Symmetry properties of Penrose type tilings

The Penrose tiling is directly related to the atomic structure of certain decagonal quasicrystals and, despite its aperiodicity, is highly symmetric. It is known that the numbers 1, $-\tau$, $(-\tau)^2$, $(-\tau)^3$, ..., where $\tau =(1+\sqrt{5})/2$, are scaling factors of the Penrose tiling. We show that the set of scaling factors is much larger, and for most of them the number of the corresponding inflation centers is infinite.Comment: Paper submitted to Phil. Mag. (for Proceedings of Quasicrystals: The Silver Jubilee, Tel Aviv, 14-19 October, 2007

Integration of X-Ray Microanalysis and Morphometry of Biological Material

It was investigated how to extract both morphometrical and X-ray elemental information from scanning electron microscopical (SEM) or scanning transmission electron microscopical (STEM)-images and how to integrate these two information streams either on line or off-line after storage. Cytochemical reaction products in cell organelles in ultrathin sections are the biological structures of interest. In such organelles four different situations can be met: morphologically the structures are homomorph or heteromorph; chemically the elements are distributed either homogeneously or heterogeneously. A new program has been proposed and described, which permits determination of both the area and the mean net-intensity value of chemical elements, inhomogeneously distributed over heteromorph organelles. The value of this integration method is demonstrated by three examples of increasing complexity, starting with two elements which are more or less homogeneously distributed over one lysosome, the establishing of a platinum discontinuity in an acidophilic granule and finally the localization of two chemical elements inhomogeneously distributed over a rather heteromorph phagolysosome. In two examples Chelex ion exchange beads, maximally loaded with the element also present in the structure of interest, are co-embedded with the tissue as internal standards. In such cases the absolute elemental concentration in the structures analysed can be established. The presence of such cross-sectioned beads in the ultrathin sections is also used: 1) to demonstrate their function as models to select the proper conditions for the digital-controlled raster analysis of the unknown cell- or tissue structures, 2) to prove the value of this method

Quantum dynamics in high codimension tilings: from quasiperiodicity to disorder

We analyze the spreading of wavepackets in two-dimensional quasiperiodic and random tilings as a function of their codimension, i.e. of their topological complexity. In the quasiperiodic case, we show that the diffusion exponent that characterizes the propagation decreases when the codimension increases and goes to 1/2 in the high codimension limit. By constrast, the exponent for the random tilings is independent of their codimension and also equals 1/2. This shows that, in high codimension, the quasiperiodicity is irrelevant and that the topological disorder leads in every case, to a diffusive regime, at least in the time scale investigated here.Comment: 4 pages, 5 EPS figure

Extraneous Background-Correction Program for Matrix Bound Multiple Point X-Ray Microanalysis

A program is described that allows online determination of extraneous background in multiple point X-ray microanalytical matrices. The program is based upon the calculations of the extraneous background for the film (when present), the standard and the unknown by (100 sec.) point analysis. The program searches for a peak-free part of the spectrum in which the calculated value for the extraneous background is about equal to the value in this region of the spectrum (=be). Online the contents of this be-region is subtracted from an unmanipulated continuum region in the vicinity of the element present in the unknown and standard (Pt). During the subsequently performed matrix analysis two arrays are acquired (P-b) and (b-be). From these two arrays, the Rx,st and subsequently the Rx,sp are calculated per pixel, which are converted to (be corrected) concentration arrays. In addition Z2/A-differences between standard and the analyzed specimen are corrected off-line. For each pixel the program judges whether the calculated concentration deviates from the value introduced for the standard. Once differences are registered, adequate corrections are made