Development of optical modulators for measurements of solar magnetic fields

The measurement of polarized light allows solar astronomers to infer the magnetic field on the Sun. The accuracy of these measurements is dependent on the stable retardation characteristics of the polarization modulators used to minimize the atmospheric effects seen in ground-based observations. This report describes the work by the Space Science Laboratory at Marshall Space Flight Center to improve two types of polarization modulators. As a result, the timing characteristics for both electrooptic crystals (KD*Ps) and liquid crystal devices (LCDs) have been studied and will be used to enhance the capabilities of the MSFC Vector Magnetograph

Duality Symmetries and G^{+++} Theories

We show that the non-linear realisations of all the very extended algebras G^{+++}, except the B and C series which we do not consider, contain fields corresponding to all possible duality symmetries of the on-shell degrees of freedom of these theories. This result also holds for G_2^{+++} and we argue that the non-linear realisation of this algebra accounts precisely for the form fields present in the corresponding supersymmetric theory. We also find a simple necessary condition for the roots to belong to a G^{+++} algebra.Comment: 35 pages. v2: 2 appendices added, other minor corrections. v3: tables corrected, other minor changes, one appendix added, refs. added. Version published in Class. Quant. Gra

E_11 and M Theory

We argue that eleven dimensional supergravity can be described by a non-linear realisation based on the group E_{11}. This requires a formulation of eleven dimensional supergravity in which the gravitational degrees of freedom are described by two fields which are related by duality. We show the existence of such a description of gravity.Comment: 21 pages, some typos corrected and two references adde

Heterobimetallic Complexes of Rhenium and Zinc: Potential Catalysts for Homogeneous Syngas Conversion

6-(Diphenylphosphino)-2,2′-bipyridine (PNN) coordinates to rhenium carbonyls in both κ^1(P) and κ^2(N,N) modes; in the former, the free bpy moiety readily binds to zinc alkyls and halides. [Re(κ^1(P)-PNN)(CO)_5][OTf] reacts with dialkylzinc reagents to form [Re(κ^1(P)-PNN·ZnR)(CO)_4(μ_(2-)C(O)R)][OTf] (R = Me, Et, Bn), in which an alkyl group has been transferred to a carbonyl carbon and the resulting monoalkyl Zn is bound both to the bpy nitrogens and the acyl oxygen. ZnCl_2 binds readily to the bpy group in Re(κ^1(P)-PNN)(CO)_4Me, and the resulting adduct undergoes facile migratory insertion, assisted by the Lewis acidic pendent Zn, to yield Re(κ^1(P)-PNN·ZnCl)(μ_(2-)Cl)(CO)_3(μ_(2-)C(O)Me), in which one of the chlorides occupies the sixth coordination site on Re. Migratory insertion is inhibited by THF or other ethers that can coordinate to ZnCl_2. Migratory insertion is also observed for Re(κ1(P)-PNN)(CO)_4(CH_2Ph) but not for Re(κ^1(P)-PNN)(CO)_4(CH_2OCH_3); coordination of the methoxy oxygen to Zn appears to block its ability to coordinate to the carbonyl oxygen and facilitate migratory insertion. Intramolecular Lewis acid promoted hydride transfer from [(dmpe)_2PtH][PF_6] to a carbonyl in [Re(κ^1(P)-PNN)(CO)_5][OTf] results in formation of a Re–formyl species; additional hydride transfer leads to a novel Re–Zn-bonded product along with some formal dehyde

The E_{11} origin of all maximal supergravities

Starting from the eleven dimensional E_{11} non-linear realisation of M-theory we compute all possible forms, that is objects with totally antisymmetrised indices, that occur in four dimensions and above as well as all the 1-forms and 2-forms in three dimensions. In any dimension D, the D-1-forms lead to maximal supergravity theories with cosmological constants and they are in precise agreement with the patterns of gauging found in any dimension using supersymmetry. The D-forms correspond to the presence of space-filling branes which are crucial for the consistency of orientifold models and have not been derived from an alternative approach, with the exception of the 10-dimensional case. It follows that the gaugings of supergravities and the spacetime-filling branes possess an eleven dimensional origin within the E_{11} formulation of M-theory. This and previous results very strongly suggest that all the fields in the adjoint representation of E_{11} have a physical interpretation.Comment: 54 page

Asynchronous Variational Integrators

We describe a new class of asynchronous variational integrators (AVI) for nonlinear elastodynamics. The AVIs are distinguished by the following attributes: (i) The algorithms permit the selection of independent time steps in each element, and the local time steps need not bear an integral relation to each other; (ii) the algorithms derive from a spacetime form of a discrete version of Hamilton’s variational principle. As a consequence of this variational structure, the algorithms conserve local momenta and a local discrete multisymplectic structure exactly. To guide the development of the discretizations, a spacetime multisymplectic formulation of elastodynamics is presented. The variational principle used incorporates both configuration and spacetime reference variations. This allows a unified treatment of all the conservation properties of the system.A discrete version of reference configuration is also considered, providing a natural definition of a discrete energy. The possibilities for discrete energy conservation are evaluated. Numerical tests reveal that, even when local energy balance is not enforced exactly, the global and local energy behavior of the AVIs is quite remarkable, a property which can probably be traced to the symplectic nature of the algorith

N=(0,2) Deformation of the N=(2,2) Wess-Zumino Model in Two Dimensions

We construct a simple N=(0,2) deformation of the two-dimensional Wess-Zumino model. In addition to superpotential, it includes a "twisted" superpotential. Supersymmetry may or may not be spontaneously broken at the classical level. In the latter case an extra right-handed fermion field \zeta_R involved in the N=(0,2) deformation plays the role of Goldstino.Comment: 6 pages; v2: 3 references added; final version accepted for publication in PR