Performance of CDF for B physics

Hadron colliders can be an abundant source of heavy flavor quarks, but pose a challenge to isolate the physics signals from the high backgrounds. The upgraded CDF II detector, with its precise tracking capabilities and powerful trigger system, is well equipped for this task. The detector is described with an emphasis on actual performance and on techniques to maximize the heavy flavor yield. Some first heavy flavor results are summarized.Comment: Invited talk at the Workshop on the CKM Unitarity Triangle, IPPP Durham, April 2003 (eConf C0304052). 4 pages LaTeX, 2 eps figure

Harmonic analysis of oscillators through standard numerical continuation tools

In this paper, we describe a numerical continuation method that enables harmonic analysis of nonlinear periodic oscillators. This method is formulated as a boundary value problem that can be readily implemented by resorting to a standard continuation package - without modification - such as AUTO, which we used. Our technique works for any kind of oscillator, including electronic, mechanical and biochemical systems. We provide two case studies. The first study concerns itself with the autonomous electronic oscillator known as the Colpitts oscillator, and the second one with a nonlinear damped oscillator, a non-autonomous mechanical oscillator. As shown in the case studies, the proposed technique can aid both the analysis and the design of the oscillators, by following curves for which a certain constraint, related to harmonic analysis, is fulfilled.Comment: 20 pages, 4 figure

Bifurcations of global reinjection orbits near a saddle-node Hopf bifurcation

The saddle-node Hopf bifurcation (SNH) is a generic codimension-two bifurcation of equilibria of vector fields in dimension at least three. It has been identified as an organizing centre in numerous vector field models arising in applications. We consider here the case that there is a global reinjection mechanism, because the centre manifold of the zero eigenvalue returns to a neighbourhood of the equilibrium. Such a SNH bifurcation with global reinjection occurs naturally in applications, most notably in models of semiconductor lasers