Pathwise Convergence of a Rescaled Super-Brownian Catalyst Reactant Process

Consider the one-dimensional catalytic super-Brownian motion X (called the reactant) in the catalytic medium which is an autonomous classical super-Brownian motion. We characterize both in terms of a martingale problem and (in dimension one) as solution of a certain stochastic partial differential equation. The focus of this paper is for dimension one the analysis of the longtime behavior via a mass-time-space rescaling. When scaling time by a factor of K, space is scaled by K ^η and mass by K ^−η. We show that for every parameter value η ≥ 0 the rescaled processes converge as K→ ∞ in path space. While the catalyst’s limiting process exhibits a phase transition at η = 1, the reactant’s limit is always the same degenerate process.      

Multiple Intersection Exponents for Planar Brownian Motion

Let p≥2, n ₁≤⋅⋅⋅≤n _p be positive integers and be independent planar Brownian motions started uniformly on the boundary of the unit circle. We define a p-fold intersection exponent ς _p (n ₁,…,n _p ), as the exponential rate of decay of the probability that the packets , i=1,…,p, have no joint intersection. The case p=2 is well-known and, following two decades of numerical and mathematical activity, Lawler et al. (Acta Math. 187:275–308, 2001) rigorously identified precise values for these exponents. The exponents have not been investigated so far for p>2. We present an extensive mathematical and numerical study, leading to an exact formula in the case n ₁=1, n ₂=2, and several interesting conjectures for other cases.     

A back-extraction procedure for the dithiocarbamate solvent extraction method. Rapid determination of metals in seawater matrices

Summary A ligand exchange liquid/liquid extraction method using dithiocarbamate complexes is elaborated for the graphite furnace atomic absorption spectrometry (GF-AAS) of seawater and marine interstitial water. Palladium is used for the exchange. This metal ensures a rapid and quantitative back-extraction. It simultaneously works as matrix modifier in the GF-AAS analysis. The proposed method is evaluated in the analysis of lead, copper, nickel, and cadmium in CASS-II marine reference seawater and samples from the North Sea. A microanalytical variant of the method is applied in marine interstitial water analysis down to sample volumes of 500 l.     

The Critical Attractive Random Polymer in Dimension One

A polymer chain with attractive and repulsive forces between the building blocks is modeled by attaching a weight e ^– for every self-intersection and e ^/(2d) for every self-contact to the probability of an n-step simple random walk on ^d , where , >0 are parameters. It is known that for d=1 and > the chain collapses down to finitely many sites, while for d=1 and < it spreads out ballistically. Here we study for d=1 the critical case = corresponding to the collapse transition and show that the end-to-end distance runs on the scale _n = (log n)^–1/4. We describe the asymptotic shape of the accordingly scaled local times in terms of an explicit variational formula and prove that the scaled polymer chain occupies a region of size _n times a constant. Moreover, we derive the asymptotics of the partition function.     

Interacting Fisher–Wright diffusions in a catalytic medium

We study the longtime behaviour of interacting systems in a randomly fluctuating (space–time) medium and focus on models from population genetics. There are two prototypes of spatial models in population genetics: spatial branching processes and interacting Fisher–Wright diffusions. Quite a bit is known on spatial branching processes where the local branching rate is proportional to a random environment (catalytic medium). Here we introduce a model of interacting Fisher–Wright diffusions where the local resampling rate (or genetic drift) is proportional to a catalytic medium. For a particular choice of the medium, we investigate the longtime behaviour in the case of nearest neighbour migration on the d-dimensional lattice. While in classical homogeneous systems the longtime behaviour exhibits a dichotomy along the transience/recurrence properties of the migration, now a more complicated behaviour arises. It turns out that resampling models in catalytic media show phenomena that are new even compared with branching in catalytic medium. Received: 15 November 1999 / Revised version: 16 June 2000 / Published online: 6 April 2001     

Darstellung Der Isomeren 1,6-DI-O-Acetyl-3,4-Didesoxy-α, β-D-Glycero-Hex-3-Enopyrahos-2-Ulosen

Abstract

Prolonged treatment of tetra-O-acetyl-1, 5-anhydro-hex-1-enitols (“tetra-O-acetyl-hydroxy-glycals”) 3 and 5 with BF₃ in CH₂Cl₂ at RT lead to anomeric mixtures of the title compounds 2 and 4a, the α-anomer 4a dominating. Reaction of 5 gave the higher yields of 4a (71%) and 2 (12%), the results being accounted mechanistic grounds. The same reaction performed in an aromatic solvent, like toluene, gave rise to competing C-alkylation., The ortho and para-tolyl derivatives 6 and 7, also with enone structure, were isolated in a combined maximum yield of 40% from 5. β-Enone 2 was also prepared in moderate yield by thermolysis of β-d-glucopyranose pentaacetate (1). In this case no α-anomer 4a was detected.     

88 W 0.5 mJ femtosecond laser pulses from two coherently combined fiber amplifiers

The generation of 0.5 mJ femtosecond laser pulses by coherent combining of two high power high energy fiber chirped-pulse amplifiers is reported. The system is running at a repetition frequency of 175 kHz producing 88 W of average power after the compressor unit. Polarizing beam splitters have been used to realize an amplifying Mach-Zehnder interferometer, which has been stabilized with a H?nsch-Couillaud measurement system. The stabilized system possesses a measured residual rms phase difference fluctuation between the two branches as low as λ/70 rad at the maximum power level. The experiment proves that coherent addition of femtosecond fiber lasers can be efficiently and reliably performed at high B-integral and considerable thermal load in the individual amplifiers.     

Ultracold neutrons extracted from a superfluid-helium converter coated with fluorinated grease

The European Physical Journal C - We report experiments on the production of ultracold neutrons (UCN) in a converter of superfluid helium coated with fluorinated grease (fomblin). We employed our...     

Spin alignment and Mössbauer hyperfine fields in the reentrant spin glass (Fe0.65Ni0.35)1-xMnx

Hyperfine Interactions - We performed Mössbauer spectroscopy on the ternary alloy system (Fe0.65Ni0.35)1-xMnx in applied external magnetic fields. From the hyperfine field distributions the...