Coxeter complexes and graph-associahedra

Given a graph Γ, we construct a simple, convex polytope, dubbed graph-associahedra, whose face poset is based on the connected subgraphs of Γ. This provides a natural generalization of the Stasheff associahedron and the Bott-Taubes cyclohedron. Moreover, we show that for any simplicial Coxeter system, the minimal blow-ups of its associated Coxeter complex has a tiling by graph-associahedra. The geometric and combinatorial properties of the complex as well as of the polyhedra are given. These spaces are natural generalizations of the Deligne-Knudsen-Mumford compactification of the real moduli space of curves.     

Study of the peak effect phenomenon in single crystals of 2H-NbSe2

The weakly pinned single crystals of the hexagonal 2H-NbSe₂ compound have emerged as prototypes for determining and characterizing the phase boundaries of the possible order-disorder transformations in the vortex matter. We present here a status report based on the ac and dc magnetization measurements of the peak effect phenomenon in three crystals of 2H-NbSe₂, in which the critical current densities vary over two orders of magnitude. We sketch the generic vortex phase diagram of a weakly pinned superconductor, which also utilizes theoretical proposals. We also establish the connection between the metastability effects and pinning.     

Scanning tunnelling microscopic images of the surface ordering of the liquid crystal 4-n-octyl-4'-cyanobiphenyl

Images of the surface ordering of 4-n-octyl-4'-cyanobiphenyl, a room temperature smectic liquid crystal deposited upon graphite, have been obtained by scanning tunnelling microscopy. The microscope was operated in air using the constant-current mode. Under certain tunnelling conditions it has been possible to resolve both the aliphatic and aromatic parts of the molecule, and to observe individual benzene rings. Two previously unreported conformations have been observed: an overlapping bilayer structure with spacing 3.7 nm, and a monolayer structure with spacing 2.4 nm. The latter structure may represent the first visual evidence for a surface polar ordered structure.     

Metastable patterns in solutions of ut = ϵ2uxx − f(u)

We consider the equation in question on the interval 0 ≦ x ≦ 1 having Neumann boundary conditions, with f(u) = F(u), where F is a double well energy density with equal minima at u = ±1. The only stable states of the system are patternless constant solutions. But given two-phase initial data, a pattern of interfacial layers typically forms far out of equilibrium. The ensuing nonlinear relaxation process is extremely slow: patterns persist for exponentially long times proportional to exp{A_±l/?, where A = F(±1) and l is the minimum distance between layers. Physically, a tiny potential jump across a layer drives its motion. We prove the existence and persistence of these metastable patterns, and characterise accurately the equations governing their motion. The point of view is reminiscent of center manifold theory: a manifold parametrising slowly evolving states is introduced, a neighbourhood is shown to be normally attracting, and the parallel flow is characterised to high relative accuracy. Proofs involve a detailed study of the Dirichlet problem, spectral gap analysis, and energy estimates.     

Photoionization of highly excited atomic sodium involving core-excited resonances

Resonant photoionization in thenl outer-shell of 2p ⁶ nl excited sodium is studied between 32.50 and 33.50 eV. Resonances are of the type 2p ⁶ nl → 2p ⁵ 3snl → 2p ⁶ ελ, i.e. corresponding to the excitation of a 2p core-electron to a 3s orbital. Experimental technique combines laser and synchrotron radiation for exciting sequentially sodium atoms. The main features of the resonances — energies and total oscillator strengths — are measured or estimated. From the results, one concludes that the valence electron is almost decoupled from the core, with respect to the core excitation.     

Derivatisation for liquid chromatography/electrospray mass spectrometry: synthesis of pyridinium compounds and their amine and carboxylic acid derivatives

A simple method has been developed for the pre-column derivatisation of low molecular weight primary and secondary amines and carboxylic acids using quaternary nitrogen compounds to enhance their detection by liquid chromatography/electrospray ionisation mass spectrometry (LC/ESI-MS). The synthesis of seven novel quaternary nitrogen reagents is described. The derivatives are designed to be relatively small molecules to avoid some of the steric hindrance problems that may be associated with larger derivatisation reagents. The compounds have amine and carboxylic acid functional groups with which to derivatise carboxylic acids and amines, respectively. Two of the compounds contain a bromine atom in order to assess the advantages of a bromine isotope pattern in the mass spectra. This acts as a simple marker for derivatisation and enables data processing by cluster analysis.Activation of the carboxylic acid group was achieved by the use of either 1-chloro-4-methylpyridinium iodide (CMPI) or the more reactive 1-fluoro-4-methylpyridinium p-toluenesulphonate (FMP).1 Using both of these active reagents, the degree of nucleophilic substitution was investigated for the derivatisation of a variety of small molecules. Whilst giving some increase in the ESI-MS response for the derivatised compounds, the FMP itself acted as a derivatising reagent in a competing reaction. In the light of this finding, FMP was reacted with the test compounds separately and gave positive results as a derivatising reagent. Detection of the 'pre-charged' derivatives of amines and carboxylic acids by LC/ESI-MS was investigated with respect to their ESI response and chromatography.