The blocks of the Brauer algebra in characteristic zero

We determine the blocks of the Brauer algebra in characteristic zero. We also give information on the submodule structure of standard modules for this algebra

Noncommutative associative superproduct for general supersymplectic forms

We define a noncommutative and nonanticommutative associative product for general supersymplectic forms, allowing the explicit treatment of non(anti)commutative field theories from general nonconstant string backgrounds like a graviphoton field. We propose a generalization of deformation quantization a la Fedosov to superspace, which considers noncommutativity in the tangent bundle instead of base space, by defining the Weyl super product of elements of Weyl super algebra bundles. Super Poincare symmetry is not broken and chirality seems not to be compromised in our formulation. We show that, for a particular case, the projection of the Weyl super product to the base space gives rise the Moyal product for non(anti)commutative theories.Comment: 22 pages, revtex4. References added. Comments added. Includes additional theorem proof

Discrete variational integrators and optimal control theory

A geometric derivation of numerical integrators for optimal control problems is proposed. It is based in the classical technique of generating functions adapted to the special features of optimal control problems.Comment: 17 page

Tulczyjew's triples and lagrangian submanifolds in classical field theories

In this paper the notion of Tulczyjew's triples in classical mechanics is extended to classical field theories, using the so-called multisymplectic formalism, and a convenient notion of lagrangian submanifold in multisymplectic geometry. Accordingly, the dynamical equations are interpreted as the local equations defining these lagrangian submanifolds.Comment: 29 page

Geometric numerical integration of nonholonomic systems and optimal control problems

A geometric derivation of numerical integrators for nonholonomic systems and optimal control problems is obtained. It is based in the classical technique of generating functions adapted to the special features of nonholonomic systems and optimal control problems.Comment: 6 pages, 1 figure. Submitted to IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control, Sevilla 200

Spinodal phase separation in semi-interpenetrating polymer networks - polystyrene-cross-polymethacrylate

Morphology control in semi-interpenetrating polymer networks has been achieved by means of a two-step process, separating morphology formation and polymerization/crosslinking. Phase textures formed during spinodal liquid/liquid demixing of a solution of atactic polystyrene in methacrylate monomers were arrested by thermoreversible gelation of the polymer-rich phase as this phase passed its glass transition temperature. The phase separated structure was permanently stabilized by low-temperature crosslinking ultraviolet (UV) polymerization of the methacrylate monomer, and studied by transmission electron microscopy. Thus, it was directly observed how the initial demixing process depended on the initial viscosity of the polymer solution and the mode of quenching. Arrest of the earliest stage of spinodal demixing resulted in separated domains of 0.05-0.08 m thickness, which were separated by a distance of the spinodal wavelength . A cocontinuous network only developed in a relatively late stage of demixing

On Some Stability Properties of Compactified D=11 Supermembranes

We desribe the minimal configurations of the bosonic membrane potential, when the membrane wraps up in an irreducible way over $S^{1}\times S^{1}$. The membrane 2-dimensional spatial world volume is taken as a Riemann Surface of genus $g$ with an arbitrary metric over it. All the minimal solutions are obtained and described in terms of 1-forms over an associated U(1) fiber bundle, extending previous results. It is shown that there are no infinite dimensional valleys at the minima.Comment: 12 pages,Latex2e lamuphys, Invited talk at International Seminar "Supersymetry and Quantum Symmetries", Dubn

Influence of the bulk and surface morphology on adhesion of polystyrene-inter-poly-cross-2-ethylhexyl-methacrylate films and particles

The adhesion behavior of semi-interpenetrating polymer networks (semi-IPNs) of linear polystyrene (PS) in crosslinked poly-2-ethylhexylmethacrylate (EHMA) was studied by variation of the bulk and surface morphology, i.e., domain size, continuity, and concentration in the domains. Semi-IPNs were prepared by liquid-liquid demixing upon cooling of a homogeneous solution of PS in methacrylate monomer, followed by gelation of the PS-rich phase and UV polymerization of the methacrylate resin. Welding of films allowed the preparation of larger objects provided that (1) the samples were phase separated to a high degree and contained domains with a high PS concentration (>90%) and (2) polystyrene was present at the interface. For semi-IPN films, a linear dependence of the adhesion strength on the (crack healing time)1/4 was obtained. Based on these considerations, a process was developed to obtain melt-processable semi-IPN particles, by quenching droplets of the polymer solution into a cold liquid. These particles obtained a PS-rich skin layer and showed good adhesion after blending with a thermoplast

Treatment of the infrared contribution: NLO QED evolution as a pedagogic example

We show that the conventional prescription used for DGLAP parton evolution at NLO has an inconsistent treatment of the contribution from the infrared (IR) region. We illustrate the problem by studying the simple example of QED evolution, treating the electron and photon as partons. The deficiency is not present in a physical approach which removes the IR divergency and allows calculation in the normal 4-dimensional space.Comment: 15 pages, 2 figures, erratum at the end of the articl