Discontinuous travelling wave solutions for certain hyperbolic systems

In an earlier paper on a malignant cell invasion model (Marchantet al., SIAM J. Appl. Math, 60, 2000) we introduced a novelform of discontinuous travelling wave solution. These solutionscould be studied easily by combining behaviour within a phaseplane with the Rankine–Hugoniot shock conditions, whichdescribe properties (such as the ratio of the jump discontinuitiesto the speed of propagation) that solutions may possess. Theseresults were new for several reasons. The shock conditions relateto hyperbolic equations (which the model is) but were appliedin a travelling wave ordinary differential equation phase planeusing techniques that usually apply to parabolic reaction–diffusionsystems. In addition the solutions possess singular behaviournear several points in the phase plane but in spite of thisthere exists a robust and stable family of physically interestingsolutions. In this paper we discuss two previously studied models, oneof detonation theory and one of angiogenesis. We show that eachof these models also possesses a family of discontinuous travellingwave solutions which was not previously discovered. Of particularinterest is the solution which has a blunt interface at thefront of the invading profile. In all three models it is thissolution that is seen to stably evolve from physically relevantinitial data, and for physically relevant parameter values. This work confirms the robustness of these novel travellingwave solutions and their applicability to a wider range of mathematicalmodelling situations.     

Beyond nanosizing: an approach to shape analysis of fluorescent nanostructures by SMI-microscopy

Using spatially modulated illumination (SMI) light microscopy it is possible to measure the sizes of fluorescent structures that have an extension far below the conventional optical resolution limit (“subresolution size”). Presently, the sizes are determined as the object extension along the optical axis of the SMI microscope. For this, however, “a priori” assumptions on the fluorochrome distribution (“shape”) within the examined fluorescent structure have to be made. Usually it is assumed that the fluorochrome follows a Gauss-distribution or a spherical distribution. In this report we overcome the necessity to make an assumption on the shape of the fluorochrome distribution. We introduce two new experimentally obtained parameters which allow the determination of a shape measure to describe the spatial distribution of the fluorescent dye. This becomes possible by independent measurements with different excitation wavelengths. As an example, we present shape parameter measurements on individual fluorescent microspheres with a nominal geometrical diameter (“size”) of 190 nm. In the case investigated, the experimental shape correlated well with a homogeneous fluorochrome distribution (“spherical shape”) but not with a variety of other “shapes”.     

An efficient electrophilic N-amination utilizing in situ generated chloramine under phase transfer conditions

An efficient, one-pot, phase transfer N-amination technology was developed. The protocol utilizes chloramine, an inexpensive and safe electrophilic aminating agent potentially viable for commercial manufacturing.     

A critical review of the chemical kinetics of SF4, SF5, and S2F10 in the gas phase

The gas phase chemical kinetics of SF₄, SF₅, and S₂F₁₀ are reviewed with particular emphasis on relevance to the general problem of the dielectric breakdown of SF₆. Specific reaction systems treated are SF₄ + F₂, SF₅ + SF₅, and the pyrolysis of S₂F₁₀. Computer modeling calculations were carried out to arrive at the best estimates of rate parameters. Based on the results of these calculations, sets of recommended rate parameters are provided. The major discrepancies and problems in establishing the kinetic data base are described. Thermochemical consequences of different model calculations are given.     

Enumeration of inequivalent irreducible Goppa codes

We consider irreducible Goppa codes over F_q of length qⁿ defined by polynomials of degree r, where q is a prime power and n,r are arbitrary positive integers. We obtain an upper bound on the number of such codes.     

Trovacenchemie. 13 [1] Weg und Irrweg zu Di([5]trovacenyl)keton

Trovacene Chemistry. 13 [1] On Being Lead and Mislead in the Synthesis of Di([5]trovacenyl)ketone Di([5]trovacenyl)ketone ( 3¨ ) has been prepared from lithio‐[5]trovacene and dimethylcarbamoyl chloride and studied by X‐ray diffraction, cyclic voltammetry, magnetic susceptometry and EPR spectroscopy. Slight variation of the synthetic protocol affords an unusual trinuclear complex 5 ? that is also fully characterized. Spin‐spin exchange interaction is smaller in 3¨ than in 1,1‐di([5]trovacenylethene ( 2¨ ), which differs from 3¨ by a replacement of O for CH₂. The novel trinuclear complex 5 ? , however, displays exchange coupling very similar to that observed in 1‐methoxy‐2,5,6‐tri([5]trovacenyl)benzene ( 7 ? ). In both cases, an unsymmetrical triangular arrangement of S = 1/2 centers is encountered. These findings are discussed in terms of the nature of the respective spacers.     

Fabrication of material-independent morphology gradients for high-throughput applications

Gradient surfaces allow rapid, high-throughput investigations and systematic studies in many disparate fields, including biology, tribology and adhesion. We describe a novel method for the fabrication of material-independent morphology gradients, involving a two-step process of particle erosion followed by a chemical polishing procedure that preferentially removes features with a small radius of curvature as a function of time. Gradients are fabricated on aluminium surfaces, but they may be readily transferred to other materials via a replication technique, which allows for the production of identical roughness gradient samples with any chosen surface chemistry. The gradients have been characterized by means of scanning electron microscopy and optical profilometry. Standard roughness parameters (Ra, Rq, Rz, Sm and Sk) were calculated from optical profilometry data. The roughness has also been assessed over different wavelength windows by means of a fast Fourier transformation approach.