Hyperuniformity of Quasicrystals

Hyperuniform systems, which include crystals, quasicrystals and special disordered systems, have attracted considerable recent attention, but rigorous analyses of the hyperuniformity of quasicrystals have been lacking because the support of the spectral intensity is dense and discontinuous. We employ the integrated spectral intensity, $Z(k)$, to quantitatively characterize the hyperuniformity of quasicrystalline point sets generated by projection methods. The scaling of $Z(k)$ as $k$ tends to zero is computed for one-dimensional quasicrystals and shown to be consistent with independent calculations of the variance, $\sigma^2(R)$, in the number of points contained in an interval of length $2R$. We find that one-dimensional quasicrystals produced by projection from a two-dimensional lattice onto a line of slope $1/\tau$ fall into distinct classes determined by the width of the projection window. For a countable dense set of widths, $Z(k) \sim k^4$; for all others, $Z(k)\sim k^2$. This distinction suggests that measures of hyperuniformity define new classes of quasicrystals in higher dimensions as well.Comment: 12 pages, 14 figure

Effects of antimitotic agents on haploid plant production from unpollinated ovules of sugar beet (beta vulgaris l.)

The effects of antimicrotubule agents on haploid embryo formation from unpollinated ovules of sugar beet (Beta vulgaris L.) were investigated. The antimitotic agent colchicine (at 100 and 150 mg/l) and trifluralin (at 5.0 mg/l) increased the frequency of haploid embryo formation whereas pronamide (at 76.9 and 128.2 mg/l) and trifluralin (at 3.4 mg/l) decreased. Ovules that were non-treated with antimicrotuble agents (i.e., ovules of the control treatment) produced higher percentages of haploid embryos (4.25 %) when compared to the pronamide and trifluralin at 3.4 mg/l concentration. Toxic effects of these agents on embryo formation from ovules were evident. A significant genotypic variation among the lines used was observed. The line M4 produced the highest yield with a mean of 14.71% haploid embryo production while the line M2 producing no embryos at all

Der Einfluß von Vascular endothelial growth factor auf die Knochenregeneration im Unterkiefer durch Beeinflussung der Angiogenese:lichtmikroskopische und histomorphometrische Untersuchung

In der Studie diente Kollagen als Träger für VEGF165 (0,8µg) in bikortikalen Defekten von 5mm Durchmesser im Unterkiefer. Als Kontrolle lagen Leer- und Kollagenproben vor.Untersucht wurden 112 Studien- und 112 Kontrollproben von 56 Kaninchen.Nach einer Verweildauer von 3, 7, 14 und 28 Tagen wurden die Tiere geopfert und die Gefäßzahl in den Proben bestimmt und die Proben nach 28 Tagen quantitativ mittels der Histomorphometrie bezüglich der regenerierten Knochenfläche und Knochenflächendichte untersucht und statistisch analysiert. Am 28. Tag konnte ein Abfall der Werte für die Gefäßzahl in den Kontrollgruppen bei gleichbleibend hoher Gefäßzahl unter dem Einfluß von VEGF165 festgestellt werden. Die Histomorphometrie des Knochens nach 28 Tagen ergab für die Knochenflächendichte einen signifikant höheren Wert der Studiengruppe im Vergleich mit den Leerproben (p=0,022) und den reinen Kollagenfüllungen (p=0,002)

Hyperuniformity and anti-hyperuniformity in one-dimensional substitution tilings

We consider the scaling properties characterizing the hyperuniformity (or anti-hyperuniformity) of long wavelength fluctuations in a broad class of one-dimensional substitution tilings. We present a simple argument that predicts the exponent $\alpha$ governing the scaling of Fourier intensities at small wavenumbers, tilings with $\alpha>0$ being hyperuniform, and confirm with numerical computations that the predictions are accurate for quasiperiodic tilings, tilings with singular continuous spectra, and limit-periodic tilings. Tilings with quasiperiodic or singular continuous spectra can be constructed with $\alpha$ arbitrarily close to any given value between $-1$ and $3$. Limit-periodic tilings can be constructed with $\alpha$ between $-1$ and $1$ or with Fourier intensities that approach zero faster than any power law.Comment: 13 pages, 9 figures, to be submitted to Acta Crystallographica special issue: Aperiodic 201