask structural weaknesses; that even a completely symmetrical impact may lead to an asymmetrical result; that downward bending is an intrinsic weakness of conventional rail vehicles and that a rigid part of the vehicle structure, such as the body bolster, may cause uncoordinated deformation and shear fracture between the vehicle sections. These findings have significance for impact simulation, the full-scale testing of rail vehicles and rail vehicle design in general.

Shear bond strengths of glass-ionomer cements to sound and to prepared carious dentine

The aim of this study was determine whether bonding of glass-ionomer cements to non-carious dentine differed from that to carious dentine. Five commercial cements were used, namely Fuji IX GP, Fuji IX capsulated, Fuji IX Fast capsulated (all GC, Japan), Ketac-Molar and Ketac-Molar Aplicap (both 3M-ESPE, Germany). Following conditioning of the substrate with 10% poly (acrylic acid) for 10 s, sets of 10 samples of the cements were bonded to prepared teeth that had been removed for orthodontic reasons. The teeth used had either sound dentine or sclerotic dentine. Shear bond strengths were determined following 24 h storage. For the auto-mixed cements, shear bond strength to sound dentine was found not to differ statistically from shear bond strength to sclerotic dentine whereas for hand-mixed cements, shear bond to sound dentine was found to be higher than to carious dentine (to at least p < 0.05). This shows that the chemical effects arising from interactions of glass-ionomer cements with the mineral phase of the tooth are the most important in developing strong bonds, at least in the shorter term.