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A theoretical investigation has been made of obliquely propagating nonlinear electrostatic shock structures. The reductive perturbation method has been used to derive the Korteweg-de Vries-Burger (KdV-Burger) equation for dust acoustic shock waves in a homogeneous system of a magnetized collisionless plasma comprising a four-component dusty plasma with massive, micron-sized, positively, negatively dust grains and non-extensive electrons and ions. The effect of dust viscosity coefficients of charged dusty plasma of opposite polarity and the non-extensive parameters of electrons and ions have been studied. The behavior of the oscillatory and monotonic shock waves in dusty plasma has been investigated. It has been found that the presence of non-extensive parameters significantly modified the basic properties of shock structures in space environments.

In this paper we extend previous work on the relation between the complex structure moduli of the underlying Calabi-Yau manifold in five dimensional supergravity with the time evolution of an embedded 3-brane. We numerically solve the fields' equations for such a construction and focus on dust and radiation filled branes; with the possible application of modeling the universe as a brane-world. It is shown that in both cases the time evolution of the moduli causally connects to the expansion of the brane-world. We also find that in most cases considered there is an early short period of rapid accelerative expansion, indicating an inflationary epoch. We report on these results; leaving analysis of the underlying causes for future work.

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