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-

Epidemic threshold in structured scale-free networks

We analyze the spreading of viruses in scale-free networks with high clustering and degree correlations, as found in the Internet graph. For the Suscetible-Infected-Susceptible model of epidemics the prevalence undergoes a phase transition at a finite threshold of the transmission probability. Comparing with the absence of a finite threshold in networks with purely random wiring, our result suggests that high clustering and degree correlations protect scale-free networks against the spreading of viruses. We introduce and verify a quantitative description of the epidemic threshold based on the connectivity of the neighborhoods of the hubs.Comment: 4 pages, 4 figure

Higher-Derivative Two-Dimensional Massive Fermion Theories

We consider the canonical quantization of a generalized two-dimensional massive fermion theory containing higher odd-order derivatives. The requirements of Lorentz invariance, hermiticity of the Hamiltonian and absence of tachyon excitations suffice to fix the mass term, which contains a derivative coupling. We show that the basic quantum excitations of a higher-derivative theory of order 2N+1 consist of a physical usual massive fermion, quantized with positive metric, plus 2N unphysical massless fermions, quantized with opposite metrics. The positive metric Hilbert subspace, which is isomorphic to the space of states of a massive free fermion theory, is selected by a subsidiary-like condition. Employing the standard bosonization scheme, the equivalent boson theory is derived. The results obtained are used as a guideline to discuss the solution of a theory including a current-current interaction.Comment: 23 pages, Late

Ice Age Epochs and the Sun's Path Through the Galaxy

We present a calculation of the Sun's motion through the Milky Way Galaxy over the last 500 million years. The integration is based upon estimates of the Sun's current position and speed from measurements with Hipparcos and upon a realistic model for the Galactic gravitational potential. We estimate the times of the Sun's past spiral arm crossings for a range in assumed values of the spiral pattern angular speed. We find that for a difference between the mean solar and pattern speed of Omega_Sun - Omega_p = 11.9 +/- 0.7 km/s/kpc the Sun has traversed four spiral arms at times that appear to correspond well with long duration cold periods on Earth. This supports the idea that extended exposure to the higher cosmic ray flux associated with spiral arms can lead to increased cloud cover and long ice age epochs on Earth.Comment: 14 pages, 3 figures, accepted for publication in Ap

Orbital Characteristics of the Subdwarf-B and F V Star Binary EC~20117-4014(=V4640 Sgr)

Among the competing evolution theories for subdwarf-B (sdB) stars is the binary evolution scenario. EC~20117-4014 (=V4640~Sgr) is a spectroscopic binary system consisting of a pulsating sdB star and a late F main-sequence companion (O'Donoghue et al. 1997), however the period and the orbit semi-major axes have not been precisely determined. This paper presents orbital characteristics of the EC 20117-4014 binary system using 20 years of photometric data. Periodic Observed minus Calculated (O-C) variations were detected in the two highest amplitude pulsations identified in the EC 20117-4014 power spectrum, indicating the binary system's precise orbital period (P = 792.3 days) and the light-travel time amplitude (A = 468.9 s). This binary shows no significant orbital eccentricity and the upper limit of the eccentricity is 0.025 (using 3 $\sigma$ as an upper limit). This upper limit of the eccentricity is the lowest among all wide sdB binaries with known orbital parameters. This analysis indicated that the sdB is likely to have lost its hydrogen envelope through stable Roche lobe overflow, thus supporting hypotheses for the origin of sdB stars. In addition to those results, the underlying pulsation period change obtained from the photometric data was $\dot{P}$ = 5.4 ($\pm$0.7) $\times$ $10^{-14}$ d d$^{-1}$, which shows that the sdB is just before the end of the core helium-burning phase