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-

Strong Reduction of the Field-Dependent Microwave Surface Resistance in YBCO with BaZrO_3 Inclusions

We present measurements of the magnetic field dependent microwave surface resistance in laser-ablated YBa$_2$Cu$_3$O$_{7-\delta}$ films on SrTiO$_3$ substrates. BaZrO$_3$ crystallites were included in the films using composite targets containing BaZrO$_3$ inclusions with mean grain size smaller than 1 $\mu$m. X-ray diffraction showed single epitaxial relationship between BaZrO$_3$ and YBa$_2$Cu$_3$O$_{7-\delta}$. The effective surface resistance was measured at 47.7 GHz for 60$< T <$90 K and 0$< \mu_0H <$0.8 T. The magnetic field had a very different effect on pristine YBa$_2$Cu$_3$O$_{7-\delta}$ and YBa$_2$Cu$_3$O$_{7-\delta}$/BaZrO$_3$, while for $\mu_0H=$0 only a reduction of $T_c$ in the YBa$_2$Cu$_3$O$_{7-\delta}$/BaZrO$_3$ film was observed, consistent with dc measurements. At low enough $T$, in moderate fields YBa$_2$Cu$_3$O$_{7-\delta}$/BaZrO$_3$ exhibited an intrinsic thin film resistance lower than the pure film. The results clearly indicate that BaZrO$_3$ inclusions determine a strong reduction of the field-dependent surface resistance. From the analysis of the data in the framework of simple models for the microwave surface impedance in the mixed state we argue that BaZrO$_3$ inclusions determine very steep pinning potentials.Comment: LaTeX, 6 pages, 4 figures, uses jpconf.cls and jpconf11.clo class files, talk given at EUCAS 2007, submitted to J. Phys.: Conf. Serie