The numerical integration of relative equilibrium solutions. The nonlinear Schrodinger equation

We analyse different error propagation mechanisms for conservativeand nonconservative time-integrators of nonlinear Schrödingerequations. We use a geometric approach based on interpretingwaves as relative equilibria.     

Concerted and stepwise proton-coupled electron transfers in aquo/hydroxo complex couples in water: oxidative electrochemistry of [Os(II)(bpy)(2)(py)(OH(2))](2+)

Successive oxidation of transition metal(II) aqua complexes (M(II)OH(2) to M(III)OH) is a domain in which proton-coupled electron transfer reactions are extremely common. The mechanism of these PCET reactions-concerted or stepwise-is an important issue in the understanding and design of natural or artificial systems catalyzing the formation of dioxygen by four-electron oxidation of water. Concerted proton-coupled electron transfer from an aqua metal(II) to a hydroxo metal(III) complex requires the close proximity of a proton-accepting group with a pK value between those of the aqua complexes. Otherwise, stepwise electron-proton or proton-electron pathways involving high-energy intermediates are followed. Concerted proton-electron pathways involving water as proton-acceptor or proton-donor group are inefficient. Cyclic voltammetry of the title complex in buffered aqueous solution and re-examination of previous results for the same complex attached to an electrode surface are used to establish these conclusions, which provide a starting point on the route to higher degrees of oxidation, such as those involved in the catalysis of water oxidation.     

The order of filling transitions in acute wedges

Using a square-gradient density functional model we test the prediction that the filling transition for a fluid in a wedge geometry changes from continuous to first-order as the wedge becomes more acute. Our numerical findings confirm such a change of order, but the value of the tilt angle at which it occurs, α* ≈ 45°, is considerably smaller than the original theoretical prediction. We critically reassess this work, which was based on allowing for the self-interaction of the fluid interface, and argue that the interfacial curvature and effective wavevector dependent surface tension can further lower the predicted value of α*, in keeping with our numerical findings. Interfacial fluctuation effects, occurring beyond mean-field level, are also discussed using effective Hamiltonian theory and are shown to substantially increase the value of α*.     

3D short-range wetting and nonlocality

Analysis of a microscopic Landau-Ginzburg-Wilson model of 3D short-ranged wetting shows that correlation functions are characterized by two length scales, not one, as previously thought. This has a simple diagrammatic explanation using a nonlocal interfacial Hamiltonian and yields a thermodynamically consistent theory of wetting in keeping with exact sum rules. For critical wetting the second length serves to lower the cutoff in the spectrum of interfacial fluctuations determining the repulsion from the wall. We show how this corrects previous renormalization group predictions for fluctuation effects, based on local interfacial Hamiltonians. In particular, lowering the cutoff leads to a substantial reduction in the effective value of the wetting parameter and prevents the transition being driven first order. Quantitative comparison with Ising model simulation studies due to Binder, Landau, and co-workers is also made.