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

The General Relativistic Instability of Massive Stars

Binding energy of massive polytrope and general relativistic instability of massive star

The Collective Dynamics of Smoking in a Large Social Network

Based on repeated surveys of 12,067 closely interconnected people between 1971 and 2000, examines the extent to which smoking spreads socially and to which groups of smokers quit together, as well as trends in the number and social centrality of smokers

Spruce Budworm Egg Mass Density on Balsam Fir and White Spruce: Low Population Levels (Lepidoptera: Tortricidae)

As part of a study to develop improved foliage sampling methods for spruce budworm, Choristoneura fumiferana (Clemens), egg masses, two balsam fir (four in one stand), Abies balsamea, and two white spruce, Picea glauca, trees were chosen from each of five spruce- fir stands in Michigan\u27s Upper Peninsula in 1980. All stands had very low to low population densities. Each tree was completely enumerated so that the number of new egg masses, foliage surface area, and egg mass density could be determined for the entire tree, three crown classes, four quadrants, and the tree top. Results indicated (1) considerable tree-to- tree and stand-to-stand variation; (2) no meaningful or consistent differences among quad- rants within or between species; (3) the average density in white spruce trees was 3.2 times larger than that in balsam fir trees; (4) the tree-la-tree variation of density in white spruce trees was 8.4 times larger than that in balsam fir trees; (5) densities in the mid-crown, upper-crown, and tree top are considerably higher than that in the lower-crown for both species; the relative differences for balsam fir are about twice that of white spruce; and (6) on the average, density at mid-crown was close to that of the entire tree for balsam fir, but density at mid-crown was 17.9% lower than that of the entire tree for white spruce. These results have important implications to the development of sampling plans for estimating egg mass density in spruce-fir stands

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