Stochastic coupled cluster theory

We describe a stochastic coupled cluster theory which represents excitation amplitudes as discrete excitors in the space of excitation amplitudes. Reexpressing the coupled cluster (CC) equations as the dynamics of excitors in this space, we show that a simple set of rules suffices to evolve a distribution of excitors to sample the CC solution and correctly evaluate the CC energy. These rules are not truncation specific and this method can calculate CC solutions to an arbitrary level of truncation. We present results of calculation on the neon atom, and nitrogen and water molecules showing the ability to recover both truncated and full CC results.     

A numerical method for the Benjamin-Ono equation

This paper is concerned with the numerical solution of the Cauchy problem for the Benjamin-Ono equationu _t +uu _x −Hu _xx =0, whereH denotes the Hilbert transform. Our numerical method first approximates this Cauchy problem by an initial-value problem for a corresponding 2L-periodic problem in the spatial variable, withL large. This periodic problem is then solved using the Crank-Nicolson approximation in time and finite difference approximations in space, treating the nonlinear term in a standard conservative fashion, and the Hilbert transform by a quadrature formula which may be computed efficiently using the Fast Fourier Transform.     

Maximum-Norm Estimates for Finite-Element Methods for a Strongly Damped Wave Equation

We return to earlier work in Larsson, Thomée, and Wahlbin, IMA J. Numer. Anal. 11 (1991), concerning the numerical solution of a homogeneous linear wave equation with strong damping, arising in viscoelasticity. In that work spatial discretization by finite elements and associated fully discrete methods were analyzed in L ₂-based norms. The analysis depended on the fact that the solution may be expressed in terms of an analytic semigroup. In the present work we combine this approach with recent results on discretization of parabolic problems to derive essentially optimal order error bounds in maximum-norm for piecewise linear finite elements combined with backward Euler and Crank–Nicolson time stepping methods. This revised version was published online in July 2006 with corrections to the Cover Date.     

Filiform corrosion of aluminium alloys after a phosphate treatment

The role on filiform corrosion (FFC), after an automotive painting process with a phosphate treatment, of the near surface deformed layer (NSDL) formed during mechanical processing on AA8006 aluminium alloys is investigated. Samples subjected to specific surface pretreatments are examined before and after different steps of the phosphating process in order to identify the characteristics of the NSDL that are responsible for the susceptibility to FFC. The thickness, the structure and the composition of this NSDL are determined by SEM, RBS, XPS and transmission electron microscopy. The presence of a 200‐nm thick NSDL which is not completely eliminated during the degreasing step of the phosphating process increases dramatically the FFC susceptibility of AA8006 aluminium alloys compared with beforehand etched samples. The influence of Pb and Mg segregation on top of the surface is found to be negligible whereas the specific microstructure of the NSDL characterised by nanograins with boundaries decorated by nano‐sized oxide intermetallic particles seems to play a major role on FFC. Copyright © 2014 John Wiley & Sons, Ltd.     

An Organic–Inorganic Hybrid Exhibiting Electrical Conduction and Single‐Ion Magnetism

The first three‐dimensional (3D) conductive single‐ion magnet (SIM), (TTF)₂[Co(pdms)₂] (TTF=tetrathiafulvalene and H₂pdms=1,2‐bis(methanesulfonamido)benzene), was electrochemically synthesised and investigated structurally, physically, and theoretically. The similar oxidation potentials of neutral TTF and the molecular precursor [HNEt₃]₂[M(pdms)₂] (M=Co, Zn) allow for multiple charge transfers (CTs) between the SIM donor [M(pdms)₂]^n? and the TTF^.+ acceptor, as well as an intradonor CT from the pdms ligand to Co ion upon electrocrystallisation. Usually TTF functions as a donor, whereas in our system TTF is both a donor and an accepter because of the similar oxidation potentials. Furthermore, the [M(pdms)₂]^n? donor and TTF^.+ acceptor are not segregated but strongly interact with each other, contrary to reported layered donor–acceptor electrical conductors. The strong intermolecular and intramolecular interactions, combined with CT, allow for relatively high electrical conductivity even down to very low temperatures. Furthermore, SIM behaviour with slow magnetic relaxation and opening of hysteresis loops was observed. (TTF)₂[Co(pdms)₂] ( 2‐Co ) is an excellent building block for preparing new conductive SIMs.     

Effect of Solvation on Chemical Reactions,I. Addition of a Single Water Molecule to the H− + H2O → OH− + H2 Reaction

The gas phase chemical reaction, H^? + H₂O → H₂ + OH, and the effect of an additional water molecule on the reaction, H^?(H₂O) + H₂O → H₂ + OH(H₂O), have been investigated. The optimal structures and energies of the reactants, products, two stable intermediates, and the transition state connecting the two intermediates have been determined. The additional water molecule does not affect the potential surface congruently: it destabilizes the H(H₂O) minimum, but stabilizes the H₂ ?OH minimum and the transition state connecting the two intermediates. However, it stabilizes the products more than the H₂ ?OH^? minimum. Finally, in line with the reduction in the barrier height, the transition state for the H(H₂0) to H₂ ?OH^? isomerization moves further along the reaction path.     

Metric ultraproducts of finite simple groups

Some new results on metric ultraproducts of finite simple groups are presented. Suppose that G is such a group, defined in terms of a non-principal ultrafilter ω   on N$\mathbb{N}$ and a sequence (G_i)_i∈N${(G_i)}_{i\in \mathbb{N}}$ of finite simple groups, and that G is neither finite nor a Chevalley group over an infinite field. Then G is isomorphic to an ultraproduct of alternating groups or to an ultraproduct of finite simple classical groups. The isomorphism type of G determines which of these two cases arises, and, in the latter case, the ω  -limit of the characteristics of the groups G_i$G_i$. Moreover, G is a complete path-connected group with respect to the natural metric on G.     

About the length of laws for finite groups

We prove new upper bounds of the form O(n/log(n)^2?ε ) for the length of laws that hold for all groups of size at most n — improving on previous results of Bou-Rabee and Kassabov–Matucci. The methods make use of the classification of finite simple groups. Stronger bounds are proved in case the groups are assumed to be nilpotent or solvable.     

Correlation between implantation defects and dopants in Fe-implanted SiC

SiC single crystals were implanted with Fe ions and the effects of implantation temperature, Fe concentration, and subsequent swift heavy ion irradiation on both dopant and damage depth distributions were evaluated by using RBS and channelling techniques. It is found that an increase of the implantation temperature above the threshold temperature for amorphization can lead to the formation of a broad layer (∼50 nm) containing a large concentration of implanted Fe atoms (∼2 at.%) but almost free of implantation defects. This particular configuration is likely due to dynamic annealing during implantation combined with defect annihilation at the surface. It is only observed when the implanted species concentration does not exceed a critical value (which lies between 2 and 5 at.% in the present system). Post-implantation swift heavy ion irradiation leads to a further decrease of the damage level, while the Fe distribution is not affected. The Fe substitutional fraction has been evaluated in the different tested conditions. A maximum value of ∼50% is found when implantation is performed at the temperature above that required to prevent amorphization (470 K in the present system). Swift-heavy ion irradiation seems to induce Fe atoms relocation at substitutional positions.