Self-destructive percolation, invasion percolation and related models

Meester, R.W.J. [Promotor]Berg, J. van den [Promotor

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

Alpine Crossroads or Origin of Genetic Diversity? Comparative Phylogeography of Two Sympatric Microgastropod Species

The Alpine Region, constituting the Alps and the Dinaric Alps, has played a major role in the formation of current patterns of biodiversity either as a contact zone of postglacial expanding lineages or as the origin of genetic diversity. In our study, we tested these hypotheses for two widespread, sympatric microgastropod taxa – Carychium minimum O.F. Müller, 1774 and Carychium tridentatum (Risso, 1826) (Gastropoda, Eupulmonata, Carychiidae) – by using COI sequence data and species potential distribution models analyzed in a statistical phylogeographical framework. Additionally, we examined disjunct transatlantic populations of those taxa from the Azores and North America. In general, both Carychium taxa demonstrate a genetic structure composed of several differentiated haplotype lineages most likely resulting from allopatric diversification in isolated refugial areas during the Pleistocene glacial periods. However, the genetic structure of Carychium minimum is more pronounced, which can be attributed to ecological constraints relating to habitat proximity to permanent bodies of water. For most of the Carychium lineages, the broader Alpine Region was identified as the likely origin of genetic diversity. Several lineages are endemic to the broader Alpine Region whereas a single lineage per species underwent a postglacial expansion to (re)colonize previously unsuitable habitats, e.g. in Northern Europe. The source populations of those expanding lineages can be traced back to the Eastern and Western Alps. Consequently, we identify the Alpine Region as a significant ‘hot-spot’ for the formation of genetic diversity within European Carychium lineages. Passive dispersal via anthropogenic means best explains the presence of transatlantic European Carychium populations on the Azores and in North America. We conclude that passive (anthropogenic) transport could mislead the interpretation of observed phylogeographical patterns in general

Join algorithms for the theory of uninterpreted functions

Abstract. The join of two sets of facts, E1 and E2, is defined as the set of all facts that are implied independently by both E1 and E2. Congruence closure is a widely used representation for sets of equational facts in the theory of uninterpreted function symbols (UFS). We present an optimal join algorithm for special classes of the theory of UFS using the abstract congruence closure framework. Several known join algorithms, which work on a strict subclass, can be cast as specific instantiations of our generic procedure. We demonstrate the limitations of any approach for computing joins that is based on the use of congruence closure. We also mention some interesting open problems in this area.

Synthesis and characterization of cobalt hydroxide, cobalt oxyhydroxide, and cobalt oxide nanodiscs

Cobalt hydroxide, cobalt oxyhydroxide and cobalt oxide nanomaterials were synthesized through simple soft chemistry. The cobalt hydroxide displays hexagonal morphology with clear edges 20 nm long. This morphology and nanosize is retained through to cobalt oxide Co3O4 through a topotactical relationship. Cobalt oxyhydroxide and cobalt oxide nanomaterials were synthesized through oxidation and low temperature calcination from the as-prepared cobalt hydroxide. Characterisation of these cobalt-based nanomaterials were fully developed, including X-ray diffraction, transmission electron microscopy combined with selected area electron diffraction, scanning electron microscopy, X-ray photoelectron spectroscopy, Raman spectroscopy, and thermal gravimetric analysis. Bonding of the divalent cobalt hydroxide from the oxyhydroxide and oxides by studying their high resolution XPS spectra for Co 2p3/2 and O 1s. Raman spectroscopy of the as-prepared Co(OH)2, CoO(OH) and Co3O4 nanomaterials characterised each material. The thermal stability of the materials Co(OH)2 and CoO(OH) were established. This research has developed methodology for the synthesis of cobalt oxide and cobalt oxyhydroxide nanodiscs at low temperatures