Fusion multiplicities as polytope volumes: -point and higher-genus su(2) fusion

We present the first polytope volume formulas for the multiplicities of affine fusion, the fusion in Wess–Zumino–Witten conformal field theories, for example. Thus, we characterise fusion multiplicities as discretised volumes of certain convex polytopes, and write them explicitly as multiple sums measuring those volumes. We focus on su(2), but discuss higher-point ( ) and higher-genus fusion in a general way. The method follows that of our previous work on tensor product multiplicities, and so is based on the concepts of generalised Berenstein–Zelevinsky diagrams, and virtual couplings. As a by-product, we also determine necessary and sufficient conditions for non-vanishing higher-point fusion multiplicities. In the limit of large level, these inequalities reduce to very simple non-vanishing conditions for the corresponding tensor product multiplicities. Finally, we find the minimum level at which the higher-point fusion and tensor product multiplicities coincide.     

X‐ray speckle visibility spectroscopy in the single‐photon limit

The technique of speckle visibility spectroscopy has been employed for the measurement of dynamics using coherent X‐ray scattering. It is shown that the X‐ray contrast within a single exposure can be related to the relaxation time of the intermediate scattering function, and this methodology is applied to the diffusion of 72 nm‐radius latex spheres in glycerol. Data were collected with exposure times as short as 2 ms by employing a resonant shutter. The weak scattering present for short exposures necessitated an analysis formalism based on the spatial correlation function of individual photon charge droplets on an area detector, rather than the usual methods employed for intensity correlations. It is demonstrated that this method gives good agreement between theory and experiment and thus holds promise for extending area‐detector‐based coherent scattering methods to the study of faster dynamics than previously obtainable.     

Multiscale modeling of submonolayer growth for Fe/Mo (110)

We use a multiscale approach to study a lattice-gas model of submonolayer growth of Fe/Mo (110) by Molecular Beam Epitaxy. To begin with, we construct a two-dimensional lattice-gas model of the Fe/Mo (110) system based on our first-principles calculations of the monomer diffusion barrier and adatom-adatom interactions. The model is investigated by equilibrium Monte Carlo (MC) simulations to compute the diffusion coefficients of Fe islands of different sizes. These diffusion coefficients are used as input to the coarse-grained kinetic rate equation (KRE) approach. We also evaluate effects of the range of Fe-Fe interaction, restriction of interaction to third nearest neighbors allowed to develop feasible atomistic kinetic Monte Carlo (KMC) model. We calculate time evolution of the island size distributions by both KMC and KRE methods and find good agreement between the two methods.     

Dynamic polarizability,dispersion coefficient C6 and dispersion energy in the effective fragment potential method

The development of a fragment–fragment dispersion energy expression, for the general effective fragment potential (EFP2) method is presented. C₆ dispersion coefficients, expressed in terms of the dynamic polarizabilties over the imaginary frequency range (α(iν)), were calculated for a set of homo and hetero dimers. Using these coefficients the dispersion energy has been calculated. The dispersion energy is expressed using a simple London series expansion terminated after the n=6 term and implemented using distributed localized molecular orbitals (LMOs). The EFP2 dispersion energy is compared to symmetry adapted perturbation theory (SAPT) values. From this comparison, it is apparent that one needs to include higher order terms in the dispersion energy. Adding an estimated C₈ term to the C₆ energy greatly improves the agreement with the benchmark SAPT energies.     

High spatial and angular resolution diffusion-weighted imaging reveals forniceal damage related to memory impairment

Introduction

Diffusion tensor imaging (DTI) measures in patients with multiple sclerosis (MS), particularly those measures associated with a specific white matter pathway, have consistently shown correlations with function. This study sought to investigate correlations between DTI measures in the fornix and common cognitive deficits in MS patients, including episodic memory, working memory and attention.

Materials and Methods

Patients with MS and group age- and sex-matched controls underwent high-resolution diffusion scanning (1-mm isotropic voxels) and cognitive testing. Manually drawn forniceal regions of interest were applied to individual maps of tensor-derived measures, and mean values of transverse diffusivity (TD), mean diffusivity (MD), longitudinal diffusivity (LD) and fractional anisotropy (FA) were calculated.

Results

In 40 patients with MS [mean age±S.D.= 42.55±9.1 years; Expanded Disability Status Scale (EDSS)=2.0±1.2; Multiple Sclerosis Functional Composite (MSFC) score=0.38±0.46] and 20 healthy controls (mean age±S.D.= 41.35±9.7 years; EDSS=0.0±0; MSFC score=0.74±0.24), we found that FA, MD and TD values in the fornix were significantly different between groups (P< .03), and patient performance on the Brief Visuospatial Memory Test-Revised (BVMT-R) was correlated with DTI measures (P< .03).

Discussion

These results are consistent with findings of axonal degeneration in MS and support the use of DTI as an indicator of disease progression.     

Relationship between experimental pKa values in aqueous solution and a gas phase bond length in bicyclo[2.2.2]octane and cubane carboxylic acids

Linear correlations were established between the calculated bond lengths and the pK_a or σ_I values for a series of 4‐substituted bicyclo[2.2.2]octane‐1‐carboxylic acid and 4‐cubane‐1‐carboxylic acid derivatives. The bond lengths have been calculated at a modest computational level, HF/6‐31G(d), both in the gas phase and with the continuum solvation model, polarisable continuum model (PCM). In general, the best correlations are obtained when the PCM model is taken into account, especially when neutral and charged molecules are considered together. The best models in each case show square correlation coefficients (R²) larger than 0.9 and indicate that they can be used as predictive tools. These results expand previous results that indicate the possibility of a relationship between gas phase bond length and pK_a values in aqueous solution and indicate that such relationships are more general than hitherto expected. Copyright © 2013 John Wiley & Sons, Ltd.