Admissible semi-linear representations

The category of admissible (in the appropriately modified sense of representation theory of totally disconnected groups) semi-linear representations of the automorphism group of an algebraically closed extension of infinite transcendence degree of the field of algebraic complex numbers is described

Nontrivial classes in H∗(Imb(S1,Rn))H^*(Imb(S^1,\R^n)) from nontrivalent graph cocycles

We construct nontrivial cohomology classes of the space $Imb(S^1,\R^n)$ of imbeddings of the circle into $\R^n$, by means of Feynman diagrams. More precisely, starting from a suitable linear combination of nontrivalent diagrams, we construct, for every even number $n\geq 4$, a de Rham cohomology class on $Imb(S^1,\R^n)$. We prove nontriviality of these classes by evaluation on the dual cycles.Comment: 10 pages, 11 figures. V2: minor changes, typos correcte

On the naturality of the Mathai-Quillen formula

We give an alternative proof for the Mathai-Quillen formula for a Thom form using its natural behaviour with respect to fiberwise integration. We also study this phenomenon in general context.Comment: 6 page

Noncommutative generalization of SU(n)-principal fiber bundles: a review

This is an extended version of a communication made at the international conference ``Noncommutative Geometry and Physics'' held at Orsay in april 2007. In this proceeding, we make a review of some noncommutative constructions connected to the ordinary fiber bundle theory. The noncommutative algebra is the endomorphism algebra of a SU(n)-vector bundle, and its differential calculus is based on its Lie algebra of derivations. It is shown that this noncommutative geometry contains some of the most important constructions introduced and used in the theory of connections on vector bundles, in particular, what is needed to introduce gauge models in physics, and it also contains naturally the essential aspects of the Higgs fields and its associated mechanics of mass generation. It permits one also to extend some previous constructions, as for instance symmetric reduction of (here noncommutative) connections. From a mathematical point of view, these geometrico-algebraic considerations highlight some new point on view, in particular we introduce a new construction of the Chern characteristic classes

Equivariant Symplectic Geometry of Gauge Fixing in Yang-Mills Theory

The Faddeev-Popov gauge fixing in Yang-Mills theory is interpreted as equivariant localization. It is shown that the Faddeev-Popov procedure amounts to a construction of a symplectic manifold with a Hamiltonian group action. The BRST cohomology is shown to be equivalent to the equivariant cohomology based on this symplectic manifold with Hamiltonian group action. The ghost operator is interpreted as a (pre)symplectic form and the gauge condition as the moment map corresponding to the Hamiltonian group action. This results in the identification of the gauge fixing action as a closed equivariant form, the sum of an equivariant symplectic form and a certain closed equivariant 4-form which ensures convergence. An almost complex structure compatible with the symplectic form is constructed. The equivariant localization principle is used to localize the path integrals onto the gauge slice. The Gribov problem is also discussed in the context of equivariant localization principle. As a simple illustration of the methods developed in the paper, the partition function of N=2 supersymmetric quantum mechanics is calculated by equivariant localizationComment: 46 pages, added remarks, typos and references correcte

An Evaluation of the Risk and Return Associated with Four Cattle Feeding Alternatives in Utah

This publication serves as an evaluation of the risk and return associated with four cattle feeding alternatives

Phase separation on the sphere: Patchy particles and self-assembly

Motivated by observations of heterogeneous domain structure on the surface of cells, we consider a minimal model to describe the dynamics of phase separation on the surface of a spherical particle. Finite-size effects on the curved particle surface lead to the formation of long-lived, metastable states for which the density is distributed in patches over the particle surface. We study the time evolution and stability of these states as a function of both the particle size and the thermodynamic parameters. Finally, by connecting our findings with studies of patchy particles, we consider the implications for self-assembly in many-particle systems

Biocide Dosing Strategies for Biofilm Control

In order to reduce environmental impact of biocide use for the control of biofilm formation in cooling water circuits, “environmentally friendly” biocides have been developed, but they are generally more expensive than the more traditional chemicals. It is imperative therefore, that the minimum quantity of biocide is employed, so that costs are kept to a minimum. To achieve this objective optimum dosing strategies are required. Using apilot plant in conjunction with a monoculture of Pseudomonas fluorecsens as the biofouling bacterium, tests were carried out using a proprietary biocide, to investigate the effects of dose concentration, duration and frequency of dosing and fluid mechanics on biofilm control. With four 15 minute applications per day, at a peak concentration of 16.8 mg/l, it was not possible to inhibit biofilm development. Control was effected however, by doubling the peak concentration using a short dosing period. Concentration, as would be expected, was shown to be a critical factor for control. A boicide concentration below that for growth inhibition, seemed to enhance biofilm formation! Increase frequency of dosing is only effective if the concentration employed is biofilm growth inhibiting