The Fallout from the Clouds of Recession are Being Felt

This article is part of the collection of writings of Marshall (Mike) Westfall, retired autoworker from General Motors in Flint, Michigan (1964-1994) and activist critic of the auto industry restructuring that led to devastating job losses. It originally appeared online in The Westfall Papers. [http://michaelwestfall.tripod.com/id79.html, accessed 12/14/2011

On the Acoustical Dynamics of Bubble Clouds

Recently, Morch [1,2,3,4] Chahine [5,6] and others have focused attention on the dynamics of a cloud or cluster of cavitating bubbles and have expanded on the work of van Wijngaarden [7,8] and others. Unfortunately, there appear to be a number of inconsistencies in this recent work which will require further study before a coherent body of knowledge on the dynamics of clouds of bubbles is established. For example, Morch and his co-workers [1,2,3] have visualized the collapse of a cloud of cavitating bubbles as involving the inward propagation of a shock wave; it is assumed that the bubbles collapse virtually completely when they encounter the shock. This implies the virtual absense of non-condensable gas in the bubbles and the predominance of vapor. Yet in these circumstances the mixture in the the cloud will not have any real sonic speed. As implied by a negative L.H.S. of equation (9), the fluid motion equations for the mixture would be elliptic not hyperbolic and hence shock wave solutions are inappropriate

Star formation triggered by SN explosions: an application to the stellar association of β\beta Pictoris

In the present study, considering the physical conditions that are relevant in interactions between supernova remnants (SNRs) and dense molecular clouds for triggering star formation we have built a diagram of SNR radius versus cloud density in which the constraints above delineate a shaded zone where star formation is allowed. We have also performed fully 3-D radiatively cooling numerical simulations of the impact between SNRs and clouds under different initial conditions in order to follow the initial steps of these interactions. We determine the conditions that may lead either to cloud collapse and star formation or to complete cloud destruction and find that the numerical results are consistent with those of the SNR-cloud density diagram. Finally, we have applied the results above to the $\beta-$Pictoris stellar association which is composed of low mass Post-T Tauri stars with an age of 11 Myr. It has been recently suggested that its formation could have been triggered by the shock wave produced by a SN explosion localized at a distance of about 62 pc that may have occurred either in the Lower Centaurus Crux (LCC) or in the Upper Centaurus Lupus (UCL) which are both nearby older subgroups of that association (Ortega and co-workers). Using the results of the analysis above we have shown that the suggested origin for the young association at the proposed distance is plausible only for a very restricted range of initial conditions for the parent molecular cloud, i.e., a cloud with a radius of the order of 10 pc and density of the order of 20 cm$^{-3}$ and a temperature of the order of 50$-$100 K.Comment: 9 pages, 10 figures, to appear in MNRA

Shock Wave Development in the Collapse of a Cloud of Bubbles

A numerical simulation of the collapse of a cloud of bubbles has been used to demonstrate the development of an inwardly propagating shock wave which grows rapidly in magnitude. The fully non-linear nonbarotropic homogeneous flow equations are coupled with single bubble dynamics and solved by a stable numerical scheme. The computational results demonstrate the structure of the shock wave as well as its strengthening effect due to the coupling of the single bubble dynamics with the global dynamics of the flow through the pressure and velocity fields. This appears to confirm the speculation of Morch and his co-workers that such shock formation is an important part of cloud collapse