The archeological and historical record is replete with evidence for prehistoric, ancient and pre-modern societal collapse. These collapses occurred quite suddenly and frequently involved regional abandonment, replacement of one subsistence base by another (such as agriculture by pastoralism

-of-the atmosphere (TOA) radiative forcing. This occurs via several pathways: (1) by absorbing the solar radiation reflected by the surface-atmosphere-cloud system, BC reduces the albedo of the planet; (2) soot deposited over snow and sea ice can decrease the surface albedo 29, 30, 31, 32 ; (3) soot inside cloud

, wall terraces, and internal rings in still larger craters. These are called "complex" craters. The transition between simple and complex craters depends on 1/g, suggesting that the collapse occurs when a strength threshold is exceeded. The apparent strength, however, is very low: only a few

instances, metastable pearl-necklace structures form in characteristic time scale that is proportional to N 4 5 where N is the number of monomers. The late stage of collapse occurs by merger of clusters with the largest one growing at the expense of smaller ones (Lifshitz- Slyozov mechanism). The time scale

In many biological systems, movement of an organism occurs in response to a diffusible or otherwise transported signal, and in its simplest form this can be modeled by diffusion equations with advection terms of the form first derived by Patlak [Bull. of Math. Biophys.,15 (1953), pp. 311

We show that the when one takes into account the global equilibrium ramifications of an unwinding of the US current account deficit, currently running at more than 6 % of GDP, the potential collapse of the dollar becomes considerably larger than our previous estimates (Obstfeld and Rogoff 2000a

for drying and the critical size of the vapor bubble required for the nucleation of the drying event. We also investigate the kinetics of hydrophobic collapse and find that the hydrophobic collapse occurs in about 100 ps. We compare these results with the simulations with the plate-water van der Waals

free shape of observed rotation curves with the simulation data. It is important to confirm these results using stellar rather than HI rotation curves for LSB galaxies. We test the effects of introducing a cut-off in the power spectrum that may occur in a universe dominated by warm dark matter

Advances in our understanding and the modeling of stellar core-collapse and supernova explosions over the past 15 years are reviewed, concentrating on the evolution of hydrodynamical simulations, the description of weak interactions and nuclear equation of state effects, and new insights

Partial combinatory algebras occur regularly in the literature as a framework for an abstract formulation of computation theory or recursion theory. In this paper we develop some general theory concerning homomorphic images (or collapses) of pca's, obtained by identification of elements in a