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431.
Rohde D Dunsch L Tabet A Hartmann H Fabian J 《The journal of physical chemistry. B》2006,110(16):8223-8231
A new homologous series of alpha,alpha'-bis(diphenylamino)-capped oligothiophenes, prepared by a palladium-catalyzed coupling reaction of stannylated 2-diphenylaminothiophenes with 2-mono- or 2,5-dibromothiophenes and their homologues, was studied by in situ ESR/UV-vis/NIR spectroelectrochemistry. In general, the oxidation potentials of these oligothiophenes were found to be proportional to the inverse number of thiophene units. However, the potential slope of the first oxidation is completely different from that of higher oxidation steps. Trication radicals were identified by electron spin resonance (ESR) for higher thiophene homologues in addition to monocation radicals (polarons). According to the ESR hyperfine structures, the unpaired electron is delocalized in the conjugated system. In contrast to the parent alpha,alpha'-bis(diphenylamino)-capped oligothiophenes, the UV-vis/NIR absorption maxima of the oxidized species strongly depend on the number of thiophene units. Spin-restricted and spin-unrestricted Kohn-Sham density functional calculations were used to explain and to understand these properties. Absorption wavelength and intensities were calculated by the time-dependent density functional response theory. Unrestricted density functional calculations of oligothiophene dications (bipolarons) with five or more thiophene rings result in spin-broken structures which may be considered as two-polaron biradicals (polaron pairs). 相似文献
432.
We investigate the thermal fluctuations of the colloidal gas-liquid interface subjected to a shear flow parallel to the interface. Strikingly, we find that the shear strongly suppresses capillary waves, making the interface smoother. This phenomenon can be described by introducing an effective interfacial tension that increases with the shear rate. The increase of sigma(eff) is a direct consequence of the loss of interfacial entropy caused by the flow, which affects especially the slow fluctuations. This demonstrates that the interfacial tension of fluids results from an intrinsic as well as a fluctuation contribution. 相似文献
433.
Kleckner D Marshall W de Dood MJ Dinyari KN Pors BJ Irvine WT Bouwmeester D 《Physical review letters》2006,96(17):173901
We report on the demonstration of a high finesse micro-optomechanical system and identify potential applications ranging from optical cooling to weak force detection to massive quantum superpositions. The system consists of a high quality diameter flat dielectric mirror cut from a larger substrate with a focused ion beam and attached to an atomic force microscope cantilever. Cavity ring-down measurements performed on a 25 mm long Fabry-Pérot cavity with the 30 microm mirror at one end show an optical finesse of 2100. Numerical calculations show that the finesse is not diffraction limited and that orders of magnitude higher finesse should be possible. A mechanical quality factor of more than 10(5) at pressures below 10(-3) mbar is demonstrated for the cantilever with a mirror attached. 相似文献
434.
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436.
Johannes Lankeit Patrizio Neff Dirk Pauly 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2013,64(6):1679-1688
Let ${\Omega \subset \mathbb{R}^{N}}$ be a Lipschitz domain and Γ be a relatively open and non-empty subset of its boundary ${\partial\Omega}$ . We show that the solution to the linear first-order system $$\nabla \zeta = G\zeta, \, \, \zeta|_\Gamma = 0 \quad \quad \quad (1)$$ is unique if ${G \in \textsf{L}^{1}(\Omega; \mathbb{R}^{(N \times N) \times N})}$ and ${\zeta \in \textsf{W}^{1,1}(\Omega; \mathbb{R}^{N})}$ . As a consequence, we prove $$||| \cdot ||| : \textsf{C}_{o}^{\infty}(\Omega, \Gamma; \mathbb{R}^{3}) \rightarrow [0, \infty), \, \, u \mapsto \parallel {\rm sym}(\nabla uP^{-1})\parallel_{\textsf{L}^{2}(\Omega)}$$ to be a norm for ${P \in \textsf{L}^{\infty}(\Omega; \mathbb{R}^{3 \times 3})}$ with Curl ${P \in \textsf{L}^{p}(\Omega; \mathbb{R}^{3 \times 3})}$ , Curl ${P^{-1} \in \textsf{L}^{q}(\Omega; \mathbb{R}^{3 \times 3})}$ for some p, q > 1 with 1/p + 1/q = 1 as well as det ${P \geq c^+ > 0}$ . We also give a new and different proof for the so-called ‘infinitesimal rigid displacement lemma’ in curvilinear coordinates: Let ${\Phi \in \textsf{H}^{1}(\Omega; \mathbb{R}^{3})}$ satisfy sym ${(\nabla\Phi^\top\nabla\Psi) = 0}$ for some ${\Psi \in \textsf{W}^{1,\infty}(\Omega; \mathbb{R}^{3}) \cap \textsf{H}^{2}(\Omega; \mathbb{R}^{3})}$ with det ${\nabla\Psi \geq c^+ > 0}$ . Then, there exist a constant translation vector ${a \in \mathbb{R}^{3}}$ and a constant skew-symmetric matrix ${A \in \mathfrak{so}(3)}$ , such that ${\Phi = A\Psi + a}$ . 相似文献
437.
Let be a Lipschitz domain and Γ be a relatively open and non-empty subset of its boundary ?Ω. We show that the solution to the linear first-order system:(1) vanishes if and . In particular, square-integrable solutions ζ of (1) with vanish. As a consequence, we prove that: is a norm if with , for some with as well as . We also give a new and different proof for the so-called ‘infinitesimal rigid displacement lemma’ in curvilinear coordinates: Let , , satisfy for some with . Then there exists a constant translation vector and a constant skew-symmetric matrix , such that . 相似文献
438.
We present some Poincaré type inequalities for quadratic matrix fields with applications e.g. in gradient plasticity or fluid dynamics. In particular, an application to the pseudostress-velocity formulation of the stationary Stokes problem is discussed. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
439.
Dirk Zeindler 《Journal of Theoretical Probability》2013,26(4):968-996
Hambly, Keevash, O’Connell, and Stark have proven a central limit theorem for the characteristic polynomial of a permutation matrix with respect to the uniform measure on the symmetric group. We generalize this result in several ways. We prove here a central limit theorem for multiplicative class functions on the symmetric group with respect to the Ewens measure and compute the covariance of the real and the imaginary part in the limit. We also estimate the rate of convergence with the Wasserstein distance. 相似文献
440.
Hartmut Stöcker Maximilian Rühl Anett Heinrich Erik Mehner Dirk C. Meyer 《Journal of Electrostatics》2013,71(5):905-909
The triboelectric effect describes electrical charging when bringing different materials into contact. We report on the generation of hard X-ray radiation by peeling various adhesive tapes under medium vacuum conditions. Beside vacuum housing and pumps as instrumentation only an electric motor, two rolls and a metal foil as target material are necessary. The spectral distribution of generated X-rays was analyzed using an energy-dispersive detector. Depending on peeling speed, pressure and choice of material combination, electrons with energies sufficient to excite emission in the hard X-ray region are produced. The results are discussed in terms of triboelectric separation of charge carriers. 相似文献