Several anomalies appear to be present in the large-angle cosmic microwave background anisotropy maps of the Wilkinson Microwave Anisotropy Probe, including the alignment of large-scale multipoles. Models in which isotropy is spontaneously broken (e.g., by a scalar field) have been proposed as explanations for these anomalies, as have models in which a preferred direction is imposed during infl...

We find the geometry of all supersymmetric type I backgrounds by solving the gravitino and dilatino Killing spinor equations, using the spinorial geometry technique, in all cases. The solutions of the gravitino Killing spinor equation are characterized by their isotropy group in Spin(9, 1), while the solutions of the dilatino Killing spinor equation are characterized by their isotropy group in ...

We introduce a new construction, the isotropy groupoid, to organize the orbit data for split Γ-spaces. We show that equivariant principal G-bundles over split Γ-CW complexes X can be effectively classified by means of representations of their isotropy groupoids. For instance, if the quotient complex A = Γ\X is a graph, with all edge stabilizers toral subgroups of Γ, we obtain a purely combinato...

Abstract In this study, wide- and small-angle scattering (WAXS, SAXS) are used to analyze the structure of polyacrylonitrile (PAN) carbon fiber. Wide angle is identify lattice parameters such as d-spacings, stacking height crystalline planes (Lc), average crystallize size various other features (void content, degree graphitization). Small results show orientation distributions pores/amorphous r...

Let G be a finite group acting on vector spaces V and W and consider a smooth G-equivariant mapping f : V → W. This paper addresses the question of the zero set near a zero x of f with isotropy subgroup G. It is known from results of Bierstone and Field on G-transversality theory that the zero set in a neighborhood of x is a stratified set. The purpose of this paper is to partially determine th...

Abstract Anisotropies exist in many sedimentary rocks, particularly naturally fractured reservoirs, causing horizontal stress anisotropies. Case studies indicate that when a rock formation contains high dip-angle fractures or factures (e.g. bedding planes), it has very distinguished stresses. In these cases, the conventional isotropic method for estimating stresses may give erroneous results. U...

Local isotropy, or the statistical isotropy of small scales, is one of the basic assumptions underlying Kolmogorov’s theory of universality of small-scale turbulent motion. The literature is replete with studies purporting to examine its validity and limitations. While, until the midseventies or so, local isotropy was accepted as a plausible approximation at high enough Reynolds numbers, variou...

We derive sum rules for the effective dielectric function ee(v) of a polycrystalline material, under the assumption of macroscopic isotropy. If the material comprising the polycrystal is a quasi-one-dimensional or quasiplanar Drude metal, we predict that part of the oscillator strength of the polycrystal is pushed up in frequency to form an ‘‘impurity’’ band of confined plasmonlike excitations....