A mean-field theory for self-propelled particles interacting by velocity alignment mechanisms

A mean-field approach (MFA) is proposed for the analysis of orientational order in a two-dimensional system of stochastic self-propelled particles interacting by local velocity alignment mechanism. The treatment is applied to the cases of ferromagnetic (F) and liquid-crystal (LC) alignment. In both cases, MFA yields a second order phase transition for a critical noise strength and a scaling exponent of 1/2 for the respective order parameters. We find that the critical noise amplitude η_c at which orientational order emerges in the LC case is smaller than in the F-alignment case, i.e. η^LC_C<η^F_C. A comparison with simulations of individual-based models with F- resp. LC-alignment shows that the predictions about the critical behavior and the qualitative relation between the respective critical noise amplitudes are correct.     

Lattice Points in Three-Dimensional Convex Bodies with Points of Gaussian Curvature Zero at the Boundary

 In this article we investigate the number of lattice points in a three-dimensional convex body which contains non-isolated points with Gaussian curvature zero but a finite number of flat points at the boundary. Especially, in case of rational tangential planes in these points we investigate not only the influence of the flat points but also of the other points with Gaussian curvature zero on the estimation of the lattice rest. Received 19 June 2001; in revised form 17 January 2002 RID="a" ID="a" Dedicated to Professor Edmund Hlawka on the occasion of his 85th birthday     

Acid-induced rearrangement reactions of reduced benzoquinone cyclopentadiene cycloadducts

Several Diels-Alder adducts between benzoquinones and cyclopentadiene were reduced to the corresponding diols 7a-c and 11. Treatment of these diols with strong acid triggered a skeletal rearrangement reaction resulting in compounds 8a-c and 12 that contain a 4,8-methanoazulene substructure. In addition, a dyotropic-like rearrangement of the tetracyclic lactone 13 to the spiro-lactone 18 was observed. Five of the structures were supported by X-ray analysis.     

Design and synthesis of a 256-membered pi-conjugated oligomer library of regioregular head-to-tail coupled quater(3-arylthiophene)s

The rapid solid-phase synthesis of pi-conjugated oligomers is demonstrated by utilizing the parallel and the "mix-and-split" methods for the preparation of a library of 256 regioregular head-to-tail coupled oligo(3-arylthiophene)s. Chemical diversity was introduced to the growing oligomer starting from four resin-bound 3-(p-X-phenyl)-2-silylthiophenes via an iterative sequence of iodinations and Suzuki cross-coupling reactions with four 3-(p-X-phenyl)thiophene boronic esters (X = CF(3), H, CH(3), OCH(3)). Liberation from the solid support with TFA and subsequent chromatographic purification by normal-phase LC-MS provided all 256 regioregular head-to-tail coupled quater(3-arylthiophene)s.     

Element specific surface reconstructions of islands during surfactant-mediated growth on Si (111)

The early stages of surfactant- (As, Sb) mediated homoepitaxial growth on Si (111) are examined by scanning tunneling microscopy and extensive ab initio calculations of Si(n) clusters (n相似文献