Coexistence of periods in a bisecting bifurcation

The inner structure of the attractor appearing when the Varley-Gradwell-Hassell population model bifurcates from regular to chaotic behaviour is studied. By algebraic and geometric arguments the coexistence of a continuum of neutrally stable limit cycles with different periods in the attractor is explained.Comment: 13 pages, 5 figure

Absolute kinematics of radio source components in the complete S5 polar cap sample. III. First wide-field high-precision astrometry at 15.4 GHz

We report on the first wide-field, high-precision astrometric analysis of the 13 extragalactic radio sources of the complete S5 polar cap sample at 15.4 GHz. We describe new algorithms developed to enable the use of differenced phase delays in wide-field astrometric observations and discuss the impact of using differenced phase delays on the precision of the wide-field astrometric analysis. From this global fit, we obtained estimates of the relative source positions with precisions ranging from 14 to 200 $\mu$as at 15.4 GHz, depending on the angular separation of the sources (from $\sim$1.6 to $\sim$20.8 degrees). These precisions are $\sim$10 times higher than the achievable precisions using the phase-reference mapping technique.Comment: 9 pages, 7 figure

Families of piecewise linear maps with constant Lyapunov exponent

We consider families of piecewise linear maps in which the moduli of the two slopes take different values. In some parameter regions, despite the variations in the dynamics, the Lyapunov exponent and the topological entropy remain constant. We provide numerical evidence of this fact and we prove it analytically for some special cases. The mechanism is very different from that of the logistic map and we conjecture that the Lyapunov plateaus reflect arithmetic relations between the slopes.Comment: 26 pages, 13 figure

Multiband polarimetric and total intensity imaging of 3C345

We monitored the superluminal QSO 3C 345 at three epochs during a one-year period in 1995--1996, observing with the VLBA at 22, 15, 8.4, and 5 GHz. We imaged the radio source both in total and in polarized intensity. In the images at 5 and 8.4 GHz, the jet emission is traced up to 20 milliarcseconds (mas) from the jet core. In the 15 and 22 GHz images, we identify several enhanced emission regions moving at apparent speeds of 5c. Images of the linear polarized emission show predominantly an alignment of the electric vector with the extremely curved jet along the inner part of the high frequency jet. At 5 GHz, the jet shows remarkably strong fractional polarization (m~15%) with the electric vector perpendicular to the jet orientation.Comment: LaTeX file, 6 pages, 2 figures, needs "elsart" style package To be published in New Astronomy Reviews, special issue: Proceedings of the 4th EVN/JIVE VLBI Symposium, Eds. Garrett, M.A., Campbell, R.M., & Gurvits, L.

Discovery of Solar Rieger Periodicities in Another Star

The Rieger periods are solar cycles with a time scale of months, which are present in both flaring activity and sunspot occurrence. These short-term periodicities, tentatively explained by equatorially trapped Rossby-type waves modulating the emergence of magnetic flux at the surface, are considered a peculiar and not yet fully understood solar phenomenon. We chose a stellar system with solar characteristics, UX Arietis, and performed a timing analysis of two 9-year datasets of radio and optical observations. The analysis reveals a 294-day cycle. When the two 9-year datasets are folded with this period, a synchronization of the peak of the optical light curve (i.e., the minimum spot coverage) with the minimum radio flaring activity is observed. This close relationship between two completly independent curves makes it very likely that the 294-day cycle is real. We conclude that the process invoked for the Sun of a periodical emergence of magnetic flux may also be applied to UX Arietis and can explain the cyclic flaring activity triggered by interactions between successive cyclic emergences of magnetic flux.Comment: 4 Pages, 1 table, 3 figures (quality of Fig. 1 degraded to match the requested size), needs aa.cls, accepted to be published as a letter in Astronomy & Astrophysic

The billiard inside an ellipse deformed by the curvature flow

The billiard dynamics inside an ellipse is integrable. It has zero topological entropy, four separatrices in the phase space, and a continuous family of convex caustics: the confocal ellipses. We prove that the curvature flow destroys the integrability, increases the topological entropy, splits the separatrices in a transverse way, and breaks all resonant convex caustics.Comment: 13 pages, 1 figur

How to Mix Molecules with Mathematics

In this paper we develop two methods to calculate thermodynamic properties of mixtures. Starting point are the basic assumptions that also form the basis for the COSMO-RS model. In this approach, the individual molecules are represented by their geometrical shape with an electrical charge density on their surfaces. Next, the surface is split up into surface segments each with its own charge. In COSMO-RS a strong reduction is introduced by treating the segments as if they are completely independent. In the present study we take into account that the coupling between two patches is essentially dependent on the charge distribution on neighboring segments and on the local geometrical structure of the surface. Two approaches are followed. The first one points out how the model equations, which comprise the optimization of the entropy and conservation of internal energy, can efficiently be solved in general, thus also if the dependency between segments and the local geometry is included in the expression for the coupling energy between segments. In the second method the configuration with maximal entropy and prescribed energy is sought via simulation. Successive molecular configurations of the mixture are simulated and updated via a genetic algorithm to optimize the entropy. The second method is more time consuming but very general