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

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

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

On the Nature of Precursors in the Radio Pulsar Profiles

In the average profiles of several radio pulsars, the main pulse is accompanied by the preceding component. This so called precursor is known for its distinctive polarization, spectral, and fluctuation properties. Recent single-pulse observations hint that the sporadic activity at the extreme leading edge of the pulse may be prevalent in pulsars. We for the first time propose a physical mechanism of this phenomenon. It is based on the induced scattering of the main pulse radiation into the background. We show that the scattered component is directed approximately along the ambient magnetic field and, because of rotational aberration in the scattering region, appears in the pulse profile as a precursor to the main pulse. Our model naturally explains high linear polarization of the precursor emission, its spectral and fluctuation peculiarities as well as suggests a specific connection between the precursor and the main pulse at widely spaced frequencies. This is believed to stimulate multifrequency single-pulse studies of intensity modulation in different pulsars.Comment: 5 pages, no figures. Accepted for publication in MNRAS Letter