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We consider large populations of phase oscillators with global nonlinear coupling. For identical oscillators such populations are known to demonstrate a transition from completely synchronized state to the state of self-organized quasiperiodicity. In this state phases of all units differ, yet the population is not completely incoherent but produces a nonzero mean field; the frequency of the latter differs from the frequency of individual units. Here we analyze the dynamics of such populations in case of uniformly distributed natural frequencies. We demonstrate numerically and describe theoretically (i) states of complete synchrony, (ii) regimes with coexistence of a synchronous cluster and a drifting subpopulation, and (iii) self-organized quasiperiodic states with nonzero mean field and all oscillators drifting with respect to it. We analyze transitions between different states with the increase of the coupling strength; in particular we show that the mean field arises via a discontinuous transition. For a further illustration we compare the results for the nonlinear model with those for the Kuramoto-Sakaguchi model.
Despite many previous Studies on the association between hyperthyroidism and the hyperadrenergic state, controversies still exist. Detrended fluctuation analysis (DFA) is a well recognized method in the nonlinear analysis of heart rate variability (HRV), and it has physiological significance related to the autonomic nervous system. In particular, an increased short-term scaling exponent alpha 1 calculated from DFA is associated with both increased sympathetic activity and decreased vagal activity. No study has investigated the DFA of HRV in hyperthyroidism. This study was designed to assess the sympathovagal balance in hyperthyroidism. We performed the DFA along with the linear analysis of HRV in 36 hyperthyroid Graves' disease patients (32 females and 4 males; age 30 +/- 1 years, means +/- SE) and 36 normal controls matched by sex, age and body mass index. Compared with the normal controls, the hyperthyroid patients revealed a significant increase (P < 0.001) in alpha 1 (hyperthyroid 1.28 +/- 0.04 versus control 0.91 +/- 0.02), long-term scaling exponent alpha 2 (1.05 +/- 0.02 versus 0.90 +/- 0.01), overall scaling exponent alpha (1.11 +/- 0.02 versus 0.89 +/- 0.01), low frequency power in normalized units (LF%) and the ratio of low frequency power to high frequency power (LF/HF); and a significant decrease (P < 0.001) in the standard deviation of the R-R intervals (SDNN) and high frequency power (HF). In conclusion, hyperthyroidism is characterized by concurrent sympathetic activation and vagal withdrawal. This sympathovagal imbalance state in hyperthyroidism helps to explain the higher prevalence of atrial fibrillation and exercise intolerance among hyperthyroid patients.
We consider the suppression of spatiotemporal chaos in the complex Ginzburg-Landau equation by a combined global and local time-delay feedback. Feedback terms are implemented as a control scheme, i.e., they are proportional to the difference between the time-delayed state of the system and its current state. We perform a linear stability analysis of uniform oscillations with respect to space-dependent perturbations and compare with numerical simulations. Similarly, for the fixed-point solution that corresponds to amplitude death in the spatially extended system, a linear stability analysis with respect to space-dependent perturbations is performed and complemented by numerical simulations.
An effective dynamical description of a general class of stochastic phase oscillators is presented. For this, the effective phase velocity is defined either by the stochastic phase oscillators invariant probability density or its first passage times. Using the first approach the effective phase exhibits the correct frequency and invariant distribution density, whereas the second approach models the proper phase resetting curve. The discrepancy of the effective models is most pronounced for noise-induced oscillations and is related to non-monotonicity of the stochastic phase variable due to fluctuations.
We develop an effective description of noise-induced oscillations based on deterministic phase dynamics. The phase equation is constructed to exhibit correct frequency and distribution density of noise-induced oscillations. In the simplest one-dimensional case the effective phase equation is obtained analytically, whereas for more complex situations a simple method of data processing is suggested. As an application an effective coupling function is constructed that quantitatively describes periodically forced noise-induced oscillations.
A new approach for efficient second-harmonic generation using diode lasers is presented. The experimental setup is based on a tapered amplifier operated in a ring resonator that is coupled to a miniaturized enhancement ring resonator containing a periodically poled lithium niobate crystal. Frequency locking of the diode laser emission to the resonance frequency of the enhancement cavity is realized purely optically, resulting in stable, single-frequency operation. Blue light at 488 nm with an output power of 310 mW is generated with an optical-to-optical conversion efficiency of 18%.
beta-phase poly(vinylidene fluoride-hexafluoropropylene) (P(VDF-HFP)) copolymer films were prepared by uniaxially stretching solution-cast or melt-quenched samples. Different preparation routes lead to different amounts of the crystalline alpha and beta phases in the films, as detected by means of Fourier-transform infrared spectroscopy and X-ray diffractometry. The beta phase is significantly enhanced in melt-quenched and stretched films in comparison to solution-cast and stretched films. This is particularly true for copolymer samples with higher HFP content. The beta- phase enhancement is also observed in ferroelectric-hysteresis experiments where a rather high polarization of 58 mC/ m(2) was found on melt-quenched and stretched samples after poling at electric fields of 140 MV/m. After poling at 160 MV/m, one of these samples exhibited a piezoelectric d(33) coefficient as high as 21 pC/N. An electric-field-induced partial transition from the alpha to the beta phase was also observed on the melt-quenched and stretched samples. This effect leads to a further increase in the applications-relevant dipole polarization. Uniaxially stretched ferroelectric- polymer films are highly anisotropic. Dielectric resonance spectroscopy reveals a strong increase of the transverse piezoelectric d(32) coefficient and a strong decrease of the transverse elastic modulus c(32) upon heating from 20 to 50 degrees C.
Interacting human activities underlie the patterns of many social, technological, and economic phenomena. Here we present clear empirical evidence from Short Message correspondence that observed human actions are the result of the interplay of three basic ingredients: Poisson initiation of tasks and decision making for task execution in individual humans as well as interaction among individuals. This interplay leads to new types of interevent time distribution, neither completely Poisson nor power-law, but a bimodal combination of them. We show that the events can be separated into independent bursts which are generated by frequent mutual interactions in short times following random initiations of communications in longer times by the individuals. We introduce a minimal model of two interacting priority queues incorporating the three basic ingredients which fits well the distributions using the parameters extracted from the empirical data. The model can also embrace a range of realistic social interacting systems such as e-mail and letter communications when taking the time scale of processing into account. Our findings provide insight into various human activities both at the individual and network level. Our analysis and modeling of bimodal activity in human communication from the viewpoint of the interplay between processes of different time scales is likely to shed light on bimodal phenomena in other complex systems, such as interevent times in earthquakes, rainfall, forest fire, and economic systems, etc.
Explicit solution of the Lindblad equation for nearly isotropic boundary driven XY spin 1/2 chain
(2010)
Explicit solution for the two-point correlation function in a non-equilibrium steady state of a nearly isotropic boundary driven open XY spin 1/2 chain in the Lindblad formulation is provided. A non-equilibrium quantum phase transition from exponentially decaying correlations to long range order is discussed analytically. In the regime of long range order a new phenomenon of correlation resonances is reported, where the correlation response of the system is unusually high for certain discrete values of the external bulk parameter, e.g. the magnetic field.
This work generates, through a sample of numerical simulations of the restricted three-body problem, diagrams of semimajor axis and eccentricity which defines stable and unstable zones for particles in S-type orbits around Pluto and Charon. Since we consider initial conditions with 0 <= e <= 0.99, we found several new stable regions. We also identified the nature of each one of these newly found stable regions. They are all associated to families of periodic orbits derived from the planar circular restricted three-body problem. We have shown that a possible eccentricity of the Pluto-Charon system slightly reduces, but does not destroy, any of the stable regions.