A Characterization for Geodsic Spheres in Space Forms

We use the maximum principle for second-order elliptic operators to establish a sufficient condition for a compact hypersurface in a space form to be a geodesic sphere in terms of a pinching for the s-mean curvature.     

Congruence of minimal surfaces and higher fundamental forms

 We show that minimal surfaces in space forms are determined, up to ambient isometries, by the induced metric and certain invariants which are defined in terms of the higher fundamental forms and the complex structure. Received: 6 May 2002 / Revised version: 5 July 2002 Current address: Institut für Mathematik, Universit?t Augsburg, Universit?tsstrasse 12, D-86135 Augsburg, Germany. e-mail: Theodoros.Vlachos@Math.Uni-Augsburg.De The author was supported by the Alexander von Humboldt Foundation Mathematics Subject Classification (2000): 53A10, 53C42 Acknowledgements. This work was written during the author's stay at the University of Augsburg as a research fellow of the Alexander von Humboldt Foundation. I wish to express my gratitude to the Alexander von Humboldt Foundation for its generous support. Moreover, I wish to thank Professor J.H. Eschenburg for many fruitful and stimulating conversations.     

Synthesis and mesomorphic behaviour of novel light-emitting liquid crystals

We report the results of a systematic study of the structure-mesomorphic behaviour relationships of a diverse range of light-emitting liquid crystals, but especially nematic 2,7-disubstituted-9,9-dialkylfluorenes. The dependence of the mesomorphic behaviour and transition temperatures on the nature and length of the terminal chains, the nature, position and number of lateral substituents and the number and nature of aromatic rings with and without heteroatoms in the central core is studied. The results of these studies are used to design polymerizable, light-emitting crystals (reactive mesogens) with a nematic phase having a high clearing point and a melting point below room temperature for facile OLED fabrication.     

An Analytic Approach to <Emphasis Type="Italic">Q</Emphasis>-Balls

We present the analytic approach for constructing Q-ball solutions in the general case of a sixth-order potential. In particular, we show that the symmetrized Woods-Saxon function describes the Q-ball profile function. The energy and charge can therefore be evaluated explicitly. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 2, pp. 342–347, August, 2005.     

Hydrogen assisted self-ignition of propane/air mixtures in catalytic microburners

A catalytic Pt-based microdevice is evaluated for the combustion of hydrogen and/or propane. It is found that in confined ceramic microchannels hydrogen/air mixtures self-ignite over a wide range of compositions. This discovery is capitalized to self-ignite propane/air mixtures with the assistance of hydrogen addition. It is shown that propane kinetically inhibits hydrogen catalytic combustion at low hydrogen fractions. The minimum hydrogen composition for self-ignition of propane/air mixture compositions is found to be relatively constant, irrespective of propane composition. The transient and steady state behavior of these systems is described, and the minimization of hydrogen usage and startup time are discussed.     

Fermi-Dirac statistics for free electrons in uniform electric and magnetic fields

In this paper we study the De Haas-Van Alphen effect when an electric field is present. We prove that for sufficiently weak electric fields, where the conditions are favorable for energy quantization, the free energy is a quasi-periodical function with respect to the fields. As a consequence we find, for the magnetic susceptibility, periodical expressions which are easily reduced to the ones known for the De Haas-Van Alphen effect when the electric field vanishes.     

Molecular dynamics study of the stabilization of the silica hexamer Si6O15(6-) in aqueous and methanolic solutions

We use molecular dynamics simulations to study the stabilization of the hexameric, cagelike silicate with double three-ring structure in aqueous and methanolic solutions. We find that in purely aqueous environments its stabilization requires the presence of both tetramethylammonium and tetraethylammonium (TEA) cations and involves the formation of a stable TMA layer which leads to a water-silicate heteronetwork clathrate. We also find that TEA alone can facilely stabilize the hexamer when methanol cosolvent is added, in accordance with experiment. The mechanism of this stabilization, however, differs from that in purely aqueous environments. Because of the unique properties of water-methanol mixtures, the organosilicate complex does not participate in heteronetwork clathrates but resides in a large solvent cavity; that is, it is forced out of true solution.     

Molecular dynamics of hydrogen dissociation on an oxygen covered Pt(111) surface

The dissociation of hydrogen on a Pt(111) surface covered with a p(2 x 2) oxygen phase was investigated using quasiclassical, six-dimensional molecular dynamics. The potential energy surface (PES) used in these simulations was obtained by an iterative novelty sampling algorithm. Compared to molecular beam experiments performed under similar conditions, the simulations give an accurate prediction of the reaction probability via a direct dissociation pathway. When compared to previously reported reaction probability curves for the clean Pt(111) surface, we find that the presence of an oxygen overlayer inhibits the direct pathway to hydrogen dissociation. This inhibition is a function of incident energy and cannot be described by a simple site blocking model. An indirect pathway to dissociation, which was observed in experiments, is not properly captured by the PES. Spatially resolved "reaction maps" indicate that the preferred site for hydrogen dissociation on an oxygen covered Pt surface is the top site of the Pt atom farthest from the adsorbed oxygen atom.