Synthesis of a novel perylene diimide derivative and its charge transfer interaction with C60

A novel organic electron acceptor, N,N′-dipyrimidinyl-3,4,9,10-perylene-tetracarboxylic diimide (DMP), was designed and synthesized. The molecular structure was characterized by FTIR spectrum and elemental analysis. By cyclic voltammetry measurements, DMP was found to possess a lower LUMO energy level than N,N′-diphenyl-3,4,9,10-perylene-tetracarboxylic diimide due to the stronger electron-withdrawing pyrimidinyl group than the phenyl group. Fluorescence quenching is observed in a dual-layer film consisting of a DMP layer and a C₆₀ layer and was attributed to the charge transfer at the interface due to the energy level offset between DMP and C₆₀. Supported by the National Natural Science Foundation of China (Grant Nos. 50433020, 50520150165 & 50403022)     

Exponential Mixing and Time Scales¶in Quantized Hyperbolic Maps on the Torus

We study the behaviour, in the simultaneous limits , of the Husimi and Wigner distributions of initial coherent states and position eigenstates, evolved under the quantized hyperbolic toral automorphisms and the quantized baker map. We show how the exponential mixing of the underlying dynamics manifests itself in those quantities on time scales logarithmic in . The phase space distributions of the coherent states, evolved under either of those dynamics, are shown to equidistribute on the torus in the limit , for times t between and , where γ is the Lyapounov exponent of the classical system. For times shorter than , they remain concentrated on the classical trajectory of the center of the coherent state. The behaviour of the phase space distributions of evolved position eigenstates, on the other hand, is not the same for the quantized automorphisms as for the baker map. In the first case, they equidistribute provided t→∞ as , and as long as t is shorter than . In the second case, they remain localized on the evolved initial position at all such times. Received: 1 October 1999/Accepted: 4 January 2000     

Corner singularity for transmission problems in three dimensions

For a transmission problem for the Laplace operator the unique solvability is proved in natural Sobolev spaces in the case when edges and corners are present. The behaviour of the solution near the corner is reduced to the question when an explicitely given meromorphic family of one-dimensional integral operators on a geodesic polygon on the two sphere has a non-trivial kernel.     

Variational principles for symmetric bilinear forms

Every compact symmetric bilinear form B on a complex Hilbert space produces, via an antilinear representing operator, a real spectrum consisting of a sequence decreasing to zero. We show that the most natural analog of Courant's minimax principle for B detects only the evenly indexed eigenvalues in this spectrum. We explain this phenomenon, analyze the extremal objects, and apply this general framework to the Friedrichs operator of a planar domain and to Toeplitz operators and their compressions. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Improving the efficiency of thin film tandem solar cells by plasmonic intermediate reflectors

Thin film tandem solar cells made of amorphous and microcrystalline silicon provide renewable energy at the benefit of low material consumption. As a drawback, these materials do not posses the high carrier mobilities of their crystalline counterpart which limits the feasible material thickness. For maintaining the light absorption as high as possible, photon management is required. Here we show that metallic nanodiscs that sustain localized plasmon polaritons can increase the efficiency of such solar cells if they are incorporated into the dielectric intermediate reflector separating the top and the bottom cell. We provide quantitative estimates for the possible absorption enhancement of optimized bi-periodic nanodiscs that are feasible for fabrication. Emphasis is also put on discussing the impact of obliquely incident sun light on the solar cell performance.     

Shearlet coorbit spaces and associated Banach frames

In this paper, we study the relationships of the newly developed continuous shearlet transform with the coorbit space theory. It turns out that all the conditions that are needed to apply the coorbit space theory can indeed be satisfied for the shearlet group. Consequently, we establish new families of smoothness spaces, the shearlet coorbit spaces. Moreover, our approach yields Banach frames for these spaces in a quite natural way. We also study the approximation power of best n-term approximation schemes and present some first numerical experiments.     

Multiscale analysis and simulation of a reaction–diffusion problem with transmission conditions

This paper considers a transmission problem for partial differential equations obtained in the recent paper [M. Neuss-Radu, W. Jäger, Effective transmission conditions for reaction-diffusion processes in domains separated by an interface, SIAM J. Math. Anal. 39 (2007) 687–720] as the effective system modeling a reaction–diffusion process in two domains separated by a membrane. For the analysis of this problem an appropriate function space, which includes the coupling conditions for the concentrations on the interface, is introduced. The transmission conditions for the flux are included in the variational formulation with respect to this function space.The solution of the transmission problem is approximated by using the Galerkin method. Numerically the problem is reduced to a system of ordinary differential equations, where the coupling of the micro- and macro-variables leads to a special structure, distinguishing the variables relevant for the transmission. Results of numerical simulations are illustrating the effect of the microscopic process in the membrane on the macroscopic reaction–diffusion process in the bulk domains.     

Straightness Measurement Using Laser Diode and CCD Camera

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