Riccati-type equations, generalised WZNW equations, and multidimensional Toda systems

We associate to an arbitrary $\mathbb Z$-gradation of the Lie algebra of a Lie group a system of Riccati-type first order differential equations. The particular cases under consideration are the ordinary Riccati and the matrix Riccati equations. The multidimensional extension of these equations is given. The generalisation of the associated Redheffer--Reid differential systems appears in a natural way. The connection between the Toda systems and the Riccati-type equations in lower and higher dimensions is established. Within this context the integrability problem for those equations is studied. As an illustration, some examples of the integrable multidimensional Riccati-type equations related to the maximally nonabelian Toda systems are given.Comment: LaTeX2e, 18 page

The complex Sine-Gordon equation as a symmetry flow of the AKNS Hierarchy

It is shown how the complex sine-Gordon equation arises as a symmetry flow of the AKNS hierarchy. The AKNS hierarchy is extended by the ``negative'' symmetry flows forming the Borel loop algebra. The complex sine-Gordon and the vector Nonlinear Schrodinger equations appear as lowest negative and second positive flows within the extended hierarchy. This is fully analogous to the well-known connection between the sine-Gordon and mKdV equations within the extended mKdV hierarchy. A general formalism for a Toda-like symmetry occupying the ``negative'' sector of sl(N) constrained KP hierarchy and giving rise to the negative Borel sl(N) loop algebra is indicated.Comment: 8 pages, LaTeX, typos corrected, references update

Hysteresis and re-entrant melting of a self-organized system of classical particles confined in a parabolic trap

A self-organized system composed of classical particles confined in a two-dimensional parabolic trap and interacting through a potential with a short-range attractive part and long-range repulsive part is studied as function of temperature. The influence of the competition between the short-range attractive part of the inter-particle potential and its long-range repulsive part on the melting temperature is studied. Different behaviors of the melting temperature are found depending on the screening length ($\kappa$) and the strength ($B$) of the attractive part of the inter-particle potential. A re-entrant behavior and a thermal induced phase transition is observed in a small region of ($\kappa,B$)-space. A structural hysteresis effect is observed as a function of temperature and physically understood as due to the presence of a potential barrier between different configurations of the system.Comment: 8 pages, 6 figure

Shelf-Ocean material exchange influencing the Atlantic chemical composition off NW Iberian margin since the last glaciation

Rivers are the main conduit of sediment to the shelf. The basin geology, the drainage area and the discharge rate are the major factors that determine their sediment load (Milliman and Syvistski, 1992). Besides suspended particles, dissolved components may also give some information on the eroded crust. Sr isotopes in carbonate shells of biological organisms have been used to study, in the geological record, the influence exerted by the chemical weathering of the continental crust on the seawater composition (Macdougall, 1991). In this work, Sr isotope ratios obtained in tests of foraminifera representing the last 40 ka are presented and discussed in the scope of the palaeogeographical evolution of NW Iberia. This work aims to present and discuss the results of Sr isotope analyses (performed, by TIMS, in the Isotope Geology Laboratory of the University of Aveiro) of tests of two species of foraminifera, from nine samples taken along the OMEX core KC 024-19 (181 cm; 42°08’98’’N, 10°29´96’’W, and 2765m), collected in the Galicia Bank area, off Galicia. Taking into account that Sr contained in the carbonate tests is usually considered as preserving the signature of the contemporaneous seawater, one planktonic species (Globigerina bulloides) and one benthic species (Cibicides wuellerstorfi) were selected in order to try to detect Sr isotope variations both through time and between two different levels of the water column. The core age model, which records the last 40 ka, is based on a combination of oxygen isotope stratigraphy, eight AMS 14C datings and the synchronisation of the last four Heinrich Events in the Iberian Margin sedimentary records. As a whole, the obtained 87Sr/86Sr ratios vary between 0.709209 and 0.709108, with a mean 2σ error of 0.000025. These values lie within the range of modern marine Sr isotope ratios (0.70910-0.70922), as previously defined using analyses of both seawater and marine carbonates (see compilation by Faure and Mensing, 2005). Despite their small variation, the 87Sr/86Sr ratios obtained in G. bulloides seem to indicate that Sr dissolved in seawater at the KC 024-19 core site became slightly less radiogenic after the Last Glacial Maximum (LGM). This decrease is concomitant with diminishing amounts of the detrital components in the sediments (Fig. 1). Therefore, both the composition of dissolved Sr, as revealed by results on tests of planktonic foraminifera, and the proportions of suspended terrigenous particulate material arriving at the KC 024-19 site point to a decreasing importance of the contribution of the erosion of the Iberian Variscan crust since the Last Glacial Maximum and in the Holocene. The 87Sr/86Sr ratios measured in tests of benthic foraminifera (C. wuellerstorfi) are more erratic and no correlation can be established with palaeogeographical/palaeoclimatic constraints. The difference between the behaviour of Sr compositions in G. bulloides and C. wuellerstorfi may indicate that whilst the planktonic foraminifera should reproduce very closely the seawater composition, the benthic organisms should, in addition to the major role of seawater, also be affected by some sort of interaction with the sediments. As such, planktonic foraminifera are probably more reliable indicators of seawater composition in studies involving very small periods and corresponding very slight variations of the 87Sr/86Sr ratios. Taking into account that G. bulloides is a common planktonic species (living mostly in the first 50m of the water column), whose tests seem to be in equilibrium with sea water composition, variations in its 87Sr/86Sr ratios can be related with changes in the chemical composition of the water of the Atlantic Ocean off NW Iberian Margin. The highest 87Sr/86Sr values are contemporaneous with a period of low sea level (about -140 m; Dias et al., 2000) during the LGM. According to Dias et al. (2000) at 18 ka BP the shoreline was close to the shelf break. The summital parts of the Gerês and Estrela mountains were covered by local glaciers and close to the coast freezing occurred frequently. The river catchments, which extended far to the shelf, received more rainfall due to a longer, compared to present day conditions, wet season, which promoted both physical and chemical weathering. Higher pluviosity combined with the effect of spring ice melting maintained high river discharge and consequently caused very important sediment supply to the coastal zone. The extremely narrow shelf was a very energetic environment due to sea bottom inclination and very limited long wave refraction. Therefore, at that time, a long wet season and very competent rivers should have caused important erosion of the Variscan basement in NW Iberia. Additionally, then, the shoreline was much closer to the KC 024-19 site. The combination of all these factors favoured an important deposition of terrigenous sediments and the local slight enrichment in radiogenic Sr of the seawater. With sea level rise, after the deglaciation and during the Holocene, the river estuaries became progressively far away from the shelf break. Their competence of transport also became progressively reduced and the offshore transport of detrital sediments became progressively lower. Conversely the biogenic carbonate proportion in the sediments increased, due to lower dilution by the terrigenous particles. Simultaneously, the values of 87Sr/86Sr in the seawater at the KC 024-19 site became lower, as a consequence of a complete homogenization with the ocean global composition, which was now more effective with the increasing distance towards shoreline

Avaliação participativa de acessos de bucha vegetal.

Publicado também na Revista Brasileira de Agroecologia, v. 4, n. 2, 2009

Transition from single-file to two-dimensional diffusion of interacting particles in a quasi-one-dimensional channel

Diffusive properties of a monodisperse system of interacting particles confined to a \textit{quasi}-one-dimensional (Q1D) channel are studied using molecular dynamics (MD) simulations. We calculate numerically the mean-squared displacement (MSD) and investigate the influence of the width of the channel (or the strength of the confinement potential) on diffusion in finite-size channels of different shapes (i.e., straight and circular). The transition from single-file diffusion (SFD) to the two-dimensional diffusion regime is investigated. This transition (regarding the calculation of the scaling exponent ($\alpha$) of the MSD $$ $\propto t^{\alpha}$) as a function of the width of the channel, is shown to change depending on the channel's confinement profile. In particular the transition can be either smooth (i.e., for a parabolic confinement potential) or rather sharp/stepwise (i.e., for a hard-wall potential), as distinct from infinite channels where this transition is abrupt. This result can be explained by qualitatively different distributions of the particle density for the different confinement potentials.Comment: 13 pages, 11 figure

Time-dependent magnetohydrodynamic self-similar extragalactic jets

Extragalactic jets are visualized as dynamic erruptive events modelled by time-dependent magnetohydrodynamic (MHD) equations. The jet structure comes through the temporally self-similar solutions in two-dimensional axisymmetric spherical geometry. The two-dimensional magnetic field is solved in the finite plasma pressure regime, or finite $\beta$ regime, and it is described by an equation where plasma pressure plays the role of an eigenvalue. This allows a structure of magnetic lobes in space, among which the polar axis lobe is strongly peaked in intensity and collimated in angular spread comparing to the others. For this reason, the polar lobe overwhelmes the other lobes, and a jet structure arises in the polar direction naturally. Furthermore, within each magnetic lobe in space, there are small secondary regions with closed two-dimensional field lines embedded along this primary lobe. In these embedded magnetic toroids, plasma pressure and mass density are much higher accordingly. These are termed as secondary plasmoids. The magnetic field lines in these secondary plasmoids circle in alternating sequence such that adjacent plasmoids have opposite field lines. In particular, along the polar primary lobe, such periodic plasmoid structure happens to be compatible with radio observations where islands of high radio intensities are mapped

Two-component mixture of charged particles confined in a channel: melting

The melting of a binary system of charged particles confined in a {\it quasi}-one-dimensional parabolic channel is studied through Monte Carlo simulations. At zero temperature the particles are ordered in parallel chains. The melting is anisotropic and different melting temperatures are obtained according to the spatial direction, and the different types of particles present in the system. Melting is very different for the single-, two- and four-chain configurations. A temperature induced structural phase transition is found between two different four chain ordered states which is absent in the mono-disperse system. In the mixed regime, where the two types of particles are only slightly different, melting is almost isotropic and a thermally induced homogeneous distribution of the distinct types of charges is observed.Comment: To appear in Journal of Physics: condensed matter ; (13 pages, 12 figures

Prediction of the cross-sectional capacity of cold-formed CHS using numerical modelling and machine learning

The use of circular hollow sections (CHS) have seen a large increase in usage in recent years mainly because of the distinctive mechanical properties and unique aesthetic appearance. The focus of this paper is the behaviour of cold-rolled CHS beam-columns made from normal and high strength steel, aiming to propose a design formula for predicting the ultimate cross-sectional load carrying capacity, employing machine learning. A finite element model is developed and validated to conduct an extensive parametric study with a total of 3410 numerical models covering a wide range of the most influential parameters. The ANN model is then trained and validated using the data obtained from the developed numerical models as well as 13 test results compiled from various research available in the literature, and accordingly a new design formula is proposed. A comprehensive comparison with the design rules given in EC3 is presented to assess the performance of the ANN model. According to the results and analysis presented in this study, the proposed ANN-based design formula is shown to be an efficient and powerful design tool to predict the cross-sectional resistance of the CHS beam-columns with a high level of accuracy and the least computational costs