Simulation of Chua's Circuit by Means of Interval Analysis

The Chua's circuit is a paradigm for nonlinear scientific studies. It is usually simulated by means of numerical methods under IEEE 754-2008 standard. Although the error propagation problem is well known, little attention has been given to the relationship between this error and inequalities presented in Chua's circuit model. Taking the average of round mode towards $+\infty$ and $-\infty$, we showed a qualitative change on the dynamics of Chua's circuit.Comment: 6th International Conference on Nonlinear Science and Complexity - S\~ao Jos\'e dos Campos, 2016, p. 1-

A photometric and spectroscopic survey of solar twin stars within 50 parsecs of the Sun: I. Atmospheric parameters and color similarity to the Sun

Solar twins and analogs are fundamental in the characterization of the Sun's place in the context of stellar measurements, as they are in understanding how typical the solar properties are in its neighborhood. They are also important for representing sunlight observable in the night sky for diverse photometric and spectroscopic tasks, besides being natural candidates for harboring planetary systems similar to ours and possibly even life-bearing environments. We report a photometric and spectroscopic survey of solar twin stars within 50 pc of the Sun. Hipparcos absolute magnitudes and (B-V)_Tycho colors were used to define a 2 sigma box around the solar values, where 133 stars were considered. Additional stars resembling the solar UBV colors in a broad sense, plus stars present in the lists of Hardorp, were also selected. All objects were ranked by a color-similarity index with respect to the Sun, defined by uvby and BV photometry. Moderately high-resolution, high-S/N spectra were used for a subsample of equatorial-southern stars to derive Teff, log g, and [Fe/H] with average internal errors better than 50 K, 0.20 dex, and 0.08 dex, respectively. Ages and masses were estimated from theoretical HR diagrams. The color-similarity index proved very successful. We identify and rank new excellent solar analogs, which are fit to represent the Sun in the night sky. Some of them are faint enough to be of interest for moderately large telescopes. We also identify two stars with near-UV spectra indistinguishable from the Sun's. We present five new "probable" solar twin stars, besides five new "possible" twins. Masses and ages for the best solar twin candidates lie very close to the solar values, but chromospheric activity levels range somewhat. We propose that the solar twins be emphasized in the ongoing searches for extra-solar planets and SETI searches.Comment: 25 pages, 15 figures, 14 table