Possible Loss and Recovery of Gibbsianness¶During the Stochastic Evolution of Gibbs Measures

We consider Ising-spin systems starting from an initial Gibbs measure ν and evolving under a spin-flip dynamics towards a reversible Gibbs measure μ≠ν. Both ν and μ are assumed to have a translation-invariant finite-range interaction. We study the Gibbsian character of the measure νS(t) at time t and show the following: (1) For all ν and μ, νS(t) is Gibbs for small t. (2) If both ν and μ have a high or infinite temperature, then νS(t) is Gibbs for all t > 0. (3) If ν has a low non-zero temperature and a zero magnetic field and μ has a high or infinite temperature, then νS(t) is Gibbs for small t and non-Gibbs for large t. (4) If ν has a low non-zero temperature and a non-zero magnetic field and μ has a high or infinite temperature, then νS(t) is Gibbs for small t, non-Gibbs for intermediate t, and Gibbs for large t. The regime where μ has a low or zero temperature and t is not small remains open. This regime presumably allows for many different scenarios. Received: 26 April 2001 / Accepted: 10 October 2001     

Assay of vecuronium in plasma using solid-phase extraction, high-performance liquid chromatography and post-column ion-pair extraction with fluorimetric detection

An assay has been developed and validated for the routine monitoring of vecuronium in plasma. It consists of solid-phase extraction using C18 disposables as sample pre-treatment, high-performance liquid chromatography and post-column ion-pair extraction with fluorimetric detection. The fluorescent anion 9,10-dimethoxyanthracene-2-sulphonate (DAS) is used as the counter ion. The detection limit is ca. 5 ng/ml in plasma with a signal-to-noise ratio of 10. The assay is also applicable for monitoring vecuronium and its potential metabolites in other biological media, e.g., urine, bile and tissue (liver, kidney) homogenates.     

Construction algorithms for polynomial lattice rules for multivariate integration

We introduce a new construction algorithm for digital nets for integration in certain weighted tensor product Hilbert spaces. The first weighted Hilbert space we consider is based on Walsh functions. Dick and Pillichshammer calculated the worst-case error for integration using digital nets for this space. Here we extend this result to a special construction method for digital nets based on polynomials over finite fields. This result allows us to find polynomials which yield a small worst-case error by computer search. We prove an upper bound on the worst-case error for digital nets obtained by such a search algorithm which shows that the convergence rate is best possible and that strong tractability holds under some condition on the weights.

We extend the results for the weighted Hilbert space based on Walsh functions to weighted Sobolev spaces. In this case we use randomly digitally shifted digital nets. The construction principle is the same as before, only the worst-case error is slightly different. Again digital nets obtained from our search algorithm yield a worst-case error achieving the optimal rate of convergence and as before strong tractability holds under some condition on the weights. These results show that such a construction of digital nets yields the until now best known results of this kind and that our construction methods are comparable to the construction methods known for lattice rules.

We conclude the article with numerical results comparing the expected worst-case error for randomly digitally shifted digital nets with those for randomly shifted lattice rules.

     

Nanostructured Ion-Selective MCM-48 Membranes

Templated MCM-48 silica was prepared using CTAB as surfactant. The MCM-48 powders and thin films were characterized by different techniques. MCM-48 layers were deposited on macroporous α-alumina supports and silicon nitride microsieves. The water permeability of MCM-48 was compared with the permeability of conventional mesoporous γ-alumina membranes. The applicability of MCM-48 as ion-selective electric field-driven switchable interconnect for microfluidic devices was demonstrated.     

On the recognition problem of quasi-homogeneous locally nilpotent derivations in dimension three

We give a criterion to decide if a given w-homogeneous derivation on A?k[X₁,X₂,X₃] is locally nilpotent. We deduce an algorithm which decides if a k-subalgebra of A, which is finitely generated by w-homogeneous elements, is the kernel of some locally nilpotent derivation.     

Picosecond control of coherent magnetisation dynamics in permalloy thin films by picosecond magnetic field pulse shaping

We have measured the response of a 20×10 μm, 8 nm thin NiFe (80:20) permalloy film due to excitation by short in-plane magnetic field pulses. We will show that using a two-pulse-technique a complete control of the precessional motion of the magnetisation can be achieved on picosecond timescales. Furthermore, we will present numerical calculations which show that a complete suppression of magnetisation ringing after switching can only be realised by a cascade of short field pulses.     

Artificial time integration

Many recent algorithmic approaches involve the construction of a differential equation model for computational purposes, typically by introducing an artificial time variable. The actual computational model involves a discretization of the now time-dependent differential system, usually employing forward Euler. The resulting dynamics of such an algorithm is then a discrete dynamics, and it is expected to be “close enough” to the dynamics of the continuous system (which is typically easier to analyze) provided that small – hence many – time steps, or iterations, are taken. Indeed, recent papers in inverse problems and image processing routinely report results requiring thousands of iterations to converge. This makes one wonder if and how the computational modeling process can be improved to better reflect the actual properties sought. In this article we elaborate on several problem instances that illustrate the above observations. Algorithms may often lend themselves to a dual interpretation, in terms of a simply discretized differential equation with artificial time and in terms of a simple optimization algorithm; such a dual interpretation can be advantageous. We show how a broader computational modeling approach may possibly lead to algorithms with improved efficiency. AMS subject classification (2000)  65L05, 65M32, 65N21, 65N22, 65D18     

Feasibility study for the preparation of certified reference materials part I – mineral oil contaminated soils

The international joint project HYCREF (Contract No. G6RD-CT-2002-00854), funded by the European Commission in the 5th Framework programme, aimed to develop methods to prepare homogeneous and stable reference materials of water, soil, and waste contaminated with mineral oil hydrocarbons and to certify the mineral oil content by gas chromatographic methods. The results of a feasibility study for the preparation of three soil reference materials are discussed in this paper, and for the preparation of three waste reference materials in the second part (Koch et al., Accred Qual Assur submitted for publication). The soil materials were selected to represent different soil types and contamination levels. The project plan set three requirements for these reference materials: uncertainty in the mineral oil content resulting from the certification exercise <5%, a sample inhomogeneity of <3% and a minimum long-term stability of 5 years. For the most part, these requirements were met within this project.