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 coordinate-dependent superspace deformation from string theory

Starting from a type II superstring model defined on $R^{2,2}\times CY_6$ in a linear graviphoton background, we derive a coordinate dependent $C$-deformed ${\cal N}=1$, $d=2+2$ superspace. The chiral fermionic coordinates $\theta$ satisfy a Clifford algebra, while the other coordinate algebra remains unchanged. We find a linear relation between the graviphoton field strength and the deformation parameter. The null coordinate dependence of the graviphoton background allows to extend the results to all orders in $\alpha'$.Comment: 14 pages, reference added, accepted for publication in JHE

Exact partition function in U(2)×U(2)U(2)\times U(2) ABJM theory deformed by mass and Fayet-Iliopoulos terms

We exactly compute the partition function for $U(2)_k\times U(2)_{-k}$ ABJM theory on $\mathbb S^3$ deformed by mass $m$ and Fayet-Iliopoulos parameter $\zeta$. For $k=1,2$, the partition function has an infinite number of Lee-Yang zeros. For general $k$, in the decompactification limit the theory exhibits a quantum (first-order) phase transition at $m=2\zeta$.Comment: 11 pages, 1 figure. v2: references adde