Synchronization and Control of Spatiotemporal Chaos using Time-Series Data from Local Regions

In this paper we show that the analysis of the dynamics in localized regions, i.e., sub-systems can be used to characterize the chaotic dynamics and the synchronization ability of the spatiotemporal systems. Using noisy scalar time-series data for driving along with simultaneous self-adaptation of the control parameter representative control goals like suppressing spatiotemporal chaos and synchronization of spatiotemporally chaotic dynamics have been discussed.Comment: File in Latex, Figures may be obtained on request at the following address - [email protected]

Frustrated spin ladder with alternating spin-1 and spin-1/2 rungs

We study the impact of the diagonal frustrating couplings on the quantum phase diagram of a two-leg ladder composed of alternating spin-1 and spin-1/2 rungs. As the coupling strength is increased the system successively exhibits two gapped paramagnetic phases (a rung-singlet and a Haldane-like non-degenerate states) and two ferrimagnetic phases with different ferromagnetic moments per rung. The first two states are similar to the phases studied in the frustrated spin-1/2 ladder, whereas the magnetic phases appear as a result of the mixed-spin structure of the model. A detailed characterization of these phases is presented using density-matrix renormalization-group calculations, exact diagonalizations of periodic clusters, and an effective Hamiltonian approach inspired by the analysis of numerical data. The present theoretical study was motivated by the recent synthesis of the quasi-one-dimensional ferrimagnetic material Fe$^{II}$Fe$^{III}$ (trans-1,4-cyclohexanedicarboxylate) exhibiting a similar ladder structure.Comment: 10 pages, 8 figure

Peak-peak correlations in the cosmic background radiation from cosmic strings

We examine the two-point correlation function of local maxima in temperature fluctuations at the last scattering surface when this stochastic field is modified by the additional fluctuations produced by straight cosmic strings via the Kaiser-Stebbins effect. We demonstrate that one can detect the imprint of cosmic strings with tension $G\mu \gtrsim 1.2 \times 10^{-8}$ on noiseless $1^\prime$ resolution cosmic microwave background (CMB) maps at 95% confidence interval. Including the effects of foregrounds and anticipated systematic errors increases the lower bound to $G\mu \gtrsim 9.0\times 10^{-8}$ at $2\sigma$ confidence level. Smearing by beams of order 4' degrades the bound further to $G\mu \gtrsim 1.6 \times 10^{-7}$. Our results indicate that two-point statistics are more powerful than 1-point statistics (e.g. number counts) for identifying the non-Gaussianity in the CMB due to straight cosmic strings.Comment: 11 pages, 7 figures and 1 table; V2: Added one figure, comments, references and moderate corrections. Accepted for publication in MNRA