Numerical treatment of the hyperboloidal initial value problem for the vacuum Einstein equations. I. The conformal field equations

This is the first in a series of articles on the numerical solution of Friedrich's conformal field equations for Einstein's theory of gravity. We will discuss in this paper why one should be interested in applying the conformal method to physical problems and why there is good hope that this might even be a good idea from the numerical point of view. We describe in detail the derivation of the conformal field equations in the spinor formalism which we use for the implementation of the equations, and present all the equations as a reference for future work. Finally, we discuss the implications of the assumptions of a continuous symmetry.Comment: 19 pages, LaTeX2

Effect of Local Electron-Electron Correlation in Hydrogen-like Impurities in Ge

We have studied the electronic and local magnetic structure of the hydrogen interstitial impurity at the tetrahedral site in diamond-structure Ge, using an empirical tight binding + dynamical mean field theory approach because within the local density approximation (LDA) Ge has no gap. We first establish that within LDA the 1s spectral density bifurcates due to entanglement with the four neighboring sp3 antibonding orbitals, providing an unanticipated richness of behavior in determining under what conditions a local moment hyperdeep donor or Anderson impurity will result, or on the other hand a gap state might appear. Using a supercell approach, we show that the spectrum, the occupation, and the local moment of the impurity state displays a strong dependence on the strength of the local on-site Coulomb interaction U, the H-Ge hopping amplitude, the depth of the bare 1s energy level epsilon_H, and we address to some extent the impurity concentration dependence. In the isolated impurity, strong interaction regime a local moment emerges over most of the parameter ranges indicating magnetic activity, and spectral density structure very near (or in) the gap suggests possible electrical activity in this regime.Comment: 9 pages, 5 figure

Analysis of stochastic time series in the presence of strong measurement noise

A new approach for the analysis of Langevin-type stochastic processes in the presence of strong measurement noise is presented. For the case of Gaussian distributed, exponentially correlated, measurement noise it is possible to extract the strength and the correlation time of the noise as well as polynomial approximations of the drift and diffusion functions from the underlying Langevin equation.Comment: 12 pages, 10 figures; corrected typos and reference

Conservation agriculture in the dry Mediterranean climate

The objective of this article is to review: (a) the concepts and principles that underpin Conservation Agriculture (CA) ecologically and operationally; (b) the potential benefits that can be harnessed through CA systems in the dry Mediterranean climates; (c) current status of adoption and spread of CA in the dry Mediterranean climate countries; and (d) opportunities for CA in the Central and West Asia and North Africa (CWANA) region. CA, comprising minimum mechanical soil disturbance and no-tillage seeding, organic mulch cover, and crop diversification is now practised on some 125 million ha, corresponding to about 9% of the global arable cropped land. Globally, the area under CA is spread across all continents and all agro-ecologies, including the dryland climates in the Mediterranean basin region as well as in the Mediterranean climates elsewhere in the world. Worldwide empirical and scientific evidence is available to show that significant productivity, economic, social and environmental benefits exist that can be harnessed through the adoption of CA principles for sustainable production intensification in the dry Mediterranean climates, including those in the CWANA region. The benefits include: fundamental change for the better in the sustainability of production systems and ecosystem services; higher stable yields and incomes; climate change adaptation and reduced vulnerability to the highly erratic rainfall distribution; and reduced greenhouse gas emissions. CA has taken off globally and is now spreading in several Mediterranean climates outside the Mediterranean basin particularly in South America, South Africa and Australia. In the dry Mediterranean climates in the CWANA region, CA is perceived to be a powerful tool of land management but CA has not yet taken off. Research on CA in the CWANA region has shown that there are opportunities for CA adoption in rainfed and irrigated farming systems involving arable and perennial crops as well as livestock

Magnetic traveling-stripe-forcing: enhanced transport in the advent of the Rosensweig instability

A new kind of contactless pumping mechanism is realized in a layer of ferrofluid via a spatio-temporally modulated magnetic field. The resulting pressure gradient leads to a liquid ramp, which is measured by means of X-rays. The transport mechanism works best if a resonance of the surface waves with the driving is achieved. The behavior can be understood semi-quantitatively by considering the magnetically influenced dispersion relation of the fluid.Comment: 6 Pages, 8 Figure

The G_2 sphere over a 4-manifold

We present a construction of a canonical G_2 structure on the unit sphere tangent bundle S_M of any given orientable Riemannian 4-manifold M. Such structure is never geometric or 1-flat, but seems full of other possibilities. We start by the study of the most basic properties of our construction. The structure is co-calibrated if, and only if, M is an Einstein manifold. The fibres are always associative. In fact, the associated 3-form results from a linear combination of three other volume 3-forms, one of which is the volume of the fibres. We also give new examples of co-calibrated structures on well known spaces. We hope this contributes both to the knowledge of special geometries and to the study of 4-manifolds.Comment: 13 page

Subordinated Langevin Equations for Anomalous Diffusion in External Potentials - Biasing and Decoupled Forces

The role of external forces in systems exhibiting anomalous diffusion is discussed on the basis of the describing Langevin equations. Since there exist different possibilities to include the effect of an external field the concept of {\it biasing} and {\it decoupled} external fields is introduced. Complementary to the recently established Langevin equations for anomalous diffusion in a time-dependent external force-field [{\it Magdziarz et al., Phys. Rev. Lett. {\bf 101}, 210601 (2008)}] the Langevin formulation of anomalous diffusion in a decoupled time-dependent force-field is derived

The near-synchronous polar V1432 Aql (RX J1940.1-1025): Accretion geometry and synchronization time scale

The magnetic Cataclysmic Variable (mCV) V1432 Aql (RX 1940.1-1025) belongs to the four-member subclass of near-synchronous polars with a slight non-synchronism (<2 %) between the spin period of the white dwarf and the binary period. In these systems the accretion geometry changes periodically with phase of the beat cycle. We present the application of a dipole accretion model for near-synchronous systems developed by Geckeler & Staubert (1997a) to extended optical and X-ray data. We detect a significant secular change of the white dwarf spin period in V1432 Aql of dP_spin/dt = -5.4 (+3.7/-3.2) 10-9 s/s from the optical data set alone. This corresponds to a synchronization time scale tau_sync = 199 (+441/-75) yr, comparable to the time scale of 170 yr for V1500 Cyg. The synchronization time scale in V1432 Aql is in excellent agreement with the theoretical prediction from the dominating magnetic torque in near-synchronous systems. We also present period analyses of optical CCD photometry and RXTE X-ray data, which argue against the existence of a 4000 s period and an interpretation of V1432 Aql as an intermediate polar. The dipole accretion model also allows to constrain the relevant parameters of the accretion geometry in this system: the optical data allow an estimate of the dimensionless parameter (R_t0'/R_wd)1/2 sin(beta) = 3.6 (+2.7/-1.1), with a lower limit for the threading radius of R_t0' > 10 R_wd (68% confidence).Comment: 12 pages, 10 figures, 6 tables accepted by A&

Theory for the single-point velocity statistics of fully developed turbulence

We investigate the single-point velocity probability density function (PDF) in three-dimensional fully developed homogeneous isotropic turbulence within the framework of PDF equations focussing on deviations from Gaussianity. A joint analytical and numerical analysis shows that these deviations may be quantified studying correlations of dynamical quantities like pressure gradient, external forcing and energy dissipation with the velocity. A stationary solution for the PDF equation in terms of these quantities is presented, and the theory is validated with the help of direct numerical simulations indicating sub-Gaussian tails of the PDF.Comment: 6 pages, 4 figures, corrected typo in eq. (4

First-order symmetrizable hyperbolic formulations of Einstein's equations including lapse and shift as dynamical fields

First-order hyperbolic systems are promising as a basis for numerical integration of Einstein's equations. In previous work, the lapse and shift have typically not been considered part of the hyperbolic system and have been prescribed independently. This can be expensive computationally, especially if the prescription involves solving elliptic equations. Therefore, including the lapse and shift in the hyperbolic system could be advantageous for numerical work. In this paper, two first-order symmetrizable hyperbolic systems are presented that include the lapse and shift as dynamical fields and have only physical characteristic speeds.Comment: 11 page