Magnetotransport and magnetocrystalline anisotropy in Ga1-xMnxAs epilayers

We present an analysis of the magnetic anisotropy in epitaxial Ga1-xMnxAs thin films through electrical transport measurements on multiterminal microdevices. The film magnetization is manipulated in 3D space by a three-axis vector magnet. Anomalous switching patterns are observed in both longitudinal and transverse resistance data. In transverse geometry in particular we observe strong interplay between the anomalous Hall effect and the giant planar Hall effect. This allows direct electrical characterization of magnetic transitions in the 3D space. These transitions reflect a competition between cubic magnetic anisotropy and an effective out-of-plane uniaxial anisotropy, with a reversal mechanism that is distinct from the in-plane magnetization. The uniaxial anisotropy field is directly calculated with high precision and compared with theoretical predictions

Cyclic cocycles on deformation quantizations and higher index theorems

We construct a nontrivial cyclic cocycle on the Weyl algebra of a symplectic vector space. Using this cyclic cocycle we construct an explicit, local, quasi-isomorphism from the complex of differential forms on a symplectic manifold to the complex of cyclic cochains of any formal deformation quantization thereof. We give a new proof of Nest-Tsygan's algebraic higher index theorem by computing the pairing between such cyclic cocycles and the $K$-theory of the formal deformation quantization. Furthermore, we extend this approach to derive an algebraic higher index theorem on a symplectic orbifold. As an application, we obtain the analytic higher index theorem of Connes--Moscovici and its extension to orbifolds.Comment: 59 pages, this is a major revision, orbifold analytic higher index is introduce

The transverse index theorem for proper cocompact actions of Lie groupoids

Given a proper, cocompact action of a Lie groupoid, we define a higher index pairing between invariant elliptic differential operators and smooth groupoid cohomology classes. We prove a cohomological index formula for this pairing by applying the van Est map and algebraic index theory. Finally we discuss in examples the meaning of the index pairing and our index formula.Comment: 29 page

The index of geometric operators on Lie groupoids

We revisit the cohomological index theorem for elliptic elements in the universal enveloping algebra of a Lie groupoid previously proved by the authors. We prove a Thom isomorphism for Lie algebroids which enables us to rewrite the "topological side" of the index theorem. This results in index formulae for Lie groupoid analogues of the familiar geometric operators on manifolds such as the signature and Dirac operator expressed in terms of the usual characteristic classes in Lie algebroid cohomology.Comment: 15 page

Quantization of Whitney functions

We propose to study deformation quantizations of Whitney functions. To this end, we extend the notion of a deformation quantization to algebras of Whitney functions over a singular set, and show the existence of a deformation quantization of Whitney functions over a closed subset of a symplectic manifold. Under the assumption that the underlying symplectic manifold is analytic and the singular subset subanalytic, we determine that the Hochschild and cyclic homology of the deformed algebra of Whitney functions over the subanalytic subset coincide with the Whitney--de Rham cohomology. Finally, we note how an algebraic index theorem for Whitney functions can be derived.Comment: 10 page

Orbifold cup products and ring structures on Hochschild cohomologies

In this paper we study the Hochschild cohomology ring of convolution algebras associated to orbifolds, as well as their deformation quantizations. In the first case the ring structure is given in terms of a wedge product on twisted polyvectorfields on the inertia orbifold. After deformation quantization, the ring structure defines a product on the cohomology of the inertia orbifold. We study the relation between this product and an $S^1$-equivariant version of the Chen--Ruan product. In particular, we give a de Rham model for this equivariant orbifold cohomology

The Characteristics and Applications of Ceramic Laser Fusion and Ceramic Laser Sintering

The aim of present study is to investigate the possible application of the ceramic parts which are fabricated with the process of Ceramic Laser Fusion or Ceramic Laser Sintering. The experimental results reveal: (1) CLF can lead to a reduction in the porosity of the ceramic part but also can induce micro-cracks. Therefore, this process cannot produce a part with the required strength by a post-process of infiltration; (2) CLS is capable of fabricating a ceramic part with high porosity. By adjusting the slurry formulation and varying the scanning energy, the open porosity can be over 90vol% of the total porosity. After a post-process of infiltration, the density can be increased to 95%; therefore, CLS can apply to produce a part with high strength. Because the high open porosity leads to a good permeability, the process of CLS is suitable for the fabrication of ceramic shell mold.Mechanical Engineerin

Fin loads and control-surface hinge moments measured in full-scale wind-tunnel tests on the X-24A flight vehicle

Fin loads and control surface hinge moments measured in full scale wind tunnel tests on X-24A flight vehicl

Prospect of Making Ceramic Shell Mold by Ceramic Laser Fusion

Manufacturing prototypical castings by conventional investment casting not only takes several weeks, but also is prohibitively expensive. Z Corporation in USA, EOS GmbH and IPT in Germany employ the techniques of 3DP and SLS respectively to make directly ceramic shell molds for metal castings. Although those techniques dramatically reduce time expenditure and production cost, each layer cannot be thinner than 50 µm because of using powder to pave layers. The dimensional accuracy and roughness of the castings still cannot meet the specification of precision casting. Therefore, in this paper the ceramic laser fusion (CLF) was used to pave layers. Each layer can be thinner than 25 µm, so that the step effect can be diminished and the workpiece surface can be smoother; drying time will be shortened dramatically. Moreover, the inherent solid-state support formed by green portion has the capability of preventing upward and downward deformation of the scanned cross sections. In order to make shell mold which meets the roughness requirement (Rq=3.048µm) of the precision casting, following issues have to be further studied: (1) design a proper ceramic shell mold structure, (2) design a paving chamber for paving a complete green layer which can be easily collapsed, (3) cut down drying time, (4) optimize laser scanning process parameters with the smallest distortion, (5) eliminate sunken area, (6) reduce layer thickness to less than13µm, (7) control power to guarantee the energy uniformly absorbed by workpiece, and (8) develop a method which can directly clean green portion in cavity from gate.Mechanical Engineerin

Two-dimensional electron-gas actuation and transduction for GaAs nanoelectromechanical systems

We have fabricated doubly clamped beams from GaAs/AlGaAs quantum-well heterostructures containing a high-mobility two-dimensional electron gas (2DEG). Applying an rf drive to in-plane side gates excites the beam's mechanical resonance through a dipole–dipole mechanism. Sensitive high-frequency displacement transduction is achieved by measuring the ac emf developed across the 2DEG in the presence of a constant dc sense current. The high mobility of the incorporated 2DEG provides low-noise, low-power, and high-gain electromechanical displacement sensing through combined piezoelectric and piezoresistive mechanisms