Invariance principles for switched systems with restrictions

In this paper we consider switched nonlinear systems under average dwell time switching signals, with an otherwise arbitrary compact index set and with additional constraints in the switchings. We present invariance principles for these systems and derive by using observability-like notions some convergence and asymptotic stability criteria. These results enable us to analyze the stability of solutions of switched systems with both state-dependent constrained switching and switching whose logic has memory, i.e., the active subsystem only can switch to a prescribed subset of subsystems.Comment: 29 pages, 2 Appendixe

A new method to find the potential center of N-body systems

We present a new and fast method to nd the potential center of an N-body distribution. The method uses an iterative algorithm which exploits the fact that the gradient of the potential is null at its center: it uses a smoothing radius to avoid getting trapped in secondary minima. We have tested this method on several random realizations of King models (in which the numerical computation of this center is rather dicult, due to the constant density within their cores), and com- pared its performance and accuracy against a more straightforward, but computer intensive method, based on cartesian meshes of increasing spatial resolution. In all cases, both methods converged to the same center, within the mesh resolution, but the new method is two orders of magnitude faster. We have also tested the method with one astronomical problem: the evolu- tion of a 105 particle King model orbiting around a xed potential that represents our Galaxy. We used a spherical harmonics expansion N-body code, in which the potential center determination is crucial for the correct force computation. We compared this simulation with another one in which a method previously used to determine the expansion center is employed (White 1983). Our routine gives better results in energy conservation and mass loss.Fil: Aguilar, L. A.. Universidad Nacional Autonoma de Mexico. Instituto de Astronomia; MéxicoFil: Cruz, F.. Universidad Nacional Autonoma de Mexico. Instituto de Astronomia; MéxicoFil: Carpintero, Daniel Diego. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentin

Infrared finite ghost propagator in the Feynman gauge

We demonstrate how to obtain from the Schwinger-Dyson equations of QCD an infrared finite ghost propagator in the Feynman gauge. The key ingredient in this construction is the longitudinal form factor of the non-perturbative gluon-ghost vertex, which, contrary to what happens in the Landau gauge, contributes non-trivially to the gap equation of the ghost. The detailed study of the corresponding vertex equation reveals that in the presence of a dynamical infrared cutoff this form factor remains finite in the limit of vanishing ghost momentum. This, in turn, allows the ghost self-energy to reach a finite value in the infrared, without having to assume any additional properties for the gluon-ghost vertex, such as the presence of massless poles. The implications of this result and possible future directions are briefly outlined.Comment: 22 pages, 9 figure

Rhythmic firing patterns in SCN: The role of circuit interactions

The suprachiasmatic nucleus (SCN) is believed to contain the main generator of circadian rhythmicity in mammals. In order to obtain further functional details of this, electrophysiological extracellular measurements in vitro were made. By means of an interspike interval distribution analysis, it is shown that there is a novel kind of neuronal firing pattern: the harmonic pattern. From these observations, we have developed a theoretical model based on possible filtering processes occurring during synaptic transmission. The model suffices to infer that regular ultradian oscillators could be an emergent property of circuit interactions of cells in the suprachiasmatic nucleus

Gluon and ghost propagators in the Landau gauge: Deriving lattice results from Schwinger-Dyson equations

We show that the application of a novel gauge invariant truncation scheme to the Schwinger-Dyson equations of QCD leads, in the Landau gauge, to an infrared finite gluon propagator and a divergent ghost propagator, in qualitative agreement with recent lattice data.Comment: 9 pages, 2 figures; v3: typos corrected; v2: discussion on numerical results expanded, considerations about the Kugo-Ojima confinement criterion adde

Gluon mass generation without seagull divergences

Dynamical gluon mass generation has been traditionally plagued with seagull divergences, and all regularization procedures proposed over the years yield finite but scheme-dependent gluon masses. In this work we show how such divergences can be eliminated completely by virtue of a characteristic identity, valid in dimensional regularization. The ability to trigger the aforementioned identity hinges crucially on the particular Ansatz employed for the three-gluon vertex entering into the Schwinger-Dyson equation governing the gluon propagator. The use of the appropriate three-gluon vertex brings about an additional advantage: one obtains two separate (but coupled) integral equations, one for the effective charge and one for the gluon mass. This system of integral equations has a unique solution, which unambiguously determines these two quantities. Most notably, the effective charge freezes in the infrared, and the gluon mass displays power-law running in the ultraviolet, in agreement with earlier considerations.Comment: 37 pages, 9 figures; minor typos corrected and a few brief explanatory remarks adde