Identification and model based assessment of the potential water retention caused by land-use changes

International audienceThe extreme summer flood in the Elbe River watershed initiated a debate on the role of forest conversion and afforestation as measures for preventive flood protection. To quantify the effect of forest conversion and afforestation on flood runoff from catchments reliable model calculations are essential. The article overviews the present state of our work and provides an example for a model- based assessment of potential water retention caused by land-use changes in a catchment in the Central Ore Mountains (Saxony, Germany). The potential of flood control by land-use management measures is highly dependant on the site-specific soil and relief conditions and the rainfall event characteristics. The pre-event soil moisture is distinctly lower under forest land-use. Furthermore, infiltration, percolation in the subsoil is increased. These effects exist for small/medium-scale events whereas they become marginal for extreme events

Quantum Spin Dynamics VIII. The Master Constraint

Recently the Master Constraint Programme (MCP) for Loop Quantum Gravity (LQG) was launched which replaces the infinite number of Hamiltonian constraints by a single Master constraint. The MCP is designed to overcome the complications associated with the non -- Lie -- algebra structure of the Dirac algebra of Hamiltonian constraints and was successfully tested in various field theory models. For the case of 3+1 gravity itself, so far only a positive quadratic form for the Master Constraint Operator was derived. In this paper we close this gap and prove that the quadratic form is closable and thus stems from a unique self -- adjoint Master Constraint Operator. The proof rests on a simple feature of the general pattern according to which Hamiltonian constraints in LQG are constructed and thus extends to arbitrary matter coupling and holds for any metric signature. With this result the existence of a physical Hilbert space for LQG is established by standard spectral analysis.Comment: 19p, no figure

Algebraic Quantum Gravity (AQG) III. Semiclassical Perturbation Theory

In the two previous papers of this series we defined a new combinatorical approach to quantum gravity, Algebraic Quantum Gravity (AQG). We showed that AQG reproduces the correct infinitesimal dynamics in the semiclassical limit, provided one incorrectly substitutes the non -- Abelean group SU(2) by the Abelean group $U(1)^3$ in the calculations. The mere reason why that substitution was performed at all is that in the non -- Abelean case the volume operator, pivotal for the definition of the dynamics, is not diagonisable by analytical methods. This, in contrast to the Abelean case, so far prohibited semiclassical computations. In this paper we show why this unjustified substitution nevertheless reproduces the correct physical result: Namely, we introduce for the first time semiclassical perturbation theory within AQG (and LQG) which allows to compute expectation values of interesting operators such as the master constraint as a power series in $\hbar$ with error control. That is, in particular matrix elements of fractional powers of the volume operator can be computed with extremely high precision for sufficiently large power of $\hbar$ in the $\hbar$ expansion. With this new tool, the non -- Abelean calculation, although technically more involved, is then exactly analogous to the Abelean calculation, thus justifying the Abelean analysis in retrospect. The results of this paper turn AQG into a calculational discipline

From the discrete to the continuous - towards a cylindrically consistent dynamics

Discrete models usually represent approximations to continuum physics. Cylindrical consistency provides a framework in which discretizations mirror exactly the continuum limit. Being a standard tool for the kinematics of loop quantum gravity we propose a coarse graining procedure that aims at constructing a cylindrically consistent dynamics in the form of transition amplitudes and Hamilton's principal functions. The coarse graining procedure, which is motivated by tensor network renormalization methods, provides a systematic approximation scheme towards this end. A crucial role in this coarse graining scheme is played by embedding maps that allow the interpretation of discrete boundary data as continuum configurations. These embedding maps should be selected according to the dynamics of the system, as a choice of embedding maps will determine a truncation of the renormalization flow.Comment: 22 page

Loop quantization of spherically symmetric midi-superspaces

We quantize the exterior of spherically symmetric vacuum space-times using a midi-superspace reduction within the Ashtekar new variables. Through a partial gauge fixing we eliminate the diffeomorphism constraint and are left with a Hamiltonian constraint that is first class. We complete the quantization in the loop representation. We also use the model to discuss the issues that will arise in more general contexts in the ``uniform discretization'' approach to the dynamics.Comment: 18 pages, RevTex, no figures, some typos corrected, published version, for some reason a series of figures were incorrectly added to the previous versio

Die Zusammensetzung der Anthocyane in den Beeren verschiedener Rebsorten

Anthocyanin composition in berries of different grape vadetiesThe percentages of the anthocyanins of 50 grape varieties were determined by HPLC. On account of the percentage differences the grape varieties couJd be classified in 5 groups : 1. Pinot noir group, 2. Trollinger group, 3. malvidin group, 4. varieties with an approximately even distribution, and 5. hybrid group. Only small changes were observed in the percentages during ripening. The differences in the percentages between the 1984 and 1985 vintage were srnall. A direct linear correlation existed between the anthocyanidin 3-glucosides and the conesponding acetates. Cyanidin 3-glucoside and peonidin 3-glucoside were the main pigments of the leaves

Laser photon merging in proton-laser collisions

The quantum electrodynamical vacuum polarization effects arising in the collision of a high-energy proton beam and a strong, linearly polarized laser field are investigated. The probability that laser photons merge into one photon by interacting with the proton`s electromagnetic field is calculated taking into account the laser field exactly. Asymptotics of the probability are then derived according to different experimental setups suitable for detecting perturbative and nonperturbative vacuum polarization effects. The experimentally most feasible setup involves the use of a strong optical laser field. It is shown that in this case measurements of the polarization of the outgoing photon and and of its angular distribution provide promising tools to detect these effects for the first time.Comment: 38 pages, 9 figure

A Note on B-observables in Ponzano-Regge 3d Quantum Gravity

We study the insertion and value of metric observables in the (discrete) path integral formulation of the Ponzano-Regge spinfoam model for 3d quantum gravity. In particular, we discuss the length spectrum and the relation between insertion of such B-observables and gauge fixing in the path integral.Comment: 17 page

On (Cosmological) Singularity Avoidance in Loop Quantum Gravity

Loop Quantum Cosmology (LQC), mainly due to Bojowald, is not the cosmological sector of Loop Quantum Gravity (LQG). Rather, LQC consists of a truncation of the phase space of classical General Relativity to spatially homogeneous situations which is then quantized by the methods of LQG. Thus, LQC is a quantum mechanical toy model (finite number of degrees of freedom) for LQG(a genuine QFT with an infinite number of degrees of freedom) which provides important consistency checks. However, it is a non trivial question whether the predictions of LQC are robust after switching on the inhomogeneous fluctuations present in full LQG. Two of the most spectacular findings of LQC are that 1. the inverse scale factor is bounded from above on zero volume eigenstates which hints at the avoidance of the local curvature singularity and 2. that the Quantum Einstein Equations are non -- singular which hints at the avoidance of the global initial singularity. We display the result of a calculation for LQG which proves that the (analogon of the) inverse scale factor, while densely defined, is {\it not} bounded from above on zero volume eigenstates. Thus, in full LQG, if curvature singularity avoidance is realized, then not in this simple way. In fact, it turns out that the boundedness of the inverse scale factor is neither necessary nor sufficient for curvature singularity avoidance and that non -- singular evolution equations are neither necessary nor sufficient for initial singularity avoidance because none of these criteria are formulated in terms of observable quantities.After outlining what would be required, we present the results of a calculation for LQG which could be a first indication that our criteria at least for curvature singularity avoidance are satisfied in LQG.Comment: 34 pages, 16 figure

Light diffraction by a strong standing electromagnetic wave

The nonlinear quantum interaction of a linearly polarized x-ray probe beam with a focused intense standing laser wave is studied theoretically. Because of the tight focusing of the standing laser pulse, diffraction effects arise for the probe beam as opposed to the corresponding plane wave scenario. A quantitative estimate for realistic experimental conditions of the ellipticity and the rotation of the main polarization plane acquired by the x-ray probe after the interaction shows that the implementation of such vacuum effects is feasible with future X-ray Free Electron Laser light.Comment: 5 pages, 2 figures. Published versio