Multiple Enrichment Processes and their Relationships in the Subcrustal Lithosphere Beneath the Eifel (Germany)

Three types of enrichment processes may be distinguished inspinel peridotite mantle xenoliths from the West Eifel (Germany):

1. Enrichmentof light rare earth elements (LREE) occurs in wholerocks andclinopyroxenes in conjunction with the formation ofTi-pooramphiboles (<0•5%) in a low-tempetature suite(900C).
2. Enrichment in high field strength elements (HFSE; Ti and Hf)is associated with strong zoning of TiO₂ in amphibole adjacentto mica hornblendite veins. A reheating from 900 to 1050C associatedwith this vein formation is reflected by the zoning profilesin orthopyroxenes with Ca, Al, and Cr increasing from core torim.
3. Moderate enrichment of LREE without amphibole formationin ahigh-temperature suite (1125C) is observed at the contactofperidotites to pyroxenite veins yielding the same temperature.
4. Based on geochemical and isotopic evidence, enrichment process(1) is inferred to be due to interaction of peridotites fromthe subcrustal lithosphere with low-density fluids. Process(2) represents a subsequent interaction of amphibole-bearingperidotites formed during the first process with basic meltsmoving through a system of cross-cutting dykes and veins. Processes(2) and (3) are linked to the Quaternary West Eifel volcanism.Geothermobarometry of the xenoliths shows that these processesare related to different depth regimes of the lower lithosphere.

     

Effects of forest roads on the hydrological response of a small‐scale mountain watershed in Greece

The effects of land use changes on the ecology and hydrology of natural watersheds have long been debated. However, less attention has been given to the hydrological effects of forest roads. Although less studied, several researchers have claimed that streamflow changes related to forest roads can cause a persistent and pervasive effect on hillslope hydrology and the functioning of the channel system. The main potential direct effects of forest roads on natural watersheds hydrologic response are runoff production on roads surfaces due to reduced infiltration rates, interruption of subsurface flow by road cutslopes and rapid transfer of the produced runoff to the stream network through roadside ditches. The aforementioned effects may significantly modify the total volume and timing of the hillslope flow to the stream network. This study uses detailed field data, spatial data, hydro‐meteorological records, as well as numerical simulation to investigate the effects of forest roads on the hydrological response of a small‐scale mountain experimental watershed, which is situated in the east side of Penteli Mountain, Attica, Greece. The results of this study highlight the possible effects of forest roads on the watersheds hydrological response that may significantly influence direct runoff depths and peak flow rates. It is demonstrated that these effects can be very important in permeable watersheds and that more emphasis should be given on the impact of roads on the watersheds hydrological response. Copyright © 2014 John Wiley & Sons, Ltd.     

SEPARATION OF REGIONAL AND RESIDUAL ANOMALIES BY LEAST-SQUARES ORTHOGONAL POLYNOMIAL AND RELAXATION TECHNIQUES: A PERFORMANCE EVALUATION1

The performances of least-squares orthogonal polynomial and relaxation techniques in the separation of regional and residual anomalies have been evaluated with a view to minimizing personal biasing. The advantage of orthogonal over nonorthogonal polynomials is their ability to estimate an optimum order of polynomial to represent the predominant regional trend in the data using an approximate 2D difference table, the Z-matrix. The correlation coefficients between residuals of two consecutive orders also give the same result. In the relaxation technique, a linear trend is assumed within each cell of the mesh of a square grid. A set of such linear segments can approximate any complicated regional trend. The performances of these two techniques have been evaluated using simulated gravity anomalies produced by 2D and 3D complex regional structures superimposed on residual fields due to cylinders and prismatic bodies, as well as three field examples taken from the published literature. The analyses have revealed that the relaxation technique produces excellent results when an optimum polynomial order rather than an arbitrary fixed one is used for computing the boundary conditions along the periphery of the map. Analyses have revealed that such boundary conditions provide minimum distortion near the two ends of the profile.     

Detection of Ordered and Chaotic Motion Using the Dynamical Spectra

Two simple and efficient numerical methods to explore the phase space structure are presented, based on the properties of the "dynamical spectra". 1) We calculate a "spectral distance" D of the dynamical spectra for two different initial deviation vectors. D → 0 in the case of chaotic orbits, while D → const ≠ 0 in the case of ordered orbits. This method is by orders of magnitude faster than the method of the Lyapunov Characteristic Number (LCN). 2) We define a sensitive indicator called ROTOR (ROtational TOri Recongnizer) for 2D maps. The ROTOR remains zero in time on a rotational torus, while it tends to infinity at a rate ∝ N = number of iterations, in any case other than a rotational torus. We use this method to locate the last KAM torus of an island of stability, as well as the most important cantori causing stickiness near it. This revised version was published online in July 2006 with corrections to the Cover Date.     

Particle distributions and X-ray spectra in single or multiple solar current sheets

The acceleration of charged particles in a site of magnetic reconnection is analysed by detailed numerical simulations. Single or multiple encounters of the particles with Harris-type reconnecting current sheets (RCSs) are modelled as an overall stochastic process taking place within an active region. RCS physical parameters are selected in a parameter space relevant to solar flares. Initially, the charged particles form a thermal (Maxwellian) distribution corresponding to coronal temperature  ≃2 × 10⁶ K  . Our main goal is to investigate how the acceleration process changes the shape of the particles' kinetic energy distribution. The evolution of the kinetic energy distribution, calculated numerically after one encounter of the particles with a single RCS, is found to be in good agreement with our previously published analytical formulae. In the case of consecutive encounters, we find that the kinetic distribution tends to converge to a practically invariant form after a relatively small number of encounters. We construct a discrete stochastic process that reproduces the numerical distributions and we provide a theoretical interpretation of the asymptotic convergence of the energy distribution. We finally compute the theoretical X-ray spectra that would be emitted by the simulated particles in a thick target model of radiation.     

Regular and chaotic dynamics in 3D reconnecting current sheets

We consider the possibility of particles being injected at the interior of a reconnecting current sheet (RCS), and study their orbits by dynamical systems methods. As an example we consider orbits in a 3D Harris type RCS. We find that, despite the presence of a strong electric field, a 'mirror' trapping effect persists, to a certain extent, for orbits with appropriate initial conditions within the sheet. The mirror effect is stronger for electrons than for protons. In summary, three types of orbits are distinguished: (i) chaotic orbits leading to escape by stochastic acceleration, (ii) regular orbits leading to escape along the field lines of the reconnecting magnetic component, and (iii) mirror-type regular orbits that are trapped in the sheet, making mirror oscillations. Dynamically, the latter orbits lie on a set of invariant KAM tori that occupy a considerable amount of the phase space of the motion of the particles. We also observe the phenomenon of 'stickiness', namely chaotic orbits that remain trapped in the sheet for a considerable time. A trapping domain, related to the boundary of mirror motions in velocity space, is calculated analytically. Analytical formulae are derived for the kinetic energy gain in regular or chaotic escaping orbits. The analytical results are compared with numerical simulations.     

Invariant manifolds, phase correlations of chaotic orbits and the spiral structure of galaxies

In the presence of a strong   m = 2  component in a rotating galaxy, the phase-space structure near corotation is shaped to a large extent by the invariant manifolds of the short-period family of unstable periodic orbits terminating at L ₁ or L ₂. The main effect of these manifolds is to create robust phase correlations among a number of chaotic orbits large enough to support a spiral density wave outside corotation. The phenomenon is described theoretically by soliton-like solutions of a Sine–Gordon equation. Numerical examples are given in an N -body simulation of a barred spiral galaxy. In these examples, we demonstrate how the projection of unstable manifolds in configuration space reproduces essentially the entire observed bar–spiral pattern.     

The coalescence of invariant manifolds and the spiral structure of barred galaxies

In a previous paper (Voglis et al., Paper I), we demonstrated that, in a rotating galaxy with a strong bar, the unstable asymptotic manifolds of the short-period family of unstable periodic orbits around the Lagrangian points L ₁ or L ₂ create correlations among the apocentric positions of many chaotic orbits, thus supporting a spiral structure beyond the bar. In this paper, we present evidence that the unstable manifolds of all the families of unstable periodic orbits near and beyond corotation contribute to the same phenomenon. Our results refer to a N -body simulation, a number of drawbacks of which, as well as the reasons why these do not significantly affect the main results, are discussed. We explain the dynamical importance of the invariant manifolds as due to the fact that they produce a phenomenon of 'stickiness' slowing down the rate of chaotic escape in an otherwise non-compact region of the phase space. We find a stickiness time of the order of 100 dynamical periods, which is sufficient to support a long-living spiral structure. Manifolds of different families become important at different ranges of values of the Jacobi constant. The projections of the manifolds of all the different families in the configuration space produce a pattern due to the 'coalescence' of the invariant manifolds. This follows closely the maxima of the observed   m = 2  component near and beyond corotation. Thus, the manifolds support both the outer edge of the bar and the spiral arms.     

Cantori, Islands and Asymptotic Curves in the Stickiness Region

The resonant structure near a noble cantorus is found. Islands of stability are located near the gaps of the cantorus. The crossing of the gaps of the cantorus by the asymptotic curves of unstable periodic orbits is shown numerically (non-schematically). We discuss how these structures influence stickiness. This revised version was published online in July 2006 with corrections to the Cover Date.