Dualisation of the D=7 Heterotic String

The dualisation and the first-order formulation of the D=7 abelian Yang-Mills supergravity which is the low energy effective limit of the D=7 fully Higssed heterotic string is discussed. The non-linear coset formulation of the scalars is enlarged to include the entire bosonic sector by introducing dual fields and by constructing the Lie superalgebra which generates the dualized coset element.Comment: 20 page

The One Loop Effective Super-Potential and Non-Holomorphicity

We calculate the Kahlerian and the lowest order non-Kahlerian contributions to the one loop effective superpotential using super-Feynman graphs in the massless Wess-Zumino Model, the massive Wess-Zumino Model and N=1, U(1) gauge theory. We also calculate the Kahlerian term in Yang-Mills Theory for a general gauge group. Using this latter result we find the one loop Kahlerian contribution for N=2 Yang-Mills Theory in terms of N=1 superfields and we show that it can only come from non-holomorphic contributions to the N=2 effective potential.Comment: LaTeX, 10 pages, 7 figures, uses bezier.sty and ifthen.sty. First amendment. The results are extended to include the Kahlerian term for a general renormalisable N=1 supersymmetric theory, containing Wess-Zumino and Yang-Mills multiplets with a cubic superpotential. One reference has been changed and one has been added. Second amendment. One acknowledgment has been altered in the `note added in proof

Representations of G+++ and the role of space-time

We consider the decomposition of the adjoint and fundamental representations of very extended Kac-Moody algebras G+++ with respect to their regular A type subalgebra which, in the corresponding non-linear realisation, is associated with gravity. We find that for many very extended algebras almost all the A type representations that occur in the decomposition of the fundamental representations also occur in the adjoint representation of G+++. In particular, for E8+++, this applies to all its fundamental representations. However, there are some important examples, such as An+++, where this is not true and indeed the adjoint representation contains no generator that can be identified with a space-time translation. We comment on the significance of these results for how space-time can occur in the non-linear realisation based on G+++. Finally we show that there is a correspondence between the A representations that occur in the fundamental representation associated with the very extended node and the adjoint representation of G+++ which is consistent with the interpretation of the former as charges associated with brane solutions.Comment: 45 pages, 9 figures, 9 tables, te

Dualisation of the Salam-Sezgin D=8 Supergravity

The first-order formulation of the Salam-Sezgin D=8 supergravity coupled to N vector multiplets is discussed. The non-linear realization of the bosonic sector of the D=8 matter coupled Salam-Sezgin supergravity is introduced by the dualisation of the fields and by constructing the Lie superalgebra of the symmetry group of the doubled field strength.Comment: 15 page

Dualisation of the D=9 Matter Coupled Supergravity

We perform the bosonic dualisation of the matter coupled N=1, D=9 supergravity. We derive the Lie superalgebra which parameterizes the coset map whose Cartan form realizes the second-order bosonic field equations. Following the non-linear coset construction we present the first-order formulation of the bosonic field equations as a twisted self-duality condition.Comment: 16 page

An Evaluation of Non-Stochastic Lattice Structures Fabricated Via Electron Beam Melting

Metal foam structures have many applications and can be used as structural supports, heat exchangers, shock absorbers, and implant materials. Stochastic metal foams having different cell sizes and densities have been commercially available for a number of years. This paper addresses a different type of foams which are known as non-stochastic foams, or lattice structures. These foams have a well defined repeating unit cell structure rather than the random cell structure in commercially available stochastic foams. The paper reports on preliminary research on the fabrication of non-stochastic Ti-6Al-4V alloy foams using the Electron Beam Melting process. Behavior of the structures in compression, bending, and low cycle repeating load tests are discussed, and recommendations about cell geometry and processing conditions are made.Mechanical Engineerin