Toward a Formal Semantics for Autonomic Components

Autonomic management can improve the QoS provided by parallel/ distributed applications. Within the CoreGRID Component Model, the autonomic management is tailored to the automatic - monitoring-driven - alteration of the component assembly and, therefore, is defined as the effect of (distributed) management code. This work yields a semantics based on hypergraph rewriting suitable to model the dynamic evolution and non-functional aspects of Service Oriented Architectures and component-based autonomic applications. In this regard, our main goal is to provide a formal description of adaptation operations that are typically only informally specified. We contend that our approach makes easier to raise the level of abstraction of management code in autonomic and adaptive applications.Comment: 11 pages + cover pag

Coloured extension of GL_q(2) and its dual algebra

We address the problem of duality between the coloured extension of the quantised algebra of functions on a group and that of its quantised universal enveloping algebra i.e. its dual. In particular, we derive explicitly the algebra dual to the coloured extension of GL_q(2) using the coloured RLL relations and exhibit its Hopf structure. This leads to a coloured generalisation of the R-matrix procedure to construct a bicovariant differential calculus on the coloured version of GL_q(2). In addition, we also propose a coloured generalisation of the geometric approach to quantum group duality given by Sudbery and Dobrev.Comment: 10 pages LaTeX. Talk given at the "XXIII International Colloquium on Group Theoretical Methods in Physics", July 31 - August 05, 2000, Dubna (Russia); to appear in the proceeding

Contraction of the G_r,s Quantum Group to its Nonstandard analogue and corresponding Coloured Quantum Groups

The quantum group G_r,s provides a realisation of the two parameter quantum GL_p,q(2) which is known to be related to the two parameter nonstandard GL_hh'(2) group via a contraction method. We apply the contraction procedure to G_r,s and obtain a new Jordanian quantum group G_m,k. Furthermore, we provide a realisation of GL_h,h'(2) in terms of G_m,k. The contraction procedure is then extended to the coloured quantum group GL_r{\lambda,\mu}(2) to yield a new Jordanian quantum group GL_m{\lambda,\mu}(2). Both G_r,s and G_m,k are then generalised to their coloured versions which inturn provide similar realisations of GL_r{\lambda,\mu}(2) and GL_m{\lambda,\mu}(2).Comment: 22 pages LaTeX, to be published in J. Math. Phy

Kinetic dissipation and anisotropic heating in a turbulent collisionless plasma

The kinetic evolution of the Orszag-Tang vortex is studied using collisionless hybrid simulations. In the magnetohydrodynamic regime this vortex leads rapidly to broadband turbulence. Significant differences from MHD arise at small scales, where the fluid scale energy dissipates into heat almost exclusively through the magnetic field because the protons are decoupled from the magnetic field. Although cyclotron resonance is absent, the protons heat preferentially in the plane perpendicular to the mean field, as in the corona and solar wind. Effective transport coefficients are calculated.Comment: 4 pages, 4 figures. Submitted to PR

Exact results for Casimir interactions between dielectric bodies: The weak-coupling or van der Waals Limit

In earlier papers we have applied multiple scattering techniques to calculate Casimir forces due to scalar fields between different bodies described by delta function potentials. When the coupling to the potentials became weak, closed-form results were obtained. We simplify this weak-coupling technique and apply it to the case of tenuous dielectric bodies, in which case the method involves the summation of van der Waals (Casimir-Polder) interactions. Once again exact results for finite bodies can be obtained. We present closed formulas describing the interaction between spheres and between cylinders, and between an infinite plate and a retangular slab of finite size. For such a slab, we consider the torque acting on it, and find non-trivial equilibrium points can occur.Comment: 4 pages, 3 figure

A (p,q) Deformation of the Universal Enveloping Superalgebra U(osp(2/2))

We investigate a two parameter quantum deformation of the universal enveloping orthosymplectic superalgebra U(osp(2/2)) by extending the Faddeev-Reshetikhin-Takhtajan formalism to the supersymetric case. It is shown that $U_{p,q}(osp(2/2))$ possesses a non-commutative, non-cocommutative Hopf algebra structure. All the results are expressed in the standard form using quantum Chevalley basis.Comment: 8 pages; IC/93/41

Reducible Correlations in Dicke States

We apply a simple observation to show that the generalized Dicke states can be determined from their reduced subsystems. In this framework, it is sufficient to calculate the expression for only the diagonal elements of the reudced density matrices in terms of the state coefficients. We prove that the correlation in generalized Dicke states $|GD_N^{(\ell)}>$ can be reduced to $2\ell$-partite level. Application to the Quantum Marginal Problem is also discussed.Comment: 12 pages, single column; accepted in J. Phys. A as FT