The finite elastodynamics of hyperelastic thin tubes

A non-linear equation governing large amplitude oscillation in a thin hyperelastic tube is reduced for a four-parameter class of strain energy potentials to a canonical form amenable to exact solution via an extension of Pinney's theorem. The displacement field associated with both free oscillation and Heaviside loading problems are thereby solved explicitly. Results due to Shahinpoor and Nowinski for Mooney-Rivlin materials emerge as special cases of the present analysis.     

Conjugative and homoconjugative effects in 2-heterobicyclo[3.2.1]octa-3,6-dienes

The ¹H-NMR, ¹³C-NMR and photoelectron spectra of a variety of 2-heterobicyclo[3.2.1]octa-3,6-dienes 6 give evidence of conjugative and homoeonjugative effects in these compounds, but there is no suggestion from the data of any special contribution from the (4n+2)π neutral bishomoaromatic system. Reaction of the dienes6 with TCNE invariably yielded the product of [2+2] addition in cases where a fully characterisable product was obtained.     

Phase titrations-V: Nitroalkanes: Improving the phase-titration end-point

End-points for direct phase titrations of binary solutions of nitropropanes in water-miscible solvents are fair and, because of the steepness of the calibration curve, results are adequate. Nitroethane, in binary combination, gives poor end-points but, over part of the optimum titration range, results are good. Nitromethane gives end-points which are almost useless. Addition of standard amounts of nitrobenzene, which gives excellent phase-titration end-points, improves the composite nitromethane-nitrobenzene-water-miscible component end-point markedly. Because the nitrobenzene concentration is constant, the water titre is a function only of the nitromethane concentration. Addition of constant amounts of nitrobenzene also increases the optimum titration range. Results given for all systems are comparable in accuracy with systems previously reported which are favourable to direct phase titration.     

A new,accurate, statistical mechanical theory for simple fluids

A new integral equation in which the hypernetted chain and Percus-Yevick approximations are “mixed” as a function of interparticle separation is described. Calculations with fluids varying from hard spheres to the one-component plasma show good agreement with Monte Carlo calculations.     

Functional MRI and multivariate autoregressive models

Connectivity refers to the relationships that exist between different regions of the brain. In the context of functional magnetic resonance imaging (fMRI), it implies a quantifiable relationship between hemodynamic signals from different regions. One aspect of this relationship is the existence of small timing differences in the signals in different regions. Delays of 100 ms or less may be measured with fMRI, and these may reflect important aspects of the manner in which brain circuits respond as well as the overall functional organization of the brain. The multivariate autoregressive time series model has features to recommend it for measuring these delays and is straightforward to apply to hemodynamic data. In this review, we describe the current usage of the multivariate autoregressive model for fMRI, discuss the issues that arise when it is applied to hemodynamic time series and consider several extensions. Connectivity measures like Granger causality that are based on the autoregressive model do not always reflect true neuronal connectivity; however, we conclude that careful experimental design could make this methodology quite useful in extending the information obtainable using fMRI.