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

A mathematical analysis of glacier surges.

Abstract. This paper describes the phenomena of glacier surges and presents a mathematical model based on realistic descriptions of glacier physics, which purports to describe the main features of the flow. The analysis reveals and predicts a variety of phenomena, many of which have been observed to occur, and gives explicit estimates for such quantities as surge front extent, "mini-surge " propagation speed, and oscillation period. Key words, glacier surges, relaxation oscillations, asymptotic methods AMS(MOS) subject classifications. 86A05, 35B2