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For the first time the atmospheric deposition of trace metals was studied over the entire territory of the Republic of Macedonia. Samples of the terrestrial mosses Hypnum cupressiforme, Camptothecium lutescens, and Homalothecium sericeum were collected in September-October 2002 at 73 sites evenly distributed over the country, and a total of 43 elements were determined by instrumental neutron activation analysis and atomic absorption spectrometry. Principal component factor analysis was used to identify the most polluted areas and characterize different pollution sources. The most important sources of trace metal deposition are ferrous and non-ferrous smelters, oil refineries, fertilizer production plants, and central heating stations. Four areas appear to be particularly exposed to metal pollution: Veles, Skopje, Tetovo, and Kavadarci-Negotino, whereas the predominantly agricultural regions in the south, southwest, and southeast show levels closer to European median values for most elements of mainly pollution origin.

We analyze the Kuramoto model of phase oscillators with natural frequencies distributed according to a unimodal asymmetric function g(omega) . It is obtained that besides a second-, also a first-order phase transition can appear if the distribution of natural frequencies possesses a sufficiently large flat section. It is derived analytically that for the first-order transitions the characteristic exponents describing the order parameter and synchronizing frequency near the critical point are equal to those for the order parameter in the corresponding symmetric case. Stability analysis of the incoherent phase shows that the synchronizing frequency at the onset of synchronization equals the perturbation rotation velocity at the border of stability. The analytic and numerical results are in agreement with numerical simulations.

We consider the Kuramoto model of phase oscillators with natural frequencies distributed according to a unimodal function with the plateau section in the middle representing the maximum and symmetric tails falling off predominantly as |omega-omega0|m, m>0, in the vicinity of the flat region. It is found that the phase transition is of first order as long as there is a finite flat region and that in the vicinity of the critical coupling the following scaling law holds r-rc proportional, variant(K-Kc)2/(2m+3), where r is the order parameter and K is the coupling strength of the interacting oscillators.

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We report on a dramatic improvement of the performance of the classical time-delayed autosynchronization method (TDAS) to control unstable steady states, by applying a time-varying delay in the TDAS control scheme in a form of a deterministic or stochastic delay-modulation in a fixed interval around a nominal value T0. The successfulness of this variable delay feedback control (VDFC) is illustrated by a numerical control simulation of the Lorenz and Rössler systems using three different types of time-delay modulations: a sawtooth wave, a sine wave, and a uniform random distribution. We perform a comparative analysis between the VDFC method and the standard TDAS method for a sawtooth-wave modulation by analytically determining the domains of control for the generic case of an unstable fixed point of focus type.

We study the stability of unstable steady states in scalar retarded time-delayed systems subjected to a variable-delay feedback control. The important aspect of such a control problem is that timedelayed systems are already infinite-dimensional before the delayed feedback control is turned on. When the frequency of the modulation is large compared to the system's dynamics, the analytic approach consists of relating the stability properties of the resulting variable-delay system with those of an analogous distributed delay system. Otherwise, the stability domains are obtained by a numerical integration of the linearized variable-delay system. The analysis shows that the control domains are significantly larger than those in the usual time-delayed feedback control, and that the complexity of the domain structure depends on the form and the frequency of the delay modulation.

Purpose This study aimed at investigating correlations between heavy metal concentrations in mosses and modelled deposition values as well as other site-specific and regional characteristics to determine which factors primarily affect cadmium, lead and mercury concentrations in mosses. The resulting relationships could potentially be used to enhance the spatial resolution of heavy metal deposition maps across Europe. Materials and methods Modelled heavy metal deposition data and data on the concentration of heavy metals in naturally growing mosses were integrated into a geographic information system and analysed by means of bivariate rank correlation analysis and multivariate decision trees. Modelled deposition data were validated annually with deposition measurements at up to 63 EMEP measurement stations within the European Monitoring and Evaluation Programme (EMEP), and mosses were collected at up to 7,000 sites at 5-year intervals between 1990 and 2005. Results and discussion Moderate to high correlations were found between cadmium and lead concentrations in mosses and modelled atmospheric deposition of these metals: Spearman rank correlation coefficients were between 0.62 and 0.67, and 0.67 and 0.73 for cadmium and lead, respectively (p<0.001). Multivariate decision tree analyses showed that cadmium and lead concentrations in mosses were primarily determined by the atmospheric deposition of these metals, followed by emissions of the metals. Low to very low correlations were observed between mercury concentrations in mosses and modelled atmospheric deposition of mercury. According to the multivariate analyses, spatial variations of the mercury concentration in mosses was primarily associated with the sampled moss species and not with the modelled deposition, but regional differences in the atmospheric chemistry of mercury and corresponding interactions with the moss may also be involved. Conclusions At least for cadmium and lead, concentrations in mosses are a valuable tool in determining and mapping the spatial variation in atmospheric deposition across Europe at a high spatial resolution. For mercury, more studies are needed to elucidate interactions of different chemical species with the moss.