Morse Theory and Central Configurations in the Spatial N-body Problem

In the spirit of Palmore and Pacella, Morse Theory is used to obtain a lower bound for the number of central configurations in the spatial N-body problem. The homology of the configuration ellipsoid with the collision and collinear manifolds removed and the SO(3) symmetry quotiented out is calculated. As intermediate steps, homology calculations are carried out for several additional manifolds naturally arising in the N-body problem.     

Theoretical approach to reactions of polyatomic molecules

A scheme for systematic reduction of the theoretical treatment of elementary reactions involving polyatomic molecules is described; it consists of (1) limitation to the energetically relevant regions of the nuclear configuration space (the reaction path and its near environs) and (2) restriction to the dynamically relevant subspace of the nuclear configuration space (the active modes). Starting from a generalized reaction path Hamiltonian of Nauts and Chapuisat allowing for the use of arbitrary curvilinear coordinates and several large-amplitude modes, the realization of the above-sketched scheme is discussed. A compilation of recent work along these lines, mostly based on the simplified Miller-Handy-Adams reaction path Hamiltonian, is given with particular emphasis on applications of a statistical adiabatic model.     

The effect of sample salt additives on capillary electrophoresis analysis of intact proteins using surface modified capillaries

The effect of adding alkali salts to protein samples for capillary electrophoretic (CE) analysis of intact proteins was studied. A high degree of peak stacking, even for large proteins, was found to occur when alkali salts were added to the sample. The addition of salt to the protein sample promotes a strong improvement in the peak efficiency of individual proteins giving up to 2.1 × 10⁶ apparent plates/m. The concentration of salt required in the sample to reach optimal peak efficiency show dependency on both the molecular weight and molar concentration of the protein. However, adding salt will, at a sufficiently high concentration, cause a mixture of proteins to co-migrate to one very sharp peak. The observed sample stacking effect was obtained with a number of different surface modified silica capillaries indicating a general phenomenon and not surface coating specific.     

Path coupling using stopping times and counting independent sets and colorings in hypergraphs

We analyse the mixing time of Markov chains using path coupling with stopping times. We apply this approach to two hypergraph problems. We show that the Glauber dynamics for independent sets in a hypergraph mixes rapidly as long as the maximum degree Δ of a vertex and the minimum size m of an edge satisfy m ≥ 2Δ + 1. We also show that the Glauber dynamics for proper q‐colorings of a hypergraph mixes rapidly if m ≥ 4 and q > Δ, and if m = 3 and q ≥ 1.65Δ. We give related results on the hardness of exact and approximate counting for both problems. © 2008 Wiley Periodicals, Inc. Random Struct. Alg., 2008     

Adsorption of polyallylamine to lignocellulosic fibres: effect of adsorption conditions on localisation of adsorbed polyelectrolyte and mechanical properties of resulting paper sheets

Cationic polyallylamine (PAH), was adsorbed onto lignocellulosic fibres, and a fluorescent label on the polyelectrolyte enabled its location to be shown by confocal fluorescence microscopy. The adsorption time and ionic strength were varied to study their effect on the localisation of the adsorbed PAH. The microscopy showed that a long adsorption time, 24 h, and a high ionic strength, 10⁻¹ M NaCl + 5 × 10⁻³ M NaHCO₃ or higher, resulted in the adsorption of polyallylamine throughout the fibre walls. Shorter adsorption times and/or lower ionic strength resulted in adsorption only to the fibre exterior. By preparing sheets from fibres with polyelectrolyte adsorbed either to the exterior parts or into the fibre cell wall and testing their mechanical behaviour, a link was established between the localisation of adsorbed polyelectrolyte and the mechanical properties. Adsorption to the fibre exterior led to an increase in tensile strength and strain at break. The creep deformation at 90%RH was also slightly reduced by the adsorption of low molecular weight PAH (15 kDa). When polyallylamine was adsorbed throughout the wall of the lignocellulosic fibres, the mechanical properties were not however improved and the creep deformation at 90%RH actually increased somewhat.