Loss without recovery of Gibbsianness during diffusion of continuous spins

We consider a specific continuous-spin Gibbs distribution μ_t=0 for a double-well potential that allows for ferromagnetic ordering. We study the time-evolution of this initial measure under independent diffusions. For `high temperature' initial measures we prove that the time-evoved measure μ<sub>t</sub> is Gibbsian for all t. For `low temperature' initial measures we prove that μ_t stays Gibbsian for small enough times t, but loses its Gibbsian character for large enough t. In contrast to the analogous situation for discrete-spin Gibbs measures, there is no recovery of the Gibbs property for large t in the presence of a non-vanishing external magnetic field. All of our results hold for any dimension d≥2. This example suggests more generally that time-evolved continuous-spin models tend to be non-Gibbsian more easily than their discrete-spin counterparts. Research carried out at EURANDOM and supported by Deutsche Forschungsgemeinschaft     

Über Sesquiselenide der Lanthanoide: Einkristalle von Ce2Se3 im C‐, Gd2Se3 im U‐ und Lu2Se3 im Z‐Typ

On Sesquiselenides of the Lanthanoids: Single Crystals of C‐type Ce₂Se₃, U‐type Gd₂Se₃, and Z‐type Lu₂Se₃ Single crystals of lanthanoid sesquiselenides (M₂Se₃; here: M = Ce, Gd, Lu) are accessible through conversion of the elements (lanthanoid and selenium) in molar ratios of 2:3 within seven days at 850 °C from evacuated silica ampoules if equimolar amounts of NaCl serve as a flux. In the case of Ce₂Se₃ (a = 897.74(6) pm) und Gd₂Se₃ (a = 872.56(5) pm) the cubic C‐type (I4¯3d, Z = 5.333) forms as dark red beads, whereas the orthorhombic Z‐type (Fddd, Z = 16) emerges for Lu₂Se₃ (a = 1125.1(1), b = 798.06(8), c = 2387.7(2) pm) as orange‐yellow bricks. Upon oxidation of monochloride hydrides (MClH_x or A_yMClH_x; M = Ce, Gd, Lu; x = 1; A = Li, Na; y = 0.5) with selenium in arc‐welded tantalum ampoules the same main products appear with C‐Ce₂Se₃ and Z‐Lu₂Se₃, even with a surplus of NaCl or LiCl as fluxing agent. In the case of Gd₂Se₃, however, black‐red needles of the orthorhombic U‐type (Pnma, Z = 4; a = 1118.2(1), b = 403.48(4); c = 1097.1(1) pm) are yielded instead of C‐Gd₂Se₃. C‐Ce₂Se₃ crystallizes in a cation‐deficient Th₃P₄‐type structure (Ce₂S₃ type) according to Ce_2.667□_0.333Se₄ (Z = 4) or with Z = 5.333 for the empirical formula Ce₂Se₃. Here, Ce³⁺ is coordinated by eight Se^2— anions trigon‐dodecahedrally. In U‐Gd₂Se₃ (U₂S₃ type) two crystallographically independent Gd³⁺ cations with coordination numbers of 7 (Gd1) and 7+1 (Gd2), respectively, are present, exhibiting mono‐ or bicapped trigonal prisms as coordination polyhedra. The crystal structure of Z‐Lu₂Se₃ (Sc₂S₃ type) shows two different Lu³⁺ cations as well, which now both reside in octahedral coordination of six Se^2— anions each.     

Microarray-based in vitro evaluation of DNA oligomer libraries designed in silico.

We report on the microarray-based in vitro evaluation of two libraries of DNA oligonucleotide sequences, designed in silico for applications in supramolecular self-assembly, such as DNA computing and DNA-based nanosciences. In this first study which is devoted to the comparison of sequence motif properties theoretically predicted with their performance in real-life, the DNA-directed immobilization (DDI) of proteins was used as an example of DNA-based self-assembly. Since DDI technologies, DNA computing, and DNA nanoconstruction essentially depend on similar prereguisites, in particular, large and uniform hybridization efficiencies combined with low nonspecific cross-reactivity between individual sequences, we anticipate that the microarray approach demonstrated here will enable rapid evaluation of other DNA sequence libraries.     

Application of the essential work of fracture concept to nanostructured polymer materials

The first part of the paper deals with a critical discussion of the methodical basis of essential work of fracture (EWF) concept with respect to the specimen geometry (especially the notch depth) and application to polymers. In the second part, an in situ testing device, which combines a tensile testing machine with an optical strain-field measuring system, has successfully demonstrated possibility of characterization of fracture behaviour of polystyrene-polybutadiene block copolymers and block copolymer/homopolymer blends as examples of nanostructured polymer materials. It has been shown that knowledge of the time evolution of the strain field close to the crack tips leads to a simple verification of the basic precondition for the applicability of the EWF concept, the precondition “plastic zone coalescence-before-stable crack propagation”.     

Adaptive approach for nonlinear sensitivity analysis of reaction kinetics

We present a unified approach for linear and nonlinear sensitivity analysis for models of reaction kinetics that are stated in terms of systems of ordinary differential equations (ODEs). The approach is based on the reformulation of the ODE problem as a density transport problem described by a Fokker-Planck equation. The resulting multidimensional partial differential equation is herein solved by extending the TRAIL algorithm originally introduced by Horenko and Weiser in the context of molecular dynamics (J. Comp. Chem. 2003, 24, 1921) and discussed it in comparison with Monte Carlo techniques. The extended TRAIL approach is fully adaptive and easily allows to study the influence of nonlinear dynamical effects. We illustrate the scheme in application to an enzyme-substrate model problem for sensitivity analysis w.r.t. to initial concentrations and parameter values.     

Dynamic light-scattering analysis of the electrostatic interaction of hexahistidine-tagged cytochrome P450 enzyme with semiconductor quantum dots.

Currently, there is great interest in the development of methods suitable for determining the stoichiometry of biomolecules attached to nanoparticles. We describe the use of the dynamic light-scattering technique (DLS) to determine the stoichiometry of the protein cytochrome P450(BSbeta) attached to CdS and CdSe quantum dots (QDs). The enzyme-conjugated QDs have different diffusion characteristics compared to the QD and enzyme precursors, expressed in their size, scattering intensity as well as zeta-potential values. The significant enhancement of the scattering intensity of QDs observed upon conjugation with the P450(BSbeta) due to the refractive-index increment and the systematic variation in zeta potential resulting from charge neutralization of the anionic QDs by the cationic histidine-tagged P450(BSbeta) have been used for stoichiometry determination.