Chaos detection and control in a typical power system

In this paper, a new chaotic system is introduced. The proposed system is a conventional power network that demonstrates a chaotic behavior under special operating conditions. Some features such as Lyapunov exponents and a strange attractor show the chaotic behavior of the system, which decreases the system performance. Two different controllers are proposed to control the chaotic system. The first one is a nonlinear conventional controller that is simple and easy to construct, but the second one is developed based on the finite time control theory and optimized for faster control. A MATLAB-based simulation verifies the results.     

Asymptotic uncorrelation for Mexican needlets

We recall Mexican needlets from [D. Geller, A. Mayeli, Continuous wavelets on compact manifolds, Math. Z. 262 (4) (2009) 895-927; D. Geller, A. Mayeli, Nearly tight frames and space-frequency analysis on compact manifolds, Math. Z. 263 (2) (2009) 234-264]. We derive an estimate for certain types of Legendre series, which we apply to the statistical properties of Mexican needlets. More precisely, we shall show that, under isotropy assumption, the Mexican needlet coefficients of a random field on the sphere are asymptotically uncorrelated, as the frequency parameter goes to infinity. This property is important in the analysis of spherical random fields, in particular in connection to the analysis of Cosmic Microwave Background (CMB) radiation data.     

Thermal Spin Squeezing as a Signature of Thermal Global Entanglement in Heisenberg Models

We study thermal spin squeezing (TSS) and thermal global entanglement (TGE) in a general Heisenberg spin chain, in the presence of Dzyaloshinskii-Moriya interaction and an external magnetic field. We derive an inequality associating the squeezing parameter and the global concurrence, which establishes (TSS) as a signature of (TGE). The inequality reduces to equality for particular symmetric chains which also associates TSS with bipartite entanglement in such systems. We also check the results by presenting two numerical examples.     

Mapping dynamical heterogeneity in structural glasses to correlated fluctuations of the time variables

Dynamical heterogeneities--strong fluctuations near the glass transition--are believed to be crucial to explain much of the glass transition phenomenology. One hypothesis for their origin is that they emerge from soft (Goldstone) modes associated with a broken continuous symmetry under time reparametrizations. To test this hypothesis, we use numerical simulation data to construct coarse grained observables and decompose their fluctuations into two transverse components associated with the postulated soft modes and a longitudinal component unrelated to them. We find that as temperature is lowered and time scales are increased, the time reparametrization fluctuations become increasingly dominant, and that their correlation volumes grow together with those of the dynamical heterogeneities, while the correlation volumes for longitudinal fluctuations remain small.