Localization for a Random Walk in Slowly Decreasing Random Potential

We consider a continuous time random walk X in a random environment on ?⁺ such that its potential can be approximated by the function V:?⁺→? given by $V(x)=\sigma W(x) -\frac {b}{1-\alpha}x^{1-\alpha}$ where σW a Brownian motion with diffusion coefficient σ>0 and parameters b, α are such that b>0 and 0<α<1/2. We show that P-a.s. (where P is the averaged law) $\lim_{t\to\infty} \frac{X_{t}}{(C^{*}(\ln\ln t)^{-1}\ln t)^{\frac{1}{\alpha}}}=1$ with $C^{*}=\frac{2\alpha b}{\sigma^{2}(1-2\alpha)}$ . In fact, we prove that by showing that there is a trap located around $(C^{*}(\ln\ln t)^{-1}\ln t)^{\frac{1}{\alpha}}$ (with corrections of smaller order) where the particle typically stays up to time t. This is in sharp contrast to what happens in the “pure” Sinai’s regime, where the location of this trap is random on the scale ln² t.     

Electromagnetic and nuclear fission of238U in the reaction of 100, 500, and 1000 A·MeV208Pb with238U

The folding- and azimuthal-angle and velocity distributions for the²³⁸U fission fragments have been measured in reactions with 100, 500, and 1000 A·MeV²⁰⁸Pb. These distributions were used to decompose the fission cross section into its electromagnetic and nuclear components. The fraction of electromagnetic fission was found to be 0.16±0.07, 0.48±0.08, and 0.60±0.04, respectively. The electromagnetic fission cross section as a function of the²⁰⁸Pb nucleus energy is compared with theoretical predictions. The measured fission cross section from nuclear reactions (≈1.5 b) is approximately constant between 100 and 1000 A·MeV.     

Magnetic microstructure of nanocrystalline FeCuNbSiB soft magnets

The soft magnetic properties and the domain patterns of optimized nanocrystalline FeCuNbSiB-alloys are typically comparable to those of highly permeable Co-based amorphous alloys. Yet the nanocrystalline alloys show some specific peculiarities absent in the amorphous case. The most prominent example is patchy magnetization patterns which reflect the residual contribution of the averaged random magneto-crystalline anisotropy to the magnetization process. The article surveys the typical characteristics and the consequences for the magnetization process.     

Mehrfachbindungen zwischen hauptgruppenelementen und übergangsmetallen: IV. Chrom-schwefel- und chrom-selen-bindungen: Knüpfung,umwandlungsreaktionen und alkylidenaddition

New dinuclear chromium—sulfur complexes containing one or two sulfur atoms are formed upon reaction of the ionic complex K[(η⁵-C₅Me₅)Cr(CO)₃] (Me = CH₃; 1) with trithiazyl trichloride at temperatures below ambient. The μ(η¹ :η²)-disulfur complex 2a of composition (η⁵-C₅Me₅)₂Cr₂(CO)₅S₂ undergoes concomitant CO-elimination and desulfurization on heating or in the presence of triphenylphosphine; the CrSCr-complex (η⁵-C₅Me₅)₂Cr₂(CO)₄S (2c) is formed in these cases. When diazomethane is treated with 2a, a novel μ,η²-thio- formaldehyde complex (2d) results, again following CO- and S-extrusion. While the triple-bonded CrSCr-skeleton present in 2c does not allow alkylidene additions, such reactions, which proceed cleanly, are observed with the corresponding μ⁵-seleno derivative (η⁵-C₅H₅)₂Cr₂(CO)₄Se (4) synthesized from Na[(η⁵-C₅H₅)Cr(CO)₃] and sodium selenite in the presence of hydrochloric acid.     

Synthesis, electronic, and electro-optical properties of emissive solvatochromic phenothiazinyl merocyanine dyes

Phenothiazinyl merocyanine dyes with variable substitution patterns on the peripheral benzene ring were synthesized in good yields by Knoevenagel condensation of the corresponding phenothiazinyl aldehydes and N-methylrhodanine or indan-1,3-dione. The electronic properties were investigated by cyclic voltammetry, absorption, electro-optical absorption, and emission spectroscopy. All these merocyanines reveal reversible redox behavior that stems from the phenothiazinyl-centered oxidation to give stable radical cations. The redox potentials strongly correlate with Hammett σ(p) parameters. All merocyanines reveal large Stokes shifts. They also display a pronounced emissive solvatochromism, which is caused by large dipole moment changes upon excitation from the ground to the excited state. These findings are supported by solvatochromism studies and time-dependent DFT computations.     

Nuclear inelastic scattering studies on a dinuclear iron(II) spin crossover complex

The vibrational properties of the (high-spin)-(high-spin) and the (high-spin)- (low-spin) states of the dinuclear Fe(II) spin crossover complex[{Fe(L-N₄Me₂)}₂(BiBzIm)](ClO₄)₂·2EtCN¹ have been studied by means of nuclear inelastic scattering. At a temperature of 80 K typical low spin marker bands are detected in the region around 400 cm^?1, these bands almost completely disappear after increasing temperature to 190 K. Corresponding density functional theory calculations using the functional B3LYP* and the basis set CEP-31G reproduce the experimental data and thus allow a deeper understanding of the vibrational properties of dinuclear Fe(II) spin crossover complexes.