Complex transitions to synchronization in delay-coupled networks of logistic maps

A network of delay-coupled logistic maps exhibits two different synchronization regimes, depending on the distribution of the coupling delay times. When the delays are homogeneous throughout the network, the network synchronizes to a time-dependent state [Atay et al., Phys. Rev. Lett. 92, 144101 (2004)], which may be periodic or chaotic depending on the delay; when the delays are sufficiently heterogeneous, the synchronization proceeds to a steady-state, which is unstable for the uncoupled map [Masoller and Marti, Phys. Rev. Lett. 94, 134102 (2005)]. Here we characterize the transition from time-dependent to steady-state synchronization as the width of the delay distribution increases. We also compare the two transitions to synchronization as the coupling strength increases. We use transition probabilities calculated via symbolic analysis and ordinal patterns. We find that, as the coupling strength increases, before the onset of steady-state synchronization the network splits into two clusters which are in anti-phase relation with each other. On the other hand, with increasing delay heterogeneity, no cluster formation is seen at the onset of steady-state synchronization; however, a rather complex unsynchronized state is detected, revealed by a diversity of transition probabilities in the network nodes

Stability of Quantum Motion: Beyond Fermi-golden-rule and Lyapunov decay

We study, analytically and numerically, the stability of quantum motion for a classically chaotic system. We show the existence of different regimes of fidelity decay which deviate from Fermi Golden rule and Lyapunov decay.Comment: 5 pages, 5 figure

Relaxation Methods for Mixed-Integer Optimal Control of Partial Differential Equations

We consider integer-restricted optimal control of systems governed by abstract semilinear evolution equations. This includes the problem of optimal control design for certain distributed parameter systems endowed with multiple actuators, where the task is to minimize costs associated with the dynamics of the system by choosing, for each instant in time, one of the actuators together with ordinary controls. We consider relaxation techniques that are already used successfully for mixed-integer optimal control of ordinary differential equations. Our analysis yields sufficient conditions such that the optimal value and the optimal state of the relaxed problem can be approximated with arbitrary precision by a control satisfying the integer restrictions. The results are obtained by semigroup theory methods. The approach is constructive and gives rise to a numerical method. We supplement the analysis with numerical experiments

Ballistic Localization in Quasi-1D Waveguides with Rough Surfaces

Structure of eigenstates in a periodic quasi-1D waveguide with a rough surface is studied both analytically and numerically. We have found a large number of "regular" eigenstates for any high energy. They result in a very slow convergence to the classical limit in which the eigenstates are expected to be completely ergodic. As a consequence, localization properties of eigenstates originated from unperturbed transverse channels with low indexes, are strongly localized (delocalized) in the momentum (coordinate) representation. These eigenstates were found to have a quite unexpeted form that manifests a kind of "repulsion" from the rough surface. Our results indicate that standard statistical approaches for ballistic localization in such waveguides seem to be unappropriate.Comment: 5 pages, 4 figure

Sonocatalytic Degradation of Rhodamine B in Aqueous Solution in the Presence of Tio2 Coated Activated Carbon

AbstractSynthesis of titanium dioxide coated activated carbon (TiO2/AC) has been undertaken using sol-gel method and its application in Rhodamine B (RB) dye removal has been investigated. The synthesized sonocatalyst (TiO2/AC) was characterized by using SEM and FTIR techniques. The effects of the TiO2/AC on the sonocatalytic degradation of RB dye and the operational parameters such as pH, temperature, ultrasonic frequency with the presence/absence of sonocatalyst of the sonocatalytic degradation of RB were concerned in this study. The degradation efficiency of RB in aqueous solution could be achieved 82.21% with the addition of TiO2/AC at the best conditions. The best conditions for sonocatalytic degradation of RB were found to be pH 6, temperature 50°C, ultrasonic frequency of 30kHz with the presence of sonocatalyst for 60minutes

Computation of protein geometry and its applications: Packing and function prediction

This chapter discusses geometric models of biomolecules and geometric constructs, including the union of ball model, the weigthed Voronoi diagram, the weighted Delaunay triangulation, and the alpha shapes. These geometric constructs enable fast and analytical computaton of shapes of biomoleculres (including features such as voids and pockets) and metric properties (such as area and volume). The algorithms of Delaunay triangulation, computation of voids and pockets, as well volume/area computation are also described. In addition, applications in packing analysis of protein structures and protein function prediction are also discussed.Comment: 32 pages, 9 figure

Bound magnetic polaron driven low-temperature ferromagnetism in Cu1−xMnxO compounds

AbstractPartial Mn atoms have been confirmed to enter the CuO lattice and form the Cu1−xMnxO compounds in the case of doping with 0≤x≤0.2 by the sol–gel method. With increasing Mn content, magnetism is observed. The magnetic critical transition temperature increases with enhanced magnetism, which obeys the bound magnetic polaron theory. The electronic transportation shows an insulating behavior as the band-gap decreases. Our results may indicate that CuO may be used as a candidate of magnetic semiconductor

Coupled Mg/Ca and clumped isotope analyses of foraminifera provide consistent water temperatures

The reliable determination of past seawater temperature is fundamental to paleoclimate studies. We test the robustness of two paleotemperature proxies by combining Mg/Ca and clumped isotopes (Δ47) on the same specimens of core top planktonic foraminifera. The strength of this approach is that Mg/Ca and Δ47 are measured on the same specimens of foraminifera, thereby providing two independent estimates of temperature. This replication constitutes a rigorous test of individual methods with the advantage that the same approach can be applied to fossil specimens. Aliquots for Mg/Ca and clumped analyses are treated in the same manner following a modified cleaning procedure of foraminifera for trace element and isotopic analyses. We analysed eight species of planktonic foraminifera from coretop samples over a wide range of temperatures from 2 to 29°C. We provide a new clumped isotope temperature calibrations using subaqueous cave carbonates, which is consistent with recent studies. Tandem Mg/Ca–Δ47 results follow an exponential curve as predicted by temperature calibration equations. Observed deviations from the predicted Mg/Ca-Δ47 relationship are attributed to the effects of Fe-Mn oxide coatings, contamination, or dissolution of foraminiferal tests. This coupled approach provides a high degree of confidence in temperature estimates when Mg/Ca and Δ47 yield concordant results, and can be used to infer the past δ18O of seawater (δ18Osw) for paleoclimate studies

Delocalization in harmonic chains with long-range correlated random masses

We study the nature of collective excitations in harmonic chains with masses exhibiting long-range correlated disorder with power spectrum proportional to $1/k^{\alpha}$, where $k$ is the wave-vector of the modulations on the random masses landscape. Using a transfer matrix method and exact diagonalization, we compute the localization length and participation ratio of eigenmodes within the band of allowed energies. We find extended vibrational modes in the low-energy region for $\alpha > 1$. In order to study the time evolution of an initially localized energy input, we calculate the second moment $M_2(t)$ of the energy spatial distribution. We show that $M_2(t)$, besides being dependent of the specific initial excitation and exhibiting an anomalous diffusion for weakly correlated disorder, assumes a ballistic spread in the regime $\alpha>1$ due to the presence of extended vibrational modes.Comment: 6 pages, 9 figure