Single dibenzoterrylene molecules in naphthalene and 2,3-dimethylnaphthalene crystals: vibronic spectra

Fluorescence excitation spectra of single dibenzoterrylene (DBT) molecules embedded in naphthalene (N) and 2,3-dimethylnaphthalene (2,3-DMN) crystals were studied at 5 K. The frequencies characterizing the vibronic structure of single DBT molecules in an N crystal agree with the theoretical prediction for the isolated DBT molecule. The 'dipolar' disorder encountered in 2,3-DMN crystals leads to a broad distribution of frequencies of the (0,0) lines of single DBT molecules. Moreover, the observed vibronic frequencies and intensities in the spectrum of DBT in 2,3-DMN crystals are slightly different to those in an N crystal. We conclude that the structure of DBT molecules in a 2,3-DMN crystal is disturbed in comparison with isolated DBT and the main change concerns its central tetracene moiety.     

Distorted fused porphyrin-phthalocyanine conjugates: synthesis and photophysics of supramolecular assembled systems with a pyridylfullerene

In the current work, we report on the synthesis and photophysical features of supramolecular hybrid systems that are based on newly fused porphyrin-phthalocyanine (P-Pc) conjugates and a pyridylfullerene. The ZnP-ZnPc conjugate was synthesized in three steps starting with a Diels-Alder reaction between β-vinylporphyrin and fumaronitrile. The resulting mixture of isomeric adducts was then dehydrogenated to yield the corresponding benzo[b]porphyrin-2(1),2(2)-dicarbonitrile. In the final step, cyclotetramerization with 4-tert-butylphthalonitrile, in the presence of zinc acetate, afforded the bis-metalated conjugate. Selective demetallation of ZnP led to the H(2)P-ZnPc conjugate. For both conjugates steric hindrance is the inception to a bent configuration, which does, however, not preclude enlargement of the π-conjugated system, that is, the porphyrins and the phthalocyanines. The two conjugates coordinate N-(4-pyridyl)fullero[c]pyrrolidine giving rise to the corresponding supramolecular porphyrin-phthalocyanine-fullerene systems. Photophysical measurements corroborate a sequential deactivation in the excited state, namely an initial intramolecular energy transfer from ZnP or H(2)P to ZnPc followed by an intramolecular charge transfer to yield ZnP-(ZnPc)˙(+)-(C(60))˙(-) and H(2)P-(ZnPc)˙(+)-(C(60))˙(-), respectively.     

A Statistical Model for Predicting the Heat Transfer of Solid Particles in Turbulent Flows

The objective of this paper is twofold: (1) to present a statistical model of particle transport and heat transfer in turbulent flows and (2) to examine the performance of this model in various turbulent flows going from a simple flow to a more complicated one. This model is based on a kinetic equation for the probability density function of the particle velocity and temperature distributions in anisotropic turbulent flow. The model predictions compare reasonable well with numerical simulations and properly reproduce the crucial trends of computations performed in various turbulent flows.     

Soft X‐ray absorption spectroscopy and resonant inelastic X‐ray scattering spectroscopy below 100 eV: probing first‐row transition‐metal M‐edges in chemical complexes

X‐ray absorption and scattering spectroscopies involving the 3d transition‐metal K‐ and L‐edges have a long history in studying inorganic and bioinorganic molecules. However, there have been very few studies using the M‐edges, which are below 100 eV. Synchrotron‐based X‐ray sources can have higher energy resolution at M‐edges. M‐edge X‐ray absorption spectroscopy (XAS) and resonant inelastic X‐ray scattering (RIXS) could therefore provide complementary information to K‐ and L‐edge spectroscopies. In this study, M_2,3‐edge XAS on several Co, Ni and Cu complexes are measured and their spectral information, such as chemical shifts and covalency effects, are analyzed and discussed. In addition, M_2,3‐edge RIXS on NiO, NiF₂ and two other covalent complexes have been performed and different d–d transition patterns have been observed. Although still preliminary, this work on 3d metal complexes demonstrates the potential to use M‐edge XAS and RIXS on more complicated 3d metal complexes in the future. The potential for using high‐sensitivity and high‐resolution superconducting tunnel junction X‐ray detectors below 100 eV is also illustrated and discussed.     

Splitting Formulas for Tutte Polynomials

We present two splitting formulas for calculating the Tutte polynomial of a matroid. The first one is for a generalized parallel connection across a 3-point line of two matroids and the second one is applicable to a 3-sum of two matroids. An important tool used is the bipointed Tutte polynomial of a matroid, an extension of the pointed Tutte polynomial introduced by Brylawski.     

Statistical Properties of Unimodal Maps

We consider typical analytic unimodal maps which possess a chaotic attractor. Our main result is an explicit combinatorial formula for the exponents of periodic orbits. Since the exponents of periodic orbits form a complete set of smooth invariants, the smooth structure is completely determined by purely topological data (“typical rigidity”), which is quite unexpected in this setting. It implies in particular that the lamination structure of spaces of analytic unimodal maps (obtained by the partition into topological conjugacy classes, see [ALM]) is not transversely absolutely continuous. As an intermediate step in the proof of the formula, we show that the distribution of the critical orbit is described by the physical measure supported in the chaotic attractor.     

Simulations of energy and switching in AFLCDs with different boundary conditions

Using standard expressions for the various terms in the Gibbs free energy, the switching in antiferroelectric liquid crystal (AFLC) displays is simulated and the time evolution of various energy terms and of the liquid crystal director distributions are calculated. It is shown that when returning from a strong positive voltage to zero, one can reach two types of antiferroelectric state: the normal alternating state with the two bulk polarizations perpendicular to the electrodes and opposite to each other, and the alternative splayed symmetric state with two bulk polarizations parallel to the electrodes and again opposite to each other. The former case gives rise to tri-state switching characteristics, the latter to V-shaped switching. In general strong polar interaction with the alignment layer favours V-shaped switching while weak or no polar interaction give rise to tri-state switching characteristics. Since the V-shaped characteristic has so far only been demonstrated experimentally in ferroelectric liquid crystals (or antiferroelectric liquid crystals being in the ferroelectric state), the difference in AFLCs is discussed and the conditions for continuous switching are modelled. The simulations show that the switching characteristics of the antiferroelectric display can be controlled by the surface parameters.     

On exotic characteristic classes for spherical fibrations

We define for every so-called admissible relation r in the Steenrod algebra $\text{A}$ and for every oriented spherical fibration ξ over a CW-space an exotic characteristic class (mod 2) ε(r)(ξ), which is primitive and vanishes for sphere bundles. The set of exotic classes associated with the universal spherical fibration and the admissible Adem relations are compared with the algebra generators of H¹(BSG;$\text{Z}$₂) due to Milgram. Moreover, their behaviour under the action of $\text{A}$ is computed. Finally, we give a secondary Wu formula for exotic classes of special Poincaré duality spaces.     

Über eine Integraldarstellung derM k,m -Funktionen und ihre asymptotische Darstellung für große Werte von\Re \mathfrak{e}k

Ohne Zusammenfassung