Theory of weakly nonlinear self sustained detonations

We propose a theory of weakly nonlinear multi-dimensional self sustained detonations based on asymptotic analysis of the reactive compressible Navier-Stokes equations. We show that these equations can be reduced to a model consisting of a forced, unsteady, small disturbance, transonic equation and a rate equation for the heat release. In one spatial dimension, the model simplifies to a forced Burgers equation. Through analysis, numerical calculations and comparison with the reactive Euler equations, the model is demonstrated to capture such essential dynamical characteristics of detonations as the steady-state structure, the linear stability spectrum, the period-doubling sequence of bifurcations and chaos in one-dimensional detonations and cellular structures in multi- dimensional detonations

Analytical treatment of stabilization

We present a summarizing account of a series of investigations whose central topic is to address the question whether atomic stabilization exists in an analytical way. We provide new aspects on several issues of the matter in the theoretical context when the dynamics is described by the Stark Hamiltonian. The main outcome of these studies is that the governing parameters for this phenomenon are the total classical momentum transfer and the total classical displacement. Whenever these two quantities vanish, asymptotically weak stabilization does exist. For all other situations we did not find any evidence for stabilization. We found no evidence that strong stabilization might occur. Our results agree qualitatively with the existing experimental findings

Categorical Groups, Knots and Knotted Surfaces

We define a knot invariant and a 2-knot invariant from any finite categorical group. We calculate an explicit example for the Spun Trefoil.Comment: 40 pages, lots of figures. Second version: Added example and discussion, clarification of the fact that the maps associated with Reidemeister Moves are well define