In situ monitoring and control of lysozyme concentration during crystallization in a hanging drop

Fiber optic Raman spectroscopy combined with a partial least-squares regression model was demonstrated as a monitor of lysozyme concentration during crystallization in a hanging drop experiment in real time. Raman spectral features of the buffer and protein were employed to build the regression model. The use of fiber optic technology coupled with Raman spectroscopy, which is ideal for use with aqueous solutions, results in a powerful noninvasive probe of the changing environment within the solution. Lysozyme concentrations were monitored in experiments at a constant reservoir ionic strength. Data from these uncontrolled experiments were used to determine rates of supersaturation, induction times, and the number and size of the resultant lysozyme crystals. Control experiments were performed by introducing step changes in the reservoir ionic strength. The step changes were initiated by comparing in situ rates of supersaturation with the rates of supersaturation calculated from the uncontrolled data. Monitoring the concentration changes of the lysozyme within the hanging drop permits a measurement of the level of supersaturation of the system and enhances the possibility of dynamic control of the crystallization process.     

Ueber Trennung von Kupfer und Zink durch Schwefelwasserstoff

Ohne Zusammenfassung     

The Averaged Dynamics of the Hydrogen Atom in Crossed Electric and Magnetic Fields as a Perturbed Kepler Problem

We treat the classical dynamics of the hydrogen atom in perpendicular electric and magnetic fields as a celestial mechanics problem. By expressing the Hamiltonian in appropriate action–angle variables, we separate the different time scales of the motion. The method of averaging then allows us to reduce the system to two degrees of freedom, and to classify the most important periodic orbits.     

Producing SI-traceable reference values for Cd, Cr and Pb amount contents in polyethylene samples from the Polymer Elemental Reference Material (PERM) project using isotope dilution mass spectrometry

 The present paper describes the certification of the amount content of Cd, Cr and Pb in two different polyethylene materials within the third phase of the Polyethylene Elemental Reference Material (PERM) project. The analytical procedure to establish the reference values for Cd, Cr and Pb amount contents in these materials is based on isotope dilution mass spectrometry used as a primary method of measurement. Cd and Pb were measured with inductively coupled plasma-mass spectrometry and Cr with positive thermal ionization-mass spectrometry. The decomposition of the polymer matrix was carried out using a high pressure asher. Reference values for amount content, traceable to the SI-system, have been obtained for these three elements in both of the polyethylene samples of PERM. For each of the certified amount content values an uncertainty budget was calculated using the method of propagation of uncertainties according to ISO and EURACHEM guidelines. The measurement procedures, as well as the uncertainty calculations, are described for all three elements. In order to keep the whole certification process as transparent as possible, the preparations of various reagents and materials as well as the sample treatment and blending are described in detail. The mass spectrometry measurements and the data treatment are also explained carefully. The various sources of uncertainty present in the procedure are displayed in the uncertainty budgets. The obtained combined uncertainties for the amount content values were less than 2% relative (k=1) for all investigated elements. The amount contents were in the μmol/kg range, corresponding to mg/kg levels. Received: 21 October 1999 / Accepted: 29 January 2000     

Model Spaces of Regularity Structures for Space-Fractional SPDEs

We study model spaces, in the sense of Hairer, for stochastic partial differential equations involving the fractional Laplacian. We prove that the fractional Laplacian is a singular kernel suitable to apply the theory of regularity structures. Our main contribution is to study the dependence of the model space for a regularity structure on the three-parameter problem involving the spatial dimension, the polynomial order of the nonlinearity, and the exponent of the fractional Laplacian. The goal is to investigate the growth of the model space under parameter variation. In particular, we prove several results in the approaching subcriticality limit leading to universal growth exponents of the regularity structure. A key role is played by the viewpoint that model spaces can be identified with families of rooted trees. Our proofs are based upon a geometrical construction similar to Newton polygons for classical Taylor series and various combinatorial arguments. We also present several explicit examples listing all elements with negative homogeneity by implementing a new symbolic software package to work with regularity structures. We use this package to illustrate our analytical results and to obtain new conjectures regarding coarse-grained network measures for model spaces.