Contrasting multi-taxa diversity patterns between abandoned and non-intensively managed forests in the southern Dolomites

The abandonment of silvicultural activities can lead to changes in species richness and composition of biological communities, when compared to those found in managed forests. The aim of this study was to compare the multi-taxonomical diversity of two mature silver fir-beech-spruce forests in the southern Dolomites (Italy), corresponding to the European Union habitat type 9130. The two sites share similar ecological and structural characteristics, but differ in their recent management histories. In the last 50 years, one site underwent non-intensive management, while the other was left unmanaged and was included in a forest reserve. The species richness and composition of eight taxa were surveyed in the two sites between 2009 and 2011. The difference in mean species richness between the two forest management types was tested through permutation tests, while differences in species composition were tested by principal coordinates analysis and the permutational multivariate analysis of variance. Mean species richness of soil macrofungi, deadwood lichens, bark beetles, and longhorn beetles were significantly higher in the abandoned than in the non-intensively managed forests. Deadwood fungi and epiphytic lichens did not differ in mean species richness between the two study sites, while mean species richness of ground beetles and birds were higher in the non-intensively managed than in the abandoned forest. Significant differences in species composition between the two sites were found for all the taxa, except for longhorn beetles. These results indicate that improving forest landscape heterogeneity through the creation of a mosaic of abandoned and extensively managed forests should better fulfill the requirements of ecologically different taxa

Automatic differentiation in geophysical inverse problems

Automatic differentiation (AD) is the technique whereby output variables of a computer code evaluating any complicated function (e.g. the solution to a differential equation) can be differentiated with respect to the input variables. Often AD tools take the form of source to source translators and produce computer code without the need for deriving and hand coding of explicit mathematical formulae by the user. The power of AD lies in the fact that it combines the generality of finite difference techniques and the accuracy and efficiency of analytical derivatives, while at the same time eliminating 'human' coding errors. It also provides the possibility of accurate, efficient derivative calculation from complex 'forward' codes where no analytical derivatives are possible and finite difference techniques are too cumbersome. AD is already having a major impact in areas such as optimization, meteorology and oceanography. Similarly it has considerable potential for use in non-linear inverse problems in geophysics where linearization is desirable, or for sensitivity analysis of large numerical simulation codes, for example, wave propagation and geodynamic modelling. At present, however, AD tools appear to be little used in the geosciences. Here we report on experiments using a state of the art AD tool to perform source to source code translation in a range of geoscience problems. These include calculating derivatives for Gibbs free energy minimization, seismic receiver function inversion, and seismic ray tracing. Issues of accuracy and efficiency are discussed

Rogue wave formation scenarios for the focusing nonlinear Schr\"odinger equation with parabolic-profile initial data on a compact support

We study the (1+1) focusing nonlinear Schroedinger (NLS) equation for an initial condition with concave parabolic profile on a compact support and phase depending quadratically on the spatial coordinate. In the absence of dispersion, using the natural class of self-similar solutions of the resulting elliptic system, we generalise a result by Talanov, Guervich and Shvartsburg, finding a criterion on the chirp and modulus coefficients at time equal zero to determine whether the dispersionless solution features asymptotic relaxation or a blow-up at fine time, providing an explicit formula for the time of catastrophe. In the presence of dispersion, we numerically show that the same criterion determines, even beyond the semi-classical regime, whether the solution relaxes or develops a higher order rogue wave, whose amplitude can be several multiples of the height of the initial parabola. In the latter case, for small dispersion, the time of catastrophe for the corresponding dispersionless solution predicts almost exactly the onset time of the rogue wave. In our numerical experiments, the sign of the chirp appears to determine the prevailing scenario, among two competing mechanisms leading to the formation of a rogue wave. For negative values, the simulations are suggestive of the dispersive regularisation of a gradient catastrophe described by Bertola and Tovbis for a different class of smooth, bell-shaped initial data. As the chirp becomes positive, the rogue wave seem to result from the interaction of counter-propagating dispersive dam break flows, as described for the box problem by El, Khamis and Tovbis. As the chirp and amplitude of the initial profile are relatively easy to manipulate in optical devices and water tank wave generators, we expect our observation to be relevant for experiments in nonlinear optics and fluid dynamics.Comment: 17 pages, 5 figures, 1 tabl

Rogue wave formation scenarios for the focusing nonlinear Schrödinger equation with parabolic-profile initial data on a compact support

We study the (1+1) focusing nonlinear Schrödinger equation for an initial condition with compactly supported parabolic profile and phase depending quadratically on the spatial coordinate. In the absence of dispersion, using the natural class of self-similar solutions, we provide a criterion for blowup in finite time, generalizing a result by Talanov et al. In the presence of dispersion, we numerically show that the same criterion determines, even beyond the semiclassical regime, whether the solution relaxes or develops a high-order rogue wave, whose onset time is predicted by the corresponding dispersionless catastrophe time. The sign of the chirp appears to determine the prevailing scenario among two competing mechanisms for rogue wave formation. For negative values, the numerical simulations are suggestive of the dispersive regularization of a gradient catastrophe described by Bertola and Tovbis for a different class of smooth, bell-shaped initial data. As the chirp becomes positive, the rogue wave seems to result from the interaction of counterpropagating dispersive dam break flows, as in the box problem recently studied by El, Khamis, and Tovbis. As the chirp and amplitude of the initial profile are relatively easy to manipulate in optical devices and water tank wave generators, we expect our observation to be relevant for experiments in nonlinear optics and fluid dynamics

Solvable nonlinear evolution PDEs in multidimensional space

A class of solvable (systems of) nonlinear evolution PDEs in multidimensional space is discussed. We focus on a rotation-invariant system of PDEs of Schrödinger type and on a relativistically-invariant system of PDEs of Klein-Gordon type. Isochronous variants of these evolution PDEs are also considered

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

Propagating two-dimensional magnetic droplets

Propagating, solitary magnetic wave solutions of the Landau-Lifshitz equation with uniaxial, easy-axis anisotropy in thin (two-dimensional) magnetic films are investigated. These localized, nontopological wave structures, parametrized by their precessional frequency and propagation speed, extend the stationary, coherently precessing "magnon droplet" to the moving frame, a non-trivial generalization due to the lack of Galilean invariance. Propagating droplets move on a spin wave background with a nonlinear droplet dispersion relation that yields a limited range of allowable droplet speeds and frequencies. An iterative numerical technique is used to compute the propagating droplet's structure and properties. The results agree with previous asymptotic calculations in the weakly nonlinear regime. Furthermore, an analytical criterion for the droplet's orbital stability is confirmed. Time-dependent numerical simulations further verify the propagating droplet's robustness to perturbation when its frequency and speed lie within the allowable range.Comment: 16 pages, 11 figure

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