An anchoring transition at surfaces with grafted liquid-crystalline chain molecules

The anchoring of nematic liquid crystals on surfaces with grafted liquid crystalline chain molecules is studied by computer simulations and within a mean field approach. The computer simulations show that a swollen layer of collectively tilted chains may induce untilted homeotropic (perpendicular) alignment in the nematic fluid. The results can be understood within a simple theoretical model. The anchoring on a layer of mutually attractive chains is determined by the structure of the interface between the layer of chain molecules and the solvent. It is controlled by an interplay between the attractive chain interactions, the translational entropy of the solvent and its elasticity. A second order anchoring transition driven by the grafting density from tilted to homeotropic alignment is predicted.Comment: To appear in European Physical Journal

Die „Reichsscherbenwoche“ nach 70 Jahren : eine Sammelrezension zum Novemberpogrom 1938

Rezension folgender Werke: Ben Barkow, Raphael Gross, Michael Lenarz (Hg.): Novemberpogrom 1938. Die Augenzeugenberichte der Wiener Library London. Frankfurt am Main: Jüdischer Verlag 2008, 933 S., ISBN: 978-3-633-54233-8, EUR 39,80. Ramona Bräu, Thomas Wenzel: „ausgebrannt, ausgeplündert, ausgestoßen“. Die Pogrome gegen die jüdischen Bürger Thüringens im November 1938. Erfurt: Landeszentrale für politische Bildung Thüringen 2008, 192 S., ISBN: 978-3-937967-41-7, kostenlos. „Reichskristallnacht“ – der Pogrom im November 1938 in Stuttgart. Ein Quellen- und Arbeitsbuch für den Geschichtsunterricht. Bearb. v. Michael Hoffmann, Jürgen Lotterer und Roland Müller. Stuttgart: Stadtarchiv Stuttgart 2008, 50 S., kostenlos. Andreas Nachama, Uwe Neumärker, Hermann Simon (Hg.): „Es brennt!“ Antijüdischer Terror im November 1938. Berlin: Stiftung Topographie des Terrors 2008, 167 S., ISBN: 978-3-9811677-4-0, EUR 15,00. Mitchell G. Bard: 48 Hours of Kristallnacht. Night of Destruction, Dawn of the Holocaust. An Oral History. Guilford, Connecticut: The Lyons Press 2008, 240 S., ISBN: 978-1-59921-445-0, $ 19,95. Martin Ruch: Das Novemberpogrom 1938 und der Synagogenprozess 1948 in Offenburg. Verfolgte berichten, Täter stehen vor Gericht. Norderstedt: Books on Demand 2008, 120 S., ISBN: 978-3-8370-5338-8, EUR 14,80. Erhard Roy Wiehn: Zum Reichspogrom 1938. Die Ereignisse in Konstanz 70 Jahre danach zum Gedenken. Konstanz: Hartung-Gorre Verlag 2008, 155 S., ISBN 3-86628-165-X, EUR 14,80. Arbeitskreis der NS-Gedenkstätten NRW (Hg.): Gewalt in der Region. Der Novemberpogrom 1938 in Rheinland und Westfalen. Düsseldorf u.a.: Landeszentrale für politische Bildung NRW 2008, 135 S., ISBN: 3-9807674-8-5, EUR 5,00. Hans D. Arntz: „Reichskristallnacht“. Der Novemberpogrom 1938 auf dem Lande – Gerichtsakten und Zeugenaussagen am Beispiel der Eifel und Voreifel. Aachen: Helios Verlag 2008, 196 S., ISBN: 978-3-938208-69-4, EUR 29,90. Bastian Fleermann, Angela Genger (Hg.): Novemberpogrom 1938 in Düsseldorf. Essen: Klartext Verlag 2008, 443 S., ISBN: 978-3-8375-0085-1, EUR 22,95. Sven F. Kellerhoff: „Kristallnacht“. Der Novemberpogrom 1938 und die Berliner Juden. Berlin: Berlin Story Verlag 2008, 95 S., ISBN: 978-3-929829-66-2, EUR 9,80. Hef

Computation of the eigenvalues for the angular and Coulomb spheroidal wave equation

In this paper we study the eigenvalues of the angular spheroidal wave equation and its generalization, the Coulomb spheroidal wave equation. An associated differential system and a formula for the connection coefficients between the various Floquet solutions give rise to an entire function whose zeros are exactly the eigenvalues of the Coulomb spheroidal wave equation. This entire function can be calculated by means of a recurrence formula with arbitrary accuracy and low computational cost. Finally, one obtains an easy-to-use method for computing spheroidal eigenvalues and the corresponding eigenfunctions.Comment: 23 pages, 5 figure

On the connection coefficients for linear differential systems with applications to the spheroidal and ellipsoidal wave equation

This paper is concerned with the connection coefficients between the local fundamental solutions of a $2\times 2$ linear ordinary differential system with two neighboring regular singular points at $z=0$ and $z=1$. We derive an asymptotic formula for the connection coefficients which can be used for numerical calculations and, in particular, for determining the eigenvalues of some spectral problems arising in mathematical physics. As an application, new algorithms for computing the eigenvalues of the ellipsoidal wave equation and the spheroidal wave equation are presented.Comment: 20 pages, 6 figure

Surface anchoring on layers of grafted liquid-crystalline chain molecules: A computer simulation

By Monte Carlo simulations of a soft ellipsoid model for liquid crystals, we study whether a layer of grafted liquid-crystalline chain molecules can induce tilt in a nematic fluid. The chains are fairly short (four monomers) and made of the same particles as the solvent. They are attached to a substrate which favors parallel (planar) alignment. At low grafting densities, the substrate dominates and we observe planar alignment. On increasing the grafting density, we find a first order transition from planar to tilted alignment. Beyond the transition, the tilt angle with respect to the surface normal decreases continuously. The range of accessible anchoring angles is quite large.Comment: To appear in J. Chem. Phy