Linear And Nonlinear Arabesques: A Study Of Closed Chains Of Negative 2-Element Circuits

In this paper we consider a family of dynamical systems that we call "arabesques", defined as closed chains of 2-element negative circuits. An $n$-dimensional arabesque system has $n$ 2-element circuits, but in addition, it displays by construction, two $n$-element circuits which are both positive vs one positive and one negative, depending on the parity (even or odd) of the dimension $n$. In view of the absence of diagonal terms in their Jacobian matrices, all these dynamical systems are conservative and consequently, they can not possess any attractor. First, we analyze a linear variant of them which we call "arabesque 0" or for short "A0". For increasing dimensions, the trajectories are increasingly complex open tori. Next, we inserted a single cubic nonlinearity that does not affect the signs of its circuits (that we call "arabesque 1" or for short "A1"). These systems have three steady states, whatever the dimension is, in agreement with the order of the nonlinearity. All three are unstable, as there can not be any attractor in their state-space. The 3D variant (that we call for short "A1\_3D") has been analyzed in some detail and found to display a complex mixed set of quasi-periodic and chaotic trajectories. Inserting $n$ cubic nonlinearities (one per equation) in the same way as above, we generate systems "A2\_$n$D". A2\_3D behaves essentially as A1\_3D, in agreement with the fact that the signs of the circuits remain identical. A2\_4D, as well as other arabesque systems with even dimension, has two positive $n$-circuits and nine steady states. Finally, we investigate and compare the complex dynamics of this family of systems in terms of their symmetries.Comment: 22 pages, 12 figures, accepted for publication at Int. J. Bif. Chao

Reference Distribution Functions for Magnetically Confined Plasmas from the Minimum Entropy Production Theorem and the MaxEnt Principle, subject to the Scale-Invariant Restrictions

We derive the expression of the reference distribution function for magnetically confined plasmas far from the thermodynamic equilibrium. The local equilibrium state is fixed by imposing the minimum entropy production theorem and the maximum entropy (MaxEnt) principle, subject to scale invariance restrictions. After a short time, the plasma reaches a state close to the local equilibrium. This state is referred to as the reference state. The aim of this letter is to determine the reference distribution function (RDF) when the local equilibrium state is defined by the above mentioned principles. We prove that the RDF is the stationary solution of a generic family of stochastic processes corresponding to an universal Landau-type equation with white parametric noise. As an example of application, we consider a simple, fully ionized, magnetically confined plasmas, with auxiliary Ohmic heating. The free parameters are linked to the transport coefficients of the magnetically confined plasmas, by the kinetic theory.Comment: 9 pages and 6 figures. arXiv admin note: substantial text overlap with arXiv:1305.592

Effects of Surface Geology on Seismic Ground Motion Deduced from Ambient-Noise Measurements in the Town of Avellino, Irpinia Region (Italy)

The effects of surface geology on ground motion provide an important tool in seismic hazard studies. It is well known that the presence of soft sediments can cause amplification of the ground motion at the surface, particularly when there is a sharp impedance contrast at shallow depth. The town of Avellino is located in an area characterised by high seismicity in Italy, about 30 km from the epicentre of the 23 November 1980, Irpinia earthquake (M = 6.9). No earthquake recordings are available in the area. The local geology is characterised by strong heterogeneity, with impedance contrasts at depth. We present the results from seismic noise measurements carried out in the urban area of Avellino to evaluate the effects of local geology on the seismic ground motion. We computed the horizontal-to-vertical (H/V) noise spectral ratios at 16 selected sites in this urban area for which drilling data are available within the first 40 m of depth. A Rayleigh wave inversion technique using the peak frequencies of the noise H/V spectral ratios is then presented for estimating Vs models, assuming that the thicknesses of the shallow soil layers are known. The results show a good correspondence between experimental and theoretical peak frequencies, which are interpreted in terms of sediment resonance. For one site, which is characterised by a broad peak in the horizontal-to-vertical spectral-ratio curve, simple one-dimensional modelling is not representative of the resonance effects. Consistent variations in peak amplitudes are seen among the sites. A site classification based on shear-wave velocity characteristics, in terms of Vs30, cannot explain these data. The differences observed are better correlated to the impedance contrast between the sediments and basement. A more detailed investigation of the physical parameters of the subsoil structure, together with earthquake data, are desirable for future research, to confirm these data in terms of site response

Distribution, sources and ecological risk assessment of polycyclic aromatic hydrocarbons in water and sediments from Tiber River and estuary, Italy

The concentration, source and ecological risk of polycyclic aromatic hydrocarbons (PAHs) in the Tiber River and its environmental impact on the Tyrrhenian Sea (Central Mediterranean Sea) were estimated. The 16 priority PAHs were determined in the water dissolved phase (DP), suspended particulate matter (SPM) and sediments collected from 21 sites in four different seasons. Total concentrations of PAHs ranged from 10.3 to 951.6ngL-1 and from 36.2 to 545.6ngg-1 in water (sum of DP and SPM) and in sediment samples, respectively. The compositions of PAHs showed that 2- to 4-ring PAHs were abundant in DP, 4- to 6-ring PAHs were predominant in SPM samples, and 4- to 5-ring PAHs were abundant in sediments. The diagnostic ratio analysis indicated that the PAHs mainly had a pyrolytic source. The toxic equivalent concentration of carcinogenic PAHs was 45.3ngTEQg-1, suggesting low carcinogenic risk for Tiber River. Total PAHs loads into the sea were calculated in about 3161.7kgyear-1 showing that this river is one of the main contribution sources of these contaminants to the Tyrrhenian Sea

Estimates of Tiber River organophosphate pesticide loads to the Tyrrhenian Sea and ecological risk

The organophosphate pesticides pollution in the Tiber River and its environmental impact on the Tyrrhenian Sea (Central Mediterranean Sea) were estimated. Eight selected organophosphate pesticides (diazinon, dimethoate, malathion, chlorpyrifos, pirimiphos-methyl, fenitrothion, methidathion, tolclofos-methyl) were determined in the water dissolved phase, suspended particulate matter and sediment samples collected from 21 sites in different seasons. Total organophosphate pesticides concentrations ranged from 0.40 to 224.48 ng L-1 in water (as the sum of the water dissolved phase and suspended particulate matter) and from 1.42 to 68.46 ng g(-1) in sediment samples. Contaminant discharges of organophosphate pesticides into the sea were calculated in about 545.36 kg year(-1) showing that this river should be consider as one of the main contribution sources of organophosphate pesticides to the Tyrrhenian Sea. In relation to the eco-toxicological assessment, the concentrations of most OPPs in the water and sediments from the Tiber River and its estuary were lower than guideline values

Polychlorinated biphenyls and organochlorine pesticides in water and sediment from Volturno River, Southern Italy: occurrence, distribution and risk assessment

Abstract Background To assess the Volturno River pollution and its environmental impact on the Tyrrhenian Sea (Central Mediterranean Sea) caused by Polychlorinated biphenyls (PCBs) and Organochlorine pesticides (OCPs), 32 PCBs and aldrin, α-BHC, β-BHC, δ-BHC, γ-BHC (lindane), 4,4′- DDD, 4,4′-DDE, 4,4′-DDT, dieldrin, endosulfan I, endosulfan II, endosulfan sulphate, endrin, heptachlor, heptachlor epoxide (isomer B) and methoxychlor have been selected and were analyzed in three different phases: dissolved phase (DP), suspended particulate matter (SPM) and sediments. PCBs and OCPs were extracted using an SPE column for the DP and glass fiber filter for SPM and sediment samples. Cleaned extracts were analyzed by gas chromatography with electron capture detector (ECD) and mass spectrometry (MS) detector for PCBs and OCPs, respectively. Results Pollutants discharges of PCBs and OCPs into the sea were calculated in about 106.9 kg year−1 (87.1 kg year−1 of PCBs and 19.7 kg year−1 of OCPs), showing that this river could be a major source of PCBs and OCPs pollution to the Central Mediterranean Sea. Total concentrations of PCBs ranged from 4.1 to 48.0 ng L−1 in water (sum of DP and SPM) and from 4.3 to 64.3 ng g−1 in sediment samples. The concentrations of total organochlorine pesticides (OCPs) obtained in water (sum of DP and SPM) ranged from 0.93 to 8.66 ng L−1 and from 0.52 to 9.89 ng g−1 in sediment samples. Principal component analysis shows that all PCB compounds are more likely to come from surface runoff than an atmospheric deposition. Conclusion The data show that higher levels of PCBs and OCPs were found in sediment samples than in DP and SPM samples, which are an indication of no fresh inputs of these compounds. Based on our results, unintentionally produced PCBs by industrial processes (and other processes) were considered to be the main sources of PCBs in Volturno River and Estuary sediments. Considering the Sediment Quality Guidelines (SQGs), the Ecological Risk Index (ERI), the Risk Quotient (RQ) and the USEPA Environmental Quality Standards (EQS), the Volturno River and its Estuary would be considered an area in which the integrity is possibly at risk