Interfacial electron transfer into functionalized crystalline polyoxotitanate nanoclusters

Interfacial electron transfer (IET) between a chromophore and a semiconductor nanoparticle is one of the key processes in a dye-sensitized solar cell. Theoretical simulations of the electron transfer in polyoxotitanate nanoclusters Ti(17)O(24)(OPr(i))(20) (Ti(17)) functionalized with four p-nitrophenyl acetylacetone (NPA-H) adsorbates, of which the atomic structure has been fully established by X-ray diffraction measurements, are presented. Complementary experimental information showing IET has been obtained by EPR spectroscopy. Evolution of the time-dependent photoexcited electron during the initial 5 fs after instantaneous excitation to the NPA LUMO + 1 has been evaluated. Evidence for delocalization of the excitation over multiple chromophores after excitation to the NPA LUMO + 2 state on a 15 fs time scale is also obtained. While chromophores are generally considered electronically isolated with respect to neighboring sensitizers, our calculations show that this is not necessarily the case. The present work is the most comprehensive study to date of a sensitized semiconductor nanoparticle in which the structure of the surface and the mode of molecular adsorption are precisely defined.     

On the Numerical Identification of System Properties in a Square Frame

In this paper the influencing factors of the nonlinear behavior of a highly deformable square frame are aimed to highlight and identify. Therefore, in a first step a square frame consisting of four slender members of equal length has been investigated experimentally. Subsequently to these investigations, a numerical model is set up with a beam finite element model, which is based on the absolute nodal coordinate formulation (ANCF), including geometrical and possible material nonlinearities. The influencing factors as well as the system properties are identified by using a genetic optimization algorithm. The final results show that the highly nonlinear behavior of the square frame can be reproduced accurately in case the nonlinear characteristics of the joints are taken into account carefully. The numerical model combined with the system parameter identification can be utilized for further numerical investigations of non-standard structures undergoing large deformations. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Essential Killing fields of parabolic geometries: projective and conformal structures

We use the general theory developed in our article [?ap A., Melnick K., Essential Killing fields of parabolic geometries, Indiana Univ. Math. J. (in press)], in the setting of parabolic geometries to reprove known results on special infinitesimal automorphisms of projective and conformal geometries.     

Loewner’s Torus Inequality with Isosystolic Defect

We show that Bonnesen’s isoperimetric defect has a systolic analog for Loewner’s torus inequality. The isosystolic defect is expressed in terms of the probabilistic variance of the conformal factor of the metric  G{\mathcal{G}} with respect to the flat metric of unit area in the conformal class of  G{\mathcal{G}} .     

The segment projection method for interface tracking

There has recently been important progress in the development of front tracking and level set methods for the numerical simulation of moving interfaces. The segment projection method is a new technique for computational geometry. It can be seen as a compromise between front tracking and level set methods. It is based on the regular mathematical representation of a manifold as an atlas of charts. Each chart or segment is evolved independently by a partial differential equation that is discretized on an Eulerian grid. The connectivity of the segments is handled by an appropriate data structure and by numerical interpolation. The method is presented and its properties are analyzed. Applications to multiphase flow, epitaxial growth, and high‐frequency wave propagation are given. © 2002 Wiley Periodicals, Inc.