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.     

Correction to: Moyennes effectives de fonctions multiplicatives complexes

The Ramanujan Journal - The original version of the article unfortunately contained a number of inaccuracies in equations and statement which however do not essentially scrutinize the validity of...     

A one-dimensional model with phase transition

Two repellent particles are bound to occupy two among thek _n +1 adjacent sites 0=x ₀ ⁽ⁿ⁾ <x ₁ ⁽ⁿ⁾ <...<x _kn ⁽ⁿ⁾ =1, sayx _q ⁽ⁿ⁾ ,x _q+1 ⁽ⁿ⁾ . Define the Hamiltonian _q ⁽ⁿ⁾ =–ln(x _q+1 ⁽ⁿ⁾ –x _q ⁽ⁿ⁾ ) and the partition function     

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.     

A spark chamber measurement of the reactions π + p → ϱ + p at 15 GeV/c

A new method, using spark chambers, for the study of the reactions π^± + p → ?^± + p is described. The charged pion and both γ rays from the π^± decay are detected. Differential and integrated cross sections σ_π⁺=50 ± 9 μb, σ_π⁻=47 ± 9 μb) for 0.0 ?|t|?1. (GeV/c)² and a laboratory momentum (p_Lab) of 15 GeV/c are presented. The momentum dependence of σ_γ^± is well fitted from 2.7 to 16 GeV/c by σ = Kp_Lab⁻ with n_γ⁺ = 1.80 ± 0.80 and n_γ⁻ = 1.87 ± 0.15.