Density outbursts in a food web model with a closed nutrient cycle

A spatial three level food web model with a closed nutrient cycle is presented and analyzed via Monte Carlo simulations. The food web consists of three trophic levels. The basal level species (called resources  , R$R$) corresponds to primary producers in real ecosystems. The species at an intermediate level (consumers  , C$C$) relates to herbivores. It feeds on the resources. The consumers themselves constitute food for the top level species (predators  , P$P$), which corresponds to carnivores. The remains of the consumers and predators (detritus  , D$D$) provide nutrient for the resources. The time evolution of the model reveals two asymptotic states: an absorbing one with all species being extinct, and a coexisting one, in which concentrations of all species are non-zero. There are two possible ways for the system to reach the absorbing state. In some cases the densities increase very quickly at the beginning of a simulation and then decline slowly and almost monotonically. In others, well pronounced peaks in the R$R$, C$C$ and D$D$ densities appear regularly before the extinction. Those peaks correspond to density outbursts (waves) traveling through the system. We investigate the mechanisms leading to the waves. In particular, we show that the percolation of the detritus (i.e. the accumulation of nutrients) is necessary for the emergence of the waves. Moreover, our results corroborate the hypothesis that top-level predators play an essential role in maintaining the stability of a food web (top-down control).     

Power law classification scheme of time series correlations. On the example of G20 group

A power law classification scheme (PLCS) of time series correlations is proposed. It is shown that PLCS provides the ability to classify nonlinear correlations and measure their stability. PLCS has been applied to gross domestic product (GDP) per capita of G20 members and their correlations analysed. It has been shown that the method does not only recognise linear correlations properly, but also allows to point out converging time series as well as to distinguish nonlinear correlations. PLCS is capable of crash recognition as it is shown in the Argentina example. Finally the strength of correlations and the stability of correlation matrices have been used to construct a minimum spanning tree (MST). The results were compared with those based on the ultrametric distance (UD). Comparing the structures of MST, UD and PLCS indicates that the latter one is more complicated, but better fits the expected economic relations within the G20.     

Linearization methods of laser interferometers for pico/nano positioning stages

Presented work introduces methods for improving linearity of a heterodyne laser interferometer system. The heterodyne configuration exhibits high potential in demanding applications, like pico/nano positioning. Those applications require superior accuracy, more difficult to obtain in a homodyne configuration of the laser interferometer. The homodyne setup is more susceptible to external light, variation of DC offset and higher noises, especially the 1/f noise. Those issues are filtered out in the heterodyne configuration. The main disadvantage of heterodyne setup are higher measurement nonlinearities. In this paper there are first introduced sources of nonlinearities and their impact on the overall accuracy. According to those findings there are proposed techniques to eliminate error caused by parasite beams, i.e. nonlinearities. Presented method is based on digital signal processing and is reliable and easy to use. In the shown approach the nonlinearities correction is completely automatic. Such system is applicable for X/Y positioning stages. Presented configuration of the laser interferometer is able to track the displacement with 100 pm resolution up to 7 m/s of translation velocity. The resolution can be improved to 10 pm by limitation of maximal velocity. In the paper there is confirmed that errors caused by nonlinearities are in range of ±0.6 nm. Achieved accuracy is comparable to capacitance gauges with presented laser interferometer having much better dynamic range.     

Phase transformations in the TiO2–SiO2 system at high pressures and temperatures

In situ X-ray diffraction study of a sol–gel-produced SiO₂–TiO₂ glass and intimately mixed ultrafine powders of SiO₂ and TiO₂ was used to investigate the effect of TiO₂ on the high-pressure phase transformations of SiO₂ and specifically on the change in the p,T-conditions of the formation of coesite and stishovite. Our findings have shown that at pressures to 7.5?GPa and temperatures up to 1300?K the presence of TiO₂ does not favor the formation of stishovite.     

High-pressure [2 + 2]cyloaddition of acyl isocyanates to glycals

Abstract

Isocyanates derived from uretanes 4, s and benzamides 6, 7 react with di-O-benzyl-D-arabinal 3 under 12 kbar pressure to afford the corresponding cycloadducts with high stereoselectivity. Alkoxycarbonyl isocyanates 4 and 5 from [2 + 2]cycloadducts almost exclusively, where benzoyl iSocyanates produce 1:1 mixtures of [2 + 21 and [4 + 2]cycloadducts.     

Some identities for Moore–Penrose inverses of matrix products

A group of identities are established for the Moore–Penrose inverses and the weighted Moore–Penrose inverses of matrix products AB and ABC. Some consequences and applications are also presented.     

On the Free Boundary Conditions for a Dynamic Shell Model Based on Intrinsic Differential Geometry

The mathematical theory behind the modeling of shells is a crucial issue in many engineering problems. Here, the authors derive the free boundary conditions and associated strong form of a dynamic shallow Kirchhoff shell model based on the intrinsic geometry methods of Michael Delfour and Jean-Paul Zolésio. This model relies on the oriented distance function which describes the geometry. This is an extension of the work done in [J. Cagnol, I. Lasiecka, C. Lebiedzik and J.-P. Zolésio (2002). Uniform stability in structural acoustic models with flexible curved walls. J. Differential Equation, 186(1), 88–121.], where the model was derived for clamped boundary conditions only. In the current article, manipulations with the model result in a cleaner form where the displacement of the shell and shell boundary is written explicitly in terms of standard tangential operators.     

Drift-diffusion in electrochemistry: thresholds for boundary flux and discontinuous optical generation

We consider an extension of the classical drift-diffusion model, which incorporates thermodynamic switching rules for generation and boundary flux. The motivation is the important case of the splitting of water molecules upon photonic irradiation of a semiconductor electrode located in an electrochemical cell. The solid state electrode forms the spatial domain of the model. The rules are motivated by the fact that the valence band of the semiconductor, which supplies positive charge to solution, has to be located at a lower energy level than the electrochemical potential of O₂ evolution in solution, and the conduction band, which supplies electrons to solution, has to be positioned at a higher energy level than the electrochemical potential of H₂ evolution. This defines thresholds in terms of electrochemical potentials before boundary flux is activated. The optical generation rate is affected, due to the increased carrier relaxation time, when these thresholds are crossed, and may be discontinuous. We thus consider a self-consistent model, in which ‘switching’ occurs only in principal variables. The steady-state model is considered, and trapping regions are derived for the solutions.