Adhesive DPO Parallelism for Monic Matches

This paper presents indispensable technical results of a general theory that will allow to systematically derive from a given reduction system a behavioral congruence that respects concurrency. The theory is developed in the setting of adhesive categories and is based on the work by Ehrig and König on borrowed contexts; the latter are an instance of relative pushouts, which have been proposed by Leifer and Milner. In order to lift the concurrency theory of dpo rewriting to borrowed contexts we will study the special case of dpo rewriting with monic matches in adhesive categories: more specifically we provide a generalized Butterfly Lemma together with a Local Church Rosser and Parallelism theorem.     

PDE methods in flow simulation post processing

Vector field visualization is an important topic in scientific visualization. The aim is to graphically represent field data in an intuitively understandable and precise way. Two novel methods are described which enable an easy perception of flow data. The texture transport method especially applies to timedependent velocity fields. Lagrangian coordinates are computed solving the corresponding linear transport equations numerically. Choosing an appropriate texture on the reference frame the coordinate mapping can be applied as a suitable texture mapping. Alternatively, the aligned diffusion methods serves as an appropriate scale space method for the visualization of complicated flow patterns. It is closely related to nonlinear diffusion methods in image analysis where images are smoothed while still retaining and enhancing edges. Here an initial noisy image is smoothed along streamlines, whereas the image is sharpened in the orthogonal direction. The two methods have in common that they are based on a continuous model and discretized only in the final implementational step. Therefore, many important properties are naturally established already in the continuous model. Received: 12 March 1999 / Accepted: 24 August 1999     

A Σ3 grain boundary in an epitaxial chalcopyrite film

We have grown epitaxial grain boundaries of CuGaSe₂ by metal organic vapour phase epitaxy onto a GaAs substrate containing a Σ3 grain boundary. SEM micrographs show a dense grain boundary. TEM micrographs prove that the grain boundary in the film is the direct continuation of the grain boundary in the substrate. HRTEM shows that the grain boundary in the film is a twin as well and thus a Σ3 boundary. Thus, by using a Σ3 grain boundary in the cubic GaAs substrate as a template a Σ3 grain boundary is obtained in the tetragonal CuGaSe₂ film. Kelvin Probe Force Microscopy gives no indication of a space charge around this grain boundary, while in Hall measurements a small barrier of a few 10 meV is evident. This is an experimental indication for the existence of neutral grain boundaries as predicted theoretically.     

The elastic rod model for DNA and its application to the tertiary structure of DNA minicircles in mononucleosomes

Explicit solutions to the equations of equilibrium in the theory of the elastic rod model for DNA are employed to develop a procedure for finding the configuration that minimizes the elastic energy of a minicircle in a mononucleosome with specified values of the minicircle size N in base pairs, the extent w of wrapping of DNA about the histone core particle, the helical repeat h(0)b of the bound DNA, and the linking number Lk of the minicircle. The procedure permits a determination of the set Y(N, w, h(0)b) of integral values of Lk for which the minimum energy configuration does not involve self-contact, and graphs of writhe versus w are presented for such values of Lk. For the range of N of interest here, 330 < N < 370, the set Y(N, w, h(0)b) is of primary importance: when Lk is not in Y(N, w, h(0)b), the configurations compatible with Lk have elastic energies high enough to preclude the occurrence of an observable concentration of topoisomer Lk in an equilibrium distribution of topoisomers. Equilibrium distributions of Lk, calculated by setting differences in the free energy of the extranucleosomal loop equal to differences in equilibrium elastic energy, are found to be very close to Gaussian when computed under the assumption that w is fixed, but far from Gaussian when it is assumed that w fluctuates between two values. The theoretical results given suggest a method by which one may calculate DNA-histone binding energies from measured equilibrium distributions of Lk.     

On detectability of stochastic systems

We discuss notions of detectability for stochastic linear control systems of Itô type. A natural concept of detectability requires a non-zero output, if the state process is unstable. We show that this property can equivalently be characterized by a generalized version of the Hautus-test. The proof is based on spectral theory for positive operators.     

Platinum Phosphinito Catalysts for Nitrile Hydration

The reaction of PEt₂OH with K₂PtCl₄ yields [PtCl{(PEt₂O)₂H}]₂ (2). The X-ray crystal structure of 2 shows that the two chloride ligands bridge the two Pt atoms. The structure is unusual in that the PtCl₂Pt unit is bent, which is the first example of a platinum phosphinito chloride-bridged dimer that is bent. Dimer 2 is a poor catalyst for the hydration of acetonitrile (and presumably other nitriles). Likewise, the monomeric catalyst that results from the reaction of 2 with sodium hydroxide is not a good hydration catalyst. In an attempt to form a more reactive monomeric catalyst, PtCl(PMe₂OH){(PMe₂O)₂H} (1) was reacted with sodium hydroxide. This reaction resulted in the formation of two species, tentatively characterized as Na[PtCl(PMe₂O){(PMe₂O)₂H}] (5) and Na[PtCl(OH){(PMe₂O)₂H}] (6). Complexes 5 and 6 could not be separated. However, the mixture of the two complexes quickly hydrated acetonitrile. The catalyst mixture of 5 and 6 was efficiently poisoned by cyanide, which prevented its use as a catalyst for the hydration of cyanohydrins.