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

Factors affecting tibial plateau expansion in healthy women over 2.5 years: a longitudinal study

SummaryObjectiveThere is evidence for tibial bone area to increase in response to risk factors for knee osteoarthritis (OA) in healthy subjects and to increase over time in subjects with knee OA. We performed a cohort study to examine whether tibial plateau bone area changes over time in healthy subjects and identify factors influencing the change.DesignEighty-one healthy women (age range 50–76 years) underwent magnetic resonance imaging (MRI) on their dominant knee at baseline and approximately 2.5 years later. Tibial plateau bone area was measured at baseline and follow-up. Risk factors assessed at baseline were tested for their association with change in tibial plateau bone area over time using multiple linear regression.ResultsThe mean tibial plateau bone area increased from 1733±209 to 1782±203mm2 for the medial, and from 1090±152 to 1109±152mm2 for the lateral over the study period, representing an annual average increase rate of 1.2% (95% CI 0.03%, 1.6%) and 0.8% (95% CI 0.7%, 1.8%), respectively. Baseline tibial plateau bone area was inversely associated with the increase rate of tibial plateau bone area. There was a trend for static knee alignment to be related to the increase rate of tibial plateau bone area.ConclusionIn healthy women, tibial plateau bone area increases over time. Baseline tibial plateau bone area is the main factor affecting the rate of increase, with biomechanical factors, such as static anatomical alignment, likely to affect the expansion of tibial plateau. Further work will be needed to determine the effect of subchondral bone change in the pathogenesis of knee OA

Strongly interacting σ\sigma-electrons and MgB2_2 superconductivity

MgB$(p^{n_{\sigma}}p^{n_{\pi}})_{2}$ is classified as a system with strongly interacting $\sigma$-electrons and non-correlated $\pi$-electrons of boron ions. The kinematic and Coulomb interaction V between the orbitally degenerated $\sigma$-electrons provide the superconducting state with an anisotropic gap of s*-wave symmetry. The critical temperature $T_c$ has a non-monotonic dependence on the distance r between the centers of gravity of $\sigma$- and $\pi$-bands. MgB$_2$ corresponds to r=0.085 eV and V=0.45 eV in our model with flat bands. The derived superconducting density of electronic states is in good agreement with available experimental and theoretical data. The possibilities for increasing $T_c$ are discussed.Comment: 8 pages, 4 figure

Short time decay of the Loschmidt echo

The Loschmidt echo measures the sensitivity to perturbations of quantum evolutions. We study its short time decay in classically chaotic systems. Using perturbation theory and throwing out all correlation imposed by the initial state and the perturbation, we show that the characteristic time of this regime is well described by the inverse of the width of the local density of states. This result is illustrated and discussed in a numerical study in a 2-dimensional chaotic billiard system perturbed by various contour deformations and using different types of initial conditions. Moreover, the influence to the short time decay of sub-Planck structures developed by time evolution is also investigated.Comment: 7 pages, 7 figures, published versio

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

Well-posedness of the Ericksen-Leslie system

In this paper, we prove the local well-posedness of the Ericksen-Leslie system, and the global well-posednss for small initial data under the physical constrain condition on the Leslie coefficients, which ensures that the energy of the system is dissipated. Instead of the Ginzburg-Landau approximation, we construct an approximate system with the dissipated energy based on a new formulation of the system.Comment: 16 page