Oscillatory combustion of liquid monopropellant droplets

A theoretical investigation was conducted on the open-loop combustion response of monopropellant droplets and sprays to imposed pressure oscillations. The theoretical model was solved as a perturbation analysis through first order, yielding linear response results. Unsteady gas phase effects were considered in some cases, but the bulk of the calculations assumed a quasi-steady gas phase. Calculations were conducted using properties corresponding to hydrazine decomposition. Zero-order results agreed with earlier measurements of hydrazine droplet burning in combustion gases. The droplet response was greatest (exceeding unity in some cases) for large droplets with liquid phase temperature gradients; at frequencies near the characteristic frequency of the liquid phase thermal wave. The response of a spray is less than that of its largest droplet, however, a relatively small percentage of large droplets provides a substantial response (exceeding unity in some cases)

Decomposition in bunches of the critical locus of a quasi-ordinary map

A polar hypersurface P of a complex analytic hypersurface germ, f=0, can be investigated by analyzing the invariance of certain Newton polyhedra associated to the image of P, with respect to suitable coordinates, by certain morphisms appropriately associated to f. We develop this general principle of Teissier (see Varietes polaires. I. Invariants polaires des singularites d'hypersurfaces, Invent. Math. 40 (1977), 3, 267-292) when f=0 is a quasi-ordinary hypersurface germ and P is the polar hypersurface associated to any quasi-ordinary projection of f=0. We build a decomposition of P in bunches of branches which characterizes the embedded topological type of the irreducible components of f=0. This decomposition is characterized also by some properties of the strict transform of P by the toric embedded resolution of f=0 given by the second author in a paper which will appear in Annal. Inst. Fourier (Grenoble). In the plane curve case this result provides a simple algebraic proof of the main theorem of Le, Michel and Weber in "Sur le comportement des polaires associees aux germes de courbes planes", Compositio Math, 72, (1989), 1, 87-113

The projectors of the decomposition theorem are motivic

We prove that the projectors arising from the decomposition theorem applied to a projective map of quasi projective varieties are absolute Hodge, Andr\'e motivated, Tate and Ogus classes. As a by-product, we introduce, in characteristic zero, the notions of algebraic de Rham intersection cohomology groups of a quasi projective variety and of intersection cohomology motive of a projective variety