Equivariant K-theory of compact Lie group actions with maximal rank isotropy

Let G denote a compact connected Lie group with torsion-free fundamental group acting on a compact space X such that all the isotropy subgroups are connected subgroups of maximal rank. Let $T\subset G$ be a maximal torus with Weyl group W. If the fixed-point set $X^T$ has the homotopy type of a finite W-CW complex, we prove that the rationalized complex equivariant K-theory of X is a free module over the representation ring of G. Given additional conditions on the W-action on the fixed-point set $X^T$ we show that the equivariant K-theory of X is free over R(G). We use this to provide computations for a number of examples, including the ordered n-tuples of commuting elements in G with the conjugation action.Comment: Accepted for publication by the Journal of Topolog

Twisted equivariant K-theory of compact Lie group actions with maximal rank isotropy

We consider twisted equivariant K--theory for actions of a compact Lie group $G$ on a space $X$ where all the isotropy subgroups are connected and of maximal rank. We show that the associated rational spectral sequence \`a la Segal has a simple $E_2$--term expressible as invariants under the Weyl group of $G$. Namely, if $T$ is a maximal torus of $G$, they are invariants of the $\pi_1(X^T)$-equivariant Bredon cohomology of the universal cover of $X^T$ with suitable coefficients. In the case of the inertia stack $\Lambda Y$ this term can be expressed using the cohomology of $Y^T$ and algebraic invariants associated to the Lie group and the twisting. A number of calculations are provided. In particular, we recover the rational Verlinde algebra when $Y=\{*\}$.Comment: To appear in Journal of Mathematical Physics. Some mistakes have been corrected in Section

Exponential convergence to equilibrium in cellular automata asymptotically emulating identity

We consider the problem of finding the density of 1's in a configuration obtained by $n$ iterations of a given cellular automaton (CA) rule, starting from disordered initial condition. While this problems is intractable in full generality for a general CA rule, we argue that for some sufficiently simple classes of rules it is possible to express the density in terms of elementary functions. Rules asymptotically emulating identity are one example of such a class, and density formulae have been previously obtained for several of them. We show how to obtain formulae for density for two further rules in this class, 160 and 168, and postulate likely expression for density for eight other rules. Our results are valid for arbitrary initial density. Finally, we conjecture that the density of 1's for CA rules asymptotically emulating identity always approaches the equilibrium point exponentially fast.Comment: 20 pages, 4 figures, 2 table

Very large stochastic resonance gains in finite sets of interacting identical subsystems driven by subthreshold rectangular pulses

We study the phenomenon of nonlinear stochastic resonance (SR) in a complex noisy system formed by a finite number of interacting subunits driven by rectangular pulsed time periodic forces. We find that very large SR gains are obtained for subthreshold driving forces with frequencies much larger than the values observed in simpler one-dimensional systems. These effects are explained using simple considerations.Comment: 4 pages, 5 figures. to appear in Phys. Rev.

Design and manufacturing of master alloys for sintering activation in high performance structural parts

Nowadays, the development of high performance structural parts, is limited by the fact that the alloying systems are being modifying by requirements associated to envorimental guideline as well as to the increase in the price of raw materials. The use of masteralloys allows to activate the mass transport processes during sintering with a minimum modification of final composition (low cost) acting on densification, and hence, on final properties. The research group of “Powder Technology” from Carlos III University, has a wide experience and qualification on the design of new alloying systems and in manufacturing the powders by atomization and mechanical alloying techniques. The Group is looking for companies interested in technical cooperation or manufacturing agreement

Equivariant complex bundles, fixed points and equivariant unitary bordism

We study the fixed points of the universal G-equivariant n-dimensional complex vector bundle and obtain a decomposition formula in terms of twisted equivariant universal complex vector bundles of smaller dimension. We use this decomposition to describe the fixed points of the complex equivariant K-theory spectrum and the equivariant unitary bordism groups for adjacent families of subgroups.Comment: Corrected version. To appear in AG&T. 27 page