Linear and nonlinear stability of heat exchangers

The hydrodynamical problem of one-dimensional flow with a uniform heat input resulting in a change of phase is considered. Equations of mass, momentum, energy and state representing the dynamic behaviour of such a system are reduced to two coupled equations for the density p{x, t) and the inlet velocity 1/(0 on the assumption that the pressure drop applied between the inlet and the outlet is "small". A linear stability analysis is carried out which leads to the problem of computing the zeros of a complicated analytic function. A non-linear analysis is applied to the case of weak instability to find the evolution of the slowly varying amplitude of a small oscillation: in certain circumstances, a "burst " occurs, and in such cases no such small oscillation can exist. 1

Precise Predictions for Higgs Production in Neutralino Decays

Complete one-loop results, supplemented by two-loop Higgs propagator-type corrections, are obtained for the class of processes chi^0_i->chi^0_j h_a in the MSSM with CP-violating phases for parameters entering the process beyond lowest order. The parameter region of the CPX benchmark scenario where a very light Higgs boson is unexcluded by present data is analysed in detail. We find that the decay chi^0_2->chi^0_1 h_1 may offer good prospects to detect such a light Higgs boson.Comment: 4 pages, 3 figures; to appear in the proceedings of the 17th International Conference on Supersymmetry and the Unification of Fundamental Interactions (SUSY09), Boston, USA, 5-10 Jun 200

The formation of freckles in binary alloys

This paper presents a synopsis of some recent work, still in progress, aimed at elucidating a quantitative explanation of the processes by which flow chimneys form when certain types of alloys are directionally solidified. If (for example) light fluid is released at the liquid-solid "mushy " (dendrite) zone, and cooling is from below, then the intermediate fluid flow undergoes convection through the porous dendrite mass. This can lead to an "instability " of the form of the mushy zone, such that upwelling light fluid flows preferentially in channels within the dendrite mass. What we seek to develop here, is a mathematical basis by which this phenomenon may be properly understood. Accordingly, a mathematical model is developed, simplified, and partially analysed, and as a result we are able to make one specific prediction concerning a criterion for the onset of convection and freckling. This prediction is equivalent to the classical Rayleigh number condition for convective instability. 1

On the rheology of till

The deformation of subglacial till is instrumental in causing certain glacier surges, the motion of rapid ice streams in ice sheets, and ice sheet surges which are associated with Heinrich events, and consequent rapid climatic shifts, during the last ice age. It may also be the means whereby drumlins are formed, and these in turn may act as a brake on large scale ice flow. It is therefore important in building models to understand the rate at which till deforms, and how this controls the basal ice velocity. In recent years, two paradigms have emerged. On the one hand, theoreticians have tended to use a viscous rheology, though this lacks quantitative support. On the other hand, field and laboratory studies suggest that till behaves plastically. In this paper I will examine some of the dynamic consequences of this latter assumption, and show how the dichotomy between viscous and plastic may be less clearcut than previously thought.