A computer model of the electrostatic positioning system

Positioning systems based upon electrstatic forces are being developed for the containerless processing of materials that cannot use acoustic or electromagnetic positioning techniques. Currently, electrode configurations for these electrostatic systems are designed on the basis of approximate analytical calculations and past experience. A three dimensional computer model is being developed that will predict the electrostatic fields and forces for a given electrode configuration and will allow for a more rapid evaluation of proposed designs. Early results of this model are presented

A general method to construct invariant PDEs on homogeneous manifolds

Let M = G/H be an (n + 1)-dimensional homogeneous manifold and Jk(n,M) =: Jk be the manifold of k-jets of hypersurfaces of M. The Lie group G acts naturally on each Jk. A G-invariant partial differential equation of order k for hypersurfaces of M (i.e., with n independent variables and 1 dependent one) is defined as a G-invariant hypersurface E of Jk. We describe a general method for constructing such invariant partial differential equations for k>1. The problem reduces to the description of hypersurfaces, in a certain vector space, which are invariant with respect to the linear action of the stability subgroup H(k-1) of the (k-1)-prolonged action of G. We apply this approach to describe invariant partial differential equations for hypersurfaces in the Euclidean space n+1 and in the conformal space n+1. Our method works under some mild assumptions on the action of G, namely: A1) the group G must have an open orbit in Jk-1, and A2) the stabilizer H(k-1) in G of the fiber Jk → Jk-1 must factorize via the group of translations of the fiber itself

Coarse distance from dynamically convex to convex

Chaidez and Edtmair have recently found the first example of dynamically convex domains in $\mathbb R^4$ that are not symplectomorphic to convex domains (called symplectically convex domains), answering a long-standing open question. In this paper, we discover new examples of such domains without referring to Chaidez-Edtmair's criterion. We also show that these domains are arbitrarily far from the set of symplectically convex domains in $\mathbb R^4$ with respect to the coarse symplectic Banach-Mazur distance by using an explicit numerical criterion for symplectic non-convexity.Comment: 18 pages, 7 figure

Methyl group dynamics in a confined glass

We present a neutron scattering investigation on methyl group dynamics in glassy toluene confined in mesoporous silicates of different pore sizes. The experimental results have been analysed in terms of a barrier distribution model, such a distribution following from the structural disorder in the glassy state. Confinement results in a strong decreasing of the average rotational barrier in comparison to the bulk state. We have roughly separated the distribution for the confined state in a bulk-like and a surface-like contribution, corresponding to rotors at a distance from the pore wall respectively larger and smaller than the spatial range of the interactions which contribute to the rotational potential for the methyl groups. We have estimated a distance of 7 Amstrong as a lower limit of the interaction range, beyond the typical nearest-neighbour distance between centers-of-mass (4.7 Amstrong).Comment: 5 pages, 3 figures. To be published in European Physical Journal E Direct. Proceedings of the 2nd International Workshop on Dynamics in Confinemen

On Two Theorems About Symplectic Reflection Algebras

We give a new proof and an improvement of two Theorems of J. Alev, M.A. Farinati, T. Lambre and A.L. Solotar : the first one about Hochschild cohomology spaces of some twisted bimodules of the Weyl algebra W and the second one about Hochschild cohomology spaces of the smash product G * W (G a finite subgroup of SP(2n)), and as an application, we then give a new proof of a Theorem of P. Etingof and V. Ginzburg, which shows that the Symplectic Reflection Algebras are deformations of G * W (and, in fact, all possible ones).Comment: corrected typo

Corner-Cube Retroreflector Instrument for Advanced Lunar Laser Ranging

A paper describes how, based on a structural-thermal-optical-performance analysis, it has been determined that a single, large, hollow corner cube (170- mm outer diameter) with custom dihedral angles offers a return signal comparable to the Apollo 11 and 14 solid-corner-cube arrays (each consisting of 100 small, solid corner cubes), with negligible pulse spread and much lower mass. The design of the corner cube, and its surrounding mounting and casing, is driven by the thermal environment on the lunar surface, which is subject to significant temperature variations (in the range between 70 and 390 K). Therefore, the corner cube is enclosed in an insulated container open at one end; a narrow-bandpass solar filter is used to reduce the solar energy that enters the open end during the lunar day, achieving a nearly uniform temperature inside the container. Also, the materials and adhesive techniques that will be used for this corner-cube reflector must have appropriate thermal and mechanical characteristics (e.g., silica or beryllium for the cube and aluminum for the casing) to further reduce the impact of the thermal environment on the instrument's performance. The instrument would consist of a single, open corner cube protected by a separate solar filter, and mounted in a cylindrical or spherical case. A major goal in the design of a new lunar ranging system is a measurement accuracy improvement to better than 1 mm by reducing the pulse spread due to orientation. While achieving this goal, it was desired to keep the intensity of the return beam at least as bright as the Apollo 100-corner-cube arrays. These goals are met in this design by increasing the optical aperture of a single corner cube to approximately 170 mm outer diameter. This use of an "open" corner cube allows the selection of corner cube materials to be based primarily on thermal considerations, with no requirements on optical transparency. Such a corner cube also allows for easier pointing requirements, because there is no dependence on total internal reflection, which can fail off-axis

Closedness of star products and cohomologies

We first review the introduction of star products in connection with deformations of Poisson brackets and the various cohomologies that are related to them. Then we concentrate on what we have called ``closed star products" and their relations with cyclic cohomology and index theorems. Finally we shall explain how quantum groups, especially in their recent topological form, are in essence examples of star products.Comment: 16 page

The Hopf Algebra of Renormalization, Normal Coordinates and Kontsevich Deformation Quantization

Using normal coordinates in a Poincar\'e-Birkhoff-Witt basis for the Hopf algebra of renormalization in perturbative quantum field theory, we investigate the relation between the twisted antipode axiom in that formalism, the Birkhoff algebraic decomposition and the universal formula of Kontsevich for quantum deformation.Comment: 21 pages, 15 figure