Conditional moment closure for chemical reactions in laminar chaotic flows

We implement conditional moment closure (CMC) for simulation of chemical reactions in laminar chaotic flows. The CMC approach predicts the expected concentration of reactive species, conditional upon the concentration of a corresponding nonreactive scalar. Closure is obtained by neglecting the difference between the local concentration of the reactive scalar and its conditional average. We first use a Monte Carlo method to calculate the evolution of the moments of a conserved scalar; we then reconstruct the corresponding probability density function and dissipation rate. Finally, the concentrations of the reactive scalars are determined. The results are compared (and show excellent agreement) with full numerical simulations of the reaction processes in a chaotic laminar flow. This is a preprint of an article published in AlChE Journal copyright (2007) American Institute of Chemical Engineers: http://www3.interscience.wiley.com/

Home based exercise programme for knee pain and knee osteoarthritis: randomised controlled trial

Objectives To determine whether a home based exercise programme can improve outcomes in patients with knee pain. Design Pragmatic, factorial randomised controlled trial of two years' duration. Setting Two general practices in Nottingham. Participants 786 men and women aged >45 years with self reported knee pain. Interventions Participants were randomised to four groups to receive exercise therapy, monthly telephone contact, exercise therapy plus telephone contact, or no intervention. Patients in the no intervention and combined exercise and telephone groups were randomised to receive or not receive a placebo health food tablet. Main outcome measures Primary outcome was self reported score for knee pain on the Western Ontario and McMaster universities (WOMAC) osteoarthritis index at two years. Secondary outcomes included knee specific physical function and stiffness (scored on WOMAC index), general physical function (scored on SF­36 questionnaire), psychological outlook (scored on hospital anxiety and depression scale), and isometric muscle strength. Results 600 (76.3%) participants completed the study. At 24 months, highly significant reductions in knee pain were apparent for the pooled exercise groups compared with the non­exercise groups (mean difference –0.82, 95% confidence interval –1.3 to –0.3). Similar improvements were observed at 6, 12, and 18 months. Regular telephone contact alone did not reduce pain. The reduction in pain was greater the closer patients adhered to the exercise plan. Conclusions A simple home based exercise programme can significantly reduce knee pain. The lack of improvement in patients who received only telephone contact suggests that improvements are not just due to psychosocial effects because of contact with the therapist.