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

Multi-walled microchannels: free-standing porous silicon membranes for use in µTAS

Electrochemically formed porous silicon (PS) can be released from the bulk silicon substrate by underetching at increased current density. Using this technique, two types of channels containing free-standing layers of PS were constructed, which were failed multi-walled microchannels (MW µCs). They can be used in devices like microsieves, microbatteries, and porous electrodes. Two types of MWµC were made: the 'conventional' version, consisting of two or more coaxially constructed microchannels separated by a suspended PS membrane, and the buried variety, where a PS membrane is suspended halfway in an etched cavity surrounded by silicon nitride walls. The latter is more robust. The pore size of the PS was measured using transmission electron microscopy and field emission gun scanning electron microscopy (FEGSEM) and found to be of the order of 7 n

Pest-predator spatial relationships in winter rape: implications for integrated crop management

Douglas Warner, Les J Allen-Williams, Andrew W Ferguson, and Ingrid H Williams, 'Pest–predator spatial relationships in winter rape: implications for integrated crop management', Pest Management Science, Vol. 56 (11): 977-982, November 2000, doi: 10.1002/1526-4998(200011)56:113.0.CO;2-U. Copyright © 2000 Society of Chemical IndustryThe brassica pod midge (Dasineura brassicae) is an important and widespread pest of winter and spring oilseed rape throughout Europe. Pods infested by D brassicae larvae split prematurely, releasing seeds, and the larvae drop to the soil into which they burrow to pupate. At this stage in its lifecycle D brassicae is potentially vulnerable to predation by carabid beetles foraging on the soil surface. This is the first study in the UK to focus on carabid beetles as predators of D brassicae in the oilseed rape crop. The spatio-temporal distributions of larvae of D brassicae dropping to the soil from the crop canopy and of adult carabid beetles active on the soil surface were analysed in two consecutive years. Insect samples were collected from spatially referenced sampling points across each crop. Counts of insects were mapped and analysed, and the degree of spatial association between predator and prey determined using Spatial Analysis by Distance Indices (SADIE). Carabid species abundant and active during peak drop of first generation D brassicae larvae included Agonum dorsale, Amara similata, Harpalus rufipes and Nebria brevicollis. The larvae of D brassicae had a marked edge distribution within the crop. SADIE analysis revealed significant spatial association between larvae of D brassicae and adult H rufipes (P <0.05) in 1998, but not with adults of A dorsale, A similata or N brevicollis. In 1999, there was strong spatial association only between larvae of D brassicae and adult A dorsale (P <0.01). Aggregation of N brevicollis adults occurred in some areas of greatest D brassicae larval counts in 1999, but overall spatial association was not signi®cant. The distributions are discussed in terms of their relevance to integrated crop management (ICM) strategies and spatial targeting of insecticides.Peer reviewe

Long spin relaxation times in wafer scale epitaxial graphene on SiC(0001)

We developed an easy, upscalable process to prepare lateral spin-valve devices on epitaxially grown monolayer graphene on SiC(0001) and perform nonlocal spin transport measurements. We observe the longest spin relaxation times tau_S in monolayer graphene, while the spin diffusion coefficient D_S is strongly reduced compared to typical results on exfoliated graphene. The increase of tau_S is probably related to the changed substrate, while the cause for the small value of D_S remains an open question.Comment: 16 pages, 3 figures, 1 tabl

Large deviations for ideal quantum systems

We consider a general d-dimensional quantum system of non-interacting particles, with suitable statistics, in a very large (formally infinite) container. We prove that, in equilibrium, the fluctuations in the density of particles in a subdomain of the container are described by a large deviation function related to the pressure of the system. That is, untypical densities occur with a probability exponentially small in the volume of the subdomain, with the coefficient in the exponent given by the appropriate thermodynamic potential. Furthermore, small fluctuations satisfy the central limit theorem.Comment: 28 pages, LaTeX 2