Angular Conditions,Relations between Breit and Light-Front Frames, and Subleading Power Corrections

We analyze the current matrix elements in the general collinear (Breit) frames and find the relation between the ordinary (or canonical) helicity amplitudes and the light-front helicity amplitudes. Using the conservation of angular momentum, we derive a general angular condition which should be satisfied by the light-front helicity amplitudes for any spin system. In addition, we obtain the light-front parity and time-reversal relations for the light-front helicity amplitudes. Applying these relations to the spin-1 form factor analysis, we note that the general angular condition relating the five helicity amplitudes is reduced to the usual angular condition relating the four helicity amplitudes due to the light-front time-reversal condition. We make some comments on the consequences of the angular condition for the analysis of the high-$Q^2$ deuteron electromagnetic form factors, and we further apply the general angular condition to the electromagnetic transition between spin-1/2 and spin-3/2 systems and find a relation useful for the analysis of the N-$\Delta$ transition form factors. We also discuss the scaling law and the subleading power corrections in the Breit and light-front frames.Comment: 24 pages,2 figure

Neutron and X-ray diffraction and empirical potential structure refinement modelling of magnesium stabilised amorphous calcium carbonate

Amorphous calcium carbonate (ACC) plays a key role in biomineralisation processes in sea organisms. Neutron and X-ray diffraction have been performed for a sample of magnesium-stabilised ACC, which was prepared with a Mg:Ca ratio of 0.05:1 and 0.25 HO molecules per molecule of CO. The empirical potential structure refinement method has been used to make a model of magnesium-stabilised ACC and the results revealed a fair agreement with the experimental diffraction data. The model has well-defined CO and HO molecules. The average coordination number of Ca is 7.4 and is composed of 6.8 oxygen atoms from CO molecules and 0.6 oxygen atoms from HO molecules. The average CaO bond length is 2.40 Å. The distribution of Ca in the model is homogeneous with a uniformly distributed Ca-rich network and no evidence of the Ca-poor channels as previously reported for a reverse Monte Carlo model of ACC

Redox-Active Bis(phenolate) N-Heterocyclic Carbene [OCO] Pincer Ligands Support Cobalt Electron Transfer Series Spanning Four Oxidation States

A new family of low-coordinate Co complexes supported by three redox-noninnocent tridentate [OCO] pincer-type bis(phenolate) N-heterocyclic carbene (NHC) ligands are described. Combined experimental and computational data suggest that the charge-neutral four-coordinate complexes are best formulated as Co(II) centers bound to closed-shell [OCO]2– dianions, of the general formula [(OCO)CoIIL] (where L is a solvent-derived MeCN or THF). Cyclic voltammograms of the [(OCO)CoIIL] complexes reveal three oxidations accessible at potentials below 1.2 V vs Fc+/Fc, corresponding to generation of formally Co(V) species, but the true physical/spectroscopic oxidation states are much lower. Chemical oxidations afford the mono- and dications of the imidazoline NHC-derived complex, which were examined by computational and magnetic and spectroscopic methods, including single-crystal X-ray diffraction. The metal and ligand oxidation states of the monocationic complex are ambiguous; data are consistent with formulation as either [(SOCO)CoIII(THF)2]+ containing a closed-shell [SOCO]2– diphenolate ligand bound to a S = 1 Co(III) center, or [(SOCO•)CoII(THF)2]+ with a low-spin Co(II) ion ferromagnetically coupled to monoanionic [SOCO•]− containing a single unpaired electron distributed across the [OCO] framework. The dication is best described as [(SOCO0)CoII(THF)3]2+, with a single unpaired electron localized on the d7 Co(II) center and a doubly oxidized, charge-neutral, closed-shell SOCO0 ligand. The combined data provide for the first time unequivocal and structural evidence for [OCO] ligand redox activity. Notably, varying the degree of unsaturation in the NHC backbone shifts the ligand-based oxidation potentials by up to 400 mV. The possible chemical origins of this unexpected shift, along with the potential utility of the [OCO] pincer ligands for base-metal-mediated organometallic coupling catalysis, are discussed

Determination of crop dynamic and aerodynamic parameters for lodging prediction

This paper considers a process through which the wind costs the agricultural industry hundreds of millions of pounds per year - crop lodging. Lodging is the displacement of crops by wind (and rain) that can result in either stem breakage or uprooting. In particular this paper builds upon recent work to develop a generalised model of the lodging process and presents the results of several experimental campaigns to identify dynamic and aerodynamic parameters that are required as inputs to the model in order to estimate lodging wind speeds. These experiments were carried out at various sites in the UK and the Republic of Ireland to determine the natural frequencies, damping ratios and drag areas of maize, oats and oil seed rape. The experimental methodology, which was based upon the tracking of plant displacements, was shown to be robust, and consistent values of the parameters were obtained, albeit with much larger experimental uncertainties than would normally be expected in wind engineering applications. The values of these parameters were also consistent with those of earlier measurements for wheat. The generalised model was then used to determine lodging wind speeds for the three crops, and an assessment was made of the effect of experimental uncertainties in dynamic, aerodynamic and agronomic variables on the predicted values. In broad terms the generalised lodging model was shown to well describe the crop behaviour for isolated crops, and it was shown that it could be used in a simplified form for interlocked crop canopies. It was also shown that uncertainties in the aerodynamic parameters resulted in uncertainties of around an order of magnitude in lodging risk, whilst typical variations between plants in some crop parameters (notably stem strength and radius) could result in lodging risk uncertainties of two orders of magnitude