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.     

Chromatographic method for diaminopimelic acid detection in calcareous rocks. Presence of a bacterial biomarker in stromatolites

The presence in the environment of diaminopimelic acid (DAP), a specific eubacterial marker, can be attributed to that of bacteria. We report a reliable and highly sensitive method for the quantification of DAP in calcareous rocks. It consists of acid hydrolysis of rock powder, purification of DAP by chromatography on Dowex 50W and Spherogel AA-NA+ columns, and quantitative analysis by high-performance liquid chromatography. Addition of tritiated DAP, the internal standard, allows one to follow the relevant fractions throughout the purification procedure and to determine their yield. The analytical step consists in pre-column derivatization with ortho-phthaldialdehyde of purified samples, and separation through a reversed-phase C18 column. Chemical controls, i.e., oxidation of samples to rule out the presence of co-eluting lanthionine and cystathionine, as well as mass spectrometry, confirm the presence of DAP in analyzed samples. Our method allows the separation of meso- from L- and/or D-stereoisomers of DAP, and reveals their presence in the examined rocks, two stromatolites of different age and geographic origin.     

1,1,3,3-Tetramethylguanidine-gallane, (Me2N)2CN(H).GaH3: an unusually strongly bound gallane adduct

The novel adduct 1,1,3,3-tetramethylguanidine-gallane, (Me2N)2CN(H).GaH3, has been prepared by the reaction of [(Me2N)2CNH2]+Cl- with LiGaH4 in Et2O solution. Its spectroscopic properties indicate a monomeric species with an unusually strong coordinate link between the imido function and GaH3, an inference confirmed by the crystal structure at 150 K which also reveals significant secondary interactions through non-classical N-H...H-Ga bridges. Despite the intrinsic strength of the Ga-N bond, however, vaporisation at ca. 310 K occurs with partial dissociation, and decomposition via more than one pathway proceeds at temperatures >330-350 K to give a variety of products, including the free base, Me2NH, H2, and a novel gallium-nitrogen compound composed of a Ga4N4 cubane-like core bridged on three edges by -N{C(NMe2)2}GaH2- units.     

Knowledge-Based Expert Systems for Toxicity and Metabolism Prediction: DEREK,StAR and METEOR

Abstract

It has long been recognised that the ability to predict the metabolic fate of a chemical substance and the potential toxicity of either the parent compound or its metabolites are important in novel drug design. The popularity of using computer models as an aid in this area has grown considerably in recent years.

LHASA Limited has been developing knowledge-based expert systems for toxicity and metabolism prediction in collaboration with industry and regulatory authorities. These systems, DEREK, StAR and METEOR, use rules to describe the relationship between chemical structure and either toxicity in the case of DEREK and StAR, or metabolic fate in the case of METEOR.

The rule refinement process for DEREK often involves assessing the predictions for a novel set of compounds and comparing them to their biological assay results as a measure of the system's performance. For example, 266 non-congeneric chemicals from the National Toxicology Program database have been processed through the DEREK mutagenicity knowledge base and the predictions compared to their Salmonella typhimurium mutagenicity data. Initially, 81 of 114 mutagens (71%) and 117 of 152 non-mutagens (77%) were correctly identified. Following further knowledge base development, the number of correctly identified mutagens has increased to 96 (84%). Further work on improving the predictive capabilities of DEREK, StAR and METEOR is in progress.     

Evolution of Higher-Order Gray Hirota Solitary Waves

The defocusing Hirota equation has dark and gray soliton solutions which are stable on a background of periodic waves of constant amplitude. In this paper, gray solitary wave evolution for a higher-order defocusing Hirota equation is examined. A direct analysis is used to identify families of higher-order gray Hirota solitary waves, which are embedded for certain parameter values. Soliton perturbation theory is used to determine the detailed behavior of an evolving higher-order gray Hirota solitary wave. An integral expression for the first-order correction to the wave is found and analytical expressions for the steady-state and transient components of the solitary wave tail are derived. A subtle and complex picture of the development of solitary wave tails emerges. It is found that solitary wave tails develop for two reasons, one is decay of the solitary wave caused by resonance, the second is corrections at first-order to the background wave. Strong agreement is found between the theoretical predictions of the perturbation theory and numerical solutions of the governing equations.