Efficient numerical methods for initial-value solid-state laser problems

The difficulties of solving initial-value solid-state laser problems numerically arise from both stiffness of the problems and near-to-zero nonnegative exact solutions. Stability and non-negativity must be maintained simultaneously in the numerical solutions. Backward differentiation formulas (BDFs) is capable of dealing with stiff problems ,but is of small oscillation when time-step is large. Therefore unfortunately BDFs suffers from severe time-step restriction . In this paper,we present an optimized numerical approach, with which 3-dimensional laser problems can be solved faster and much more efficiently. These techniques can not only be used for solid-state laser systems, but can also be applied to solve other stiff problems which have near-to-zero nonnegative exact solutions. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermodynamic equilibrium between locally excited and charge-transfer states through thermally activated charge transfer in 1-(pyren-2′-yl)-o-carborane

Reversible conversion between excited-states plays an important role in many photophysical phenomena. Using 1-(pyren-2′-yl)-o-carborane as a model, we studied the photoinduced reversible charge-transfer (CT) process and the thermodynamic equilibrium between the locally-excited (LE) state and CT state, by combining steady state, time-resolved, and temperature-dependent fluorescence spectroscopy, fs- and ns-transient absorption, and DFT and LR-TDDFT calculations. Our results show that the energy gaps and energy barriers between the LE, CT, and a non-emissive ‘mixed’ state of 1-(pyren-2′-yl)-o-carborane are very small, and all three excited states are accessible at room temperature. The internal-conversion and reverse internal-conversion between LE and CT states are significantly faster than the radiative decay, and the two states have the same lifetimes and are in thermodynamic equilibrium.

Reversible conversion between excited-states is key to many photophysical phenomena. We studied the equilibrium between LE and CT states by time-resolved and temperature-dependent fluorescence, fs- and ns-transient absorption, and LR-TDDFT calculations.     

Differential calculi on noncommutative bundles

We introduce a category of noncommutative bundles. To establish geometry in this category we construct suitable noncommutative differential calculi on these bundles and study their basic properties. Furthermore we define the notion of a connection with respect to a differential calculus and consider questions of existence and uniqueness. At the end these constructions are applied to basic examples of noncommutative bundles over a coquasitriangular Hopf algebra.     

Chemical and structural effects on the electronic transport in organic single crystals

Effects induced by chemical and structural inhomogeneities on the electronic transport in organic crystals with the focus on highly-ordered polyacenes are discussed in this paper. The material class chosen is of great importance as polyacenes are widely studied with perspectives on applications in thin film devices. As will be shown, the charge carrier mobility in these long-range ordered molecular systems is limited by chemical impurities rather than by structural inhomogeneities. Time-of-flight spectroscopy on polyacenes purified by zone-refinement does not only show coherent carrier movement for holes but also for electrons, which is rarely observed for compounds that can be purified by sublimation only. Finally, we will present a direct comparison between the chemical species and their amount on the surface and in the volume of tetracene crystals. The significantly higher impurity concentration at the surfaces is relevant for the mobility estimated by field-effect transistor (FET) studies on single crystals in planar-geometry.     

Stability of alkali-atom clusters

A detailed study of the stability of alkali-atom clusters is presented and discussed. Free clusters are produced in an unseeded adiabatic expansion and ionized by a pulsed laser beam. A tandem time-of-flight system provides a size selection of ionized species and mass spectrometry of fragments. We have investigated for sodium and potassium clusters containing up to fifty atoms: the metastable decay following ionization, the photo-induced dissociation, the collisional induced dissociation and the collisional charge exchange. Experimental evidence is shown for dissociative process involving evaporation of monomers and dimers. This is explained by the statistical unimolecular theory and by the energetics of the systems.     

One dimensional molecular dipole chain arrays on graphite via nanoscale phase separation

Molecular dipole chain arrays of chloroaluminium phthalocyanine (ClAlPc) on the graphite surface have been investigated by scanning tunneling microscopy. The inter-chain spacing can be tuned by the co-adsorption of di-indenoperylene (DIP) via nanoscale phase separation.     

Inorganic salts in non-aqueous solvents: Absorption spectra of transition metal salts in dimethylformamide

Absorption spectra of Cr, Mn, Fe, Co, Ni and Cu salts have been determined in dimethylformamide. In most cases the spectra differed considerably from those in aqueous solutions. The absorption maxima and the molar absorptivities of these salts in dimethylformamide are tabulated. The spectra are strongly influenced by the presence of certain anions, the order of decreasing effect being Cl^-, Oac^-, NO₃^- and ClO₄^-.     

Algebraic analysis of multigrid algorithms

We study the convergence rate of multilevel algorithms from an algebraic point of view. This requires a detailed analysis of the constant in the strengthened Cauchy–Schwarz inequality between the coarse‐grid space and a so‐called complementary space. This complementary space may be spanned by standard hierarchical basis functions, prewavelets or generalized prewavelets. Using generalized prewavelets, we are able to derive a constant in the strengthened Cauchy–Schwarz inequality which is less than 0.31 for the L² and H¹ bilinear form. This implies a convergence rate less than 0.15. So, we are able to prove fast multilevel convergence. Furthermore, we obtain robust estimations of the convergence rate for a large class of anisotropic ellipic equations, even for some that are not H¹‐elliptic. Copyright © 1999 John Wiley & Sons, Ltd.     

Traces on algebras of parameter dependent pseudodifferential operators and the eta-invariant

We identify Melrose's suspended algebra of pseudodifferential operators with a subalgebra of the algebra of parametric pseudodifferential operators with parameter space . For a general algebra of parametric pseudodifferential operators, where the parameter space may now be a cone , we construct a unique ``symbol valued trace', which extends the -trace on operators of small order. This construction is in the spirit of a trace due to Kontsevich and Vishik in the nonparametric case. Our trace allows us to construct various trace functionals in a systematic way. Furthermore, we study the higher-dimensional eta-invariants on algebras with parameter space . Using Clifford representations we construct for each first order elliptic differential operator a natural family of parametric pseudodifferential operators over . The eta-invariant of this family coincides with the spectral eta-invariant of the operator.