A modified version of frozen percolation on the binary tree

We consider the following, intuitively described process: at time zero, all sites of a binary tree are at rest. Each site becomes activated at a random uniform [0,1] time, independent of the other sites. As soon as a site is in an infinite cluster of activated sites, this cluster of activated sites freezes. The main question is whether a process like this exists. Aldous [Ald00] proved that this is the case for a slightly different version of frozen percolation. In this paper we construct a process that fits the intuitive description and discuss some properties.Comment: 19 pages, 2 figure

The chiral symplectic universality class

We report a numerical investigation of localization in the SU(2) model without diagonal disorder. At the band center, chiral symmetry plays an important role. Our results indicate that states at the band center are critical. States away from the band center but not too close to the edge of the spectrum are metallic as expected for Hamiltonians with symplectic symmetry.Comment: accepted in Proceedings of Localisation 2002 Conference, Tokyo, Japan (to be published as supplement of J. Phys. Soc. Japan

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

Functional equilibrium: sense or nonsense?

DM distribution in shoots and roots of vegetative plants depending on various environmental conditions and experimental interventions is discussed. Because of the difficulties in maintaining conditions at a sufficiently constant level for some time, functional equilibria are not likely to exist during prolonged periods of time. From the responses occurring after transferring plants including perennial ryegrass and maize from one condition to another or after disturbance of existing relationships, it is demonstrated once more that nutritional control, i.e. functional control, of distribution is still the most reasonable interpretation of the observed reaction patterns. (Abstract retrieved from CAB Abstracts by CABI’s permission

The Twente humanoid head

This video shows the results of the project on the mechatronic development of the Twente humanoid head. The mechanical structure consists of a neck with four degrees of freedom (DOFs) and two eyes (a stereo pair system) which tilt on a common axis and rotate sideways freely providing a three more DOFs. The motion control algorithm is designed to receive, as an input, the output of a biological-inspired vision processing algorithm and to exploit the redundancy of the joints for the realization of the movements. The expressions of the humanoid head are implemented by projecting light from the internal part of the translucent plastic cover