Understanding complex dynamics by means of an associated Riemann surface

We provide an example of how the complex dynamics of a recently introduced model can be understood via a detailed analysis of its associated Riemann surface. Thanks to this geometric description an explicit formula for the period of the orbits can be derived, which is shown to depend on the initial data and the continued fraction expansion of a simple ratio of the coupling constants of the problem. For rational values of this ratio and generic values of the initial data, all orbits are periodic and the system is isochronous. For irrational values of the ratio, there exist periodic and quasi-periodic orbits for different initial data. Moreover, the dependence of the period on the initial data shows a rich behavior and initial data can always be found such the period is arbitrarily high.Comment: 25 pages, 14 figures, typed in AMS-LaTe

Experimental and modelled reactions of CO2 and SO2 with core from a low salinity aquifer overlying a target CO2 storage complex

CO2‐induced reactions in low salinity aquifers overlying CO2 storage sites are of interest to understand potential reactions or impacts in the possible case of a leak. Previous investigations of overlying aquifers in the context of CO2 storage have focused on pure CO2 streams, however captured industrial CO2 streams may contain ancillary gases, including SO2, O2, NOx, H2S, N2, etc., some of which may be more reactive than CO2 when dissolved in formation water. Eight drill cores from two wells in a low salinity sandstone aquifer that overlies a target CO2 storage complex are characterised for porosity (helium, mercury injection, or micro CT), permeability, and mineral content. The eight Hutton Sandstone cores are variable with porosities of 5.2–19.6%, including carbonaceous mudstones, calcite cemented sandstones, and quartz rich sandstones, common lithologies that may be found generally in overlying aquifers of CO2 storage sites. A chlorite rich sandstone was experimentally reacted with CO2 and low concentrations of SO2 to investigate the potential reactions and possible mineral trapping in the unlikely event of a leak. Micro CT characterisation before and after the reaction indicated no significant change in porosity, although some fines movement was observed that could affect permeability. Dissolved concentrations of Fe, Ca, Mn, Cr, Mg, Rb, Li, Zn, etc., increased during the reaction, including from dissolution of chlorite and trace amounts of ankerite. After ~40 days dissolved concentrations including Fe, Zn, Al, Ba, As and Cr decreased. Chlorite was corroded, and Fe‐rich precipitates mainly Fe‐Cr oxides were observed to be precipitated on rock surfaces after experimental reaction. Concentrations of Rb and Li increased steadily and deserve further investigation as potential monitoring indicators for a leak. The reaction of chlorite rich sandstone with CO2 and SO2 was geochemically modelled over 10 years, with mainly chlorite alteration to siderite mineral trapping 1.55 kg/m of CO2 and removing dissolved Fe from solution. Kaolinite and chalcedony precipitation was also predicted, with minor pyrite precipitation trapping SO2, however no changes to porosity were predicted

A fresh approach to investigating CO2 storage: Experimental CO2-water-rock interactions in a low-salinity reservoir system

The interactions between CO2, water and rock in low-salinity host formations remain largely unexplored for conditions relevant to CO2 injection and storage. Core samples and sub-plugs from five Jurassic-aged Surat Basin sandstones and siltstones of varying mineralogy have been experimentally reacted in low-salinity water with supercritical CO2 at simulated in situ reservoir conditions (P=12MPa and T=60°C) for 16days (384h), with a view to characterising potential CO2-water-rock interactions in fresh or low-salinity potential siliclastic CO2 storage targets located in Queensland, Australia. CO2-water-rock reactions were coupled with detailed mineral and porosity characterisation, obtained prior to and following reaction, to identify changes in the mineralogy and porosity of selected reservoir and seal rocks during simulated CO2 injection. Aqueous element concentrations were measured from fluid extracts obtained periodically throughout the experiments to infer fluid-rock reactions over time. Fluid analyses show an evolution of dissolved concentration over time, with most major (e.g. Ca, Fe, Si, Mg, Mn) and minor (e.g. S, Sr, Ba, Zn) components increasing in concentration during reaction with CO2. Similar trends between elements reflect shared sources and/or similar release mechanisms, such as dissolution and desorption with decreasing pH. Small decreases in concentration of selected elements were observed towards the end of some experiments; however, no precipitation of minerals was directly observed in petrography. Sample characterisation on a fine scale allowed direct scrutiny of mineralogical and porosity changes by comparing pre- and post-reaction observations. Scanning electron microscopy and registered 3D images from micro-computed tomography (micro-CT) indicate dissolution of minerals, including carbonates, chlorite, biotite members, and, to a lesser extent, feldspars. Quantitative mineral mapping of sub-plugs identified dissolution of calcite from carbonate cemented core, with a decrease in calcite content from 17vol.% to 15vol.% following reaction, and a subsequent increase in porosity of 1.1vol.%. Kinetic geochemical modelling of the CO2-water-rock experiments successfully reproduced the general trends observed in aqueous geochemistry for the investigated major elements. After coupling experimental geochemistry with detailed sample characterisation and numerical modelling, expected initial reactions in the near-well region include partial dissolution and desorption of calcite, mixed carbonates, chloritic clays and annite due to pH decrease, followed in the longer-term by dissolution of additional silicates, such as feldspars. Dissolution of carbonates is predicted to improve injectivity in the near-well environment and contribute to the eventual re-precipitation of carbonates in the far field

Periodic Solutions of a System of Complex ODEs. II. Higher Periods

In a previous paper the real evolution of the system of ODEs ¨zn + zn = N m=1, m=n gnm(zn - zm) -3 , zn zn(t), zn dzn(t) dt , n = 1, . . . , N is discussed in CN , namely the N dependent variables zn, as well as the N(N - 1) (arbitrary!) "coupling constants" gnm, are considered to be complex numbers, while the independent variable t ("time") is real. In that context it was proven that there exists, in the phase space of the initial data zn(0), zn(0), an open domain having infinite measure, such that all trajectories emerging from it are completely periodic with period 2, zn(t + 2) = zn(t). In this paper we investigate, both by analytcal techniques and via the display of numerical simulations, the remaining solutions, and in particular we show that there exist many -- emerging out of sets of initial data having nonvanishing measures in the phase space of such data -- that are also completely periodic but with periods which are integer multiples of 2. We also elcidate the mechanism that yields nonperiodic solutions, including those characterized by a "chaotic" behavior, namely those associated, in the context of the initial-value problem, with a sensitive dependence on the initial data

Some remarks on generalised multipole expansions

Models for the mutual potential energy between two molecules proposed in the scientific literature often contain a sum of inverse-power interactions involving pairs of sites belonging to the two particles; in turn, these quantities are functions of a few scalar invariants involved in the problem at hand, and one is often interested in directly obtaining an explicit expression of the potential in terms of the latter; the extensively studied two-centre multipole expansion for the mutual electrostatic energy between two charge distributions is a well-known example of this procedure and of its restrictions. We consider here another, less widely known and possibly complementary, approach, proposed by Šebek some years ago [J. Šebek, Czech. J. Phys. B 38, 1185 (1988)];
the resulting formulae show that this procedure can become computationally favourable for sufficiently high molecular symmetry

Double-blind comparison of astemizole, terfenadine and placebo in hay fever with special regard to onset of action

In this double-blind study forty-seven patients with hay fever were treated for 8 days with either terfenadine 60 mg twice a day, astemizole 10 mg once a day or placebo. On the second day of treatment terfenadine was statistically significantly superior to astemizole and placebo according to the ratings of symptomatology, efficacy and individual symptoms. The median onset of symptom alleviation was 3 hours for terfenadine and 2 days for astemizole. On the eighth day both astemizole and terfenadine were statistically significantly more efficacious than placebo, but no significant differences were found between the two drugs. Both drugs were well tolerated

Wildlife conservation through forestry abandonment: responses of beetle communities to habitat change in the Eastern Alps

Research on changes in biodiversity due to the abandonment of forestry is important in understanding the role of reserves in conservation. The aim of this study was to investigate whether changes have occurred in species richness, abundance and composition of ground, longhorn and bark beetles due to habitat changes as a result of the cessation of forest management. We surveyed ten managed and ten abandoned forest plots in two watersheds located in the north-eastern Italian alpine region, which share a common history of use, climate regimes, stand structure and topography. Ground beetles, and longhorn and bark beetles were collected with pitfall and flight-intercept window traps, respectively, from May to mid-October 2010. The three beetle taxa responded differently to changes in habitat features and management cessation. Differences in individual species responses between the two watersheds may indicate a role of management abandonment through its impact on forest habitat structure. For instance, ground beetle species mainly responded negatively to soil moisture and positively to understorey vegetation cover. Unexpectedly, saproxylic species responded variably, and often negatively, to deadwood features in these forests, but did respond positively to the volume of standing Abies alba trees. The assemblages of carabids and bark beetles differed between the two watersheds. Our results confirmed that 50 years of forest management cessation resulted in changes in the biodiversity of beetles in alpine forests, likely due to their response to changes in habitat structure. Moreover, we expect that where the unplanned abandonment of forestry practices and habitat rewilding are undergoing, like in many marginal areas of Europe, similar habitat structure dynamics and beetle responses are likely to occur spontaneously