Continuity for self-destructive percolation in the plane

A few years ago two of us introduced, motivated by the study of certain forest-fireprocesses, the self-destructive percolation model (abbreviated as sdp model). A typical configuration for the sdp model with parameters p and delta is generated in three steps: First we generate a typical configuration for the ordinary percolation model with parameter p. Next, we make all sites in the infinite occupied cluster vacant. Finally, each site that was already vacant in the beginning or made vacant by the above action, becomes occupied with probability delta (independent of the other sites). Let theta(p, delta) be the probability that some specified vertex belongs, in the final configuration, to an infinite occupied cluster. In our earlier paper we stated the conjecture that, for the square lattice and other planar lattices, the function theta has a discontinuity at points of the form (p_c, delta), with delta sufficiently small. We also showed remarkable consequences for the forest-fire models. The conjecture naturally raises the question whether the function theta is continuous outside some region of the above mentioned form. We prove that this is indeed the case. An important ingredient in our proof is a (somewhat stronger form of a) recent ingenious RSW-like percolation result of Bollob\'{a}s and Riordan

Morse theory on spaces of braids and Lagrangian dynamics

In the first half of the paper we construct a Morse-type theory on certain spaces of braid diagrams. We define a topological invariant of closed positive braids which is correlated with the existence of invariant sets of parabolic flows defined on discretized braid spaces. Parabolic flows, a type of one-dimensional lattice dynamics, evolve singular braid diagrams in such a way as to decrease their topological complexity; algebraic lengths decrease monotonically. This topological invariant is derived from a Morse-Conley homotopy index and provides a gloablization of `lap number' techniques used in scalar parabolic PDEs. In the second half of the paper we apply this technology to second order Lagrangians via a discrete formulation of the variational problem. This culminates in a very general forcing theorem for the existence of infinitely many braid classes of closed orbits.Comment: Revised version: numerous changes in exposition. Slight modification of two proofs and one definition; 55 pages, 20 figure

The chicken embryo and its micro environment during egg storage and early incubation

When egg storage periods are prolonged (>7 days), hatchability and chick quality declines. The reason for this decline has been investigated, but is still not completely understood. At oviposition the developmental stage of the chicken embryo varies and so do the total number of viable cells. During storage, changes can occur in the embryo. Embryo viability at the end of storage seems to be dependent on the number of viable cells and the developmental stage of the embryo at oviposition. When the hypoblast is completely formed (during the quiescent developmental stage), the embryo seems to be more able to endure prolonged storage periods than embryos that are less or more advanced. During storage, changes also occur in egg characteristics such as albumen viscosity, albumen pH and yolk pH. There appears to be an interaction between albumen pH and embryo viability during early incubation and perhaps also during storage. An albumen pH of 8.2 seems to be optimal for embryo development. Albumen pH may influence embryo viability, but embryo viability may in turn, affect albumen pH. It has been hypothesised that an embryo in which the hypoblast is completely formed is better able to provide an effective barrier between the internal embryo and the exterior (yolk and albumen) and/or is better able to produce sufficient amount of carbon dioxide, which will reduce the pH level in the micro environment of the embryo to the optimal pH of 8.2. It appears that, to maintain hatchability and chick quality after prolonged storage periods, embryonic development should be advanced to the stage in which the hypoblast is completely formed or the atmosphere during storage and early incubation should be altered in such a way that albumen pH is maintained at the optimal level of 8.2

Cold trapped atoms detected with evanescent waves

We demonstrate the in situ detection of cold 87 Rb atoms near a dielectric surface using the absorption of a weak, resonant evanescent wave. We have used this technique in time of flight experiments determining the density of atoms falling on the surface. A quantitative understanding of the measured curve was obtained using a detailed calculation of the evanescent intensity distribution. We have also used it to detect atoms trapped near the surface in a standing-wave optical dipole potential. This trap was loaded by inelastic bouncing on a strong, repulsive evanescent potential. We estimate that we trap 1.5 x 10 4 atoms at a density 100 times higher than the falling atoms.Comment: 5 pages, 3 figure

KCrF_3: Electronic Structure, Magnetic and Orbital Ordering from First Principles

The electronic, magnetic and orbital structures of KCrF_3 are determined in all its recently identified crystallographic phases (cubic, tetragonal, and monoclinic) with a set of {\it ab initio} LSDA and LSDA+U calculations. The high-temperature undistorted cubic phase is metallic within the LSDA, but at the LSDA+U level it is a Mott insulator with a gap of 1.72 eV. The tetragonal and monoclinic phases of KCrF_3 exhibit cooperative Jahn-Teller distortions concomitant with staggered 3x^2-r^2/3y^2-r^2 orbital order. We find that the energy gain due to the Jahn-Teller distortion is 82/104 meV per chromium ion in the tetragonal/monoclinic phase, respectively. These phases show A-type magnetic ordering and have a bandgap of 2.48 eV. In this Mott insulating state KCrF_3 has a substantial conduction bandwidth of 2.1 eV, leading to the possibility for the kinetic energy of charge carriers in electron- or hole-doped derivatives of KCrF_3 to overcome the polaron localization at low temperatures, in analogy with the situation encountered in the colossal magnetoresistive manganites.Comment: 7 pages, 11 figure

Purely radiative irrotational dust spacetimes

We consider irrotational dust spacetimes in the full non-linear regime which are "purely radiative" in the sense that the gravitational field satisfies the covariant transverse conditions div(H) = div(E) = 0. Within this family we show that the Bianchi class A spatially homogeneous dust models are uniquely characterised by the condition that $H$ is diagonal in the shear-eigenframe.Comment: 6 pages, ERE 2006 conference, minor correction

Parameter Sensitivity in LSMs: An Analysis Using Stochastic Soil Moisture Models and ELDAS Soil Parameters

Integration of simulated and observed states through data assimilation as well as model evaluation requires a realistic representation of soil moisture in land surface models (LSMs). However, soil moisture in LSMs is sensitive to a range of uncertain input parameters, and intermodel differences in parameter values are often large. Here, the effect of soil parameters on soil moisture and evapotranspiration are investigated by using parameters from three different LSMs participating in the European Land Data Assimilation System (ELDAS) project. To prevent compensating effects from other than soil parameters, the effects are evaluated within a common framework of parsimonious stochastic soil moisture models. First, soil parameters are shown to affect soil moisture more strongly than the average evapotranspiration. In arid climates, the effect of soil parameters is on the variance rather than the mean, and the intermodel flux differences are smallest. Soil parameters from the ELDAS LSMs differ strongly, most notably in the available moisture content between the wilting point and the critical moisture content, which differ by a factor of 3. The ELDAS parameters can lead to differences in mean volumetric soil moisture as high as 0.10 and an average evapotranspiration of 10%–20% for the investigated parameter range. The parsimonious framework presented here can be used to investigate first-order parameter sensitivities under a range of climate conditions without using full LSM simulations. The results are consistent with many other studies using different LSMs under a more limited range of possible forcing condition