Approach to chaos in ultracold atomic and molecular physics: Statistics of near-threshold bound states for Li+CaH and Li+CaF

We calculate near-threshold bound states and Feshbach resonance positions for atom–rigid-rotor models of the highly anisotropic systems Li+CaH and Li+CaF. We perform statistical analysis on the resonance positions to compare with the predictions of random matrix theory. For Li+CaH with total angular momentum J=0 we find fully chaotic behavior in both the nearest-neighbor spacing distribution and the level number variance. However, for J>0 we find different behavior due to the presence of a nearly conserved quantum number. Li+CaF (J=0) also shows apparently reduced levels of chaotic behavior despite its stronger effective coupling. This may indicate the development of another good quantum number relating to a bending motion of the complex. However, continuously varying the rotational constant over a wide range shows unexpected structure in the degree of chaotic behavior, including a dramatic reduction around the rotational constant of CaF. This demonstrates the complexity of the relationship between coupling and chaotic behavior.

SYSTEMATIC REVIEW AND META-ANALYSIS: EFFECTS OF WALKING EXERCISE IN CHRONIC MUSCULOSKELETAL PAIN

SYSTEMATIC REVIEW AND META-ANALYSIS: EFFECTS OF WALKING EXERCISE IN CHRONIC MUSCULOSKELETAL PAIN O'Connor S.R.1, Tully M.A.2, Ryan B.3, Baxter D.G.3, Bradley J.M.1, McDonough S.M.11University of Ulster, Health & Rehabilitation Sciences Research Institute, Newtownabbey, United Kingdom, 2Queen's University, UKCRC Centre of Excellence for Public Health (NI), Belfast, United Kingdom, 3University of Otago, Centre for Physiotherapy Research, Dunedin, New ZealandPurpose: To examine the effects of walking exercise on pain and self-reported function in adults with chronic musculoskeletal pain.Relevance: Chronic musculoskeletal pain is a major cause of morbidity, exerting a substantial influence on long-term health status and overall quality of life. Current treatment recommendations advocate various aerobic exercise interventions for such conditions. Walking may represent an ideal form of exercise due to its relatively low impact. However, there is currently limited evidence for its effectiveness.Participants: Not applicable.Methods: A comprehensive search strategy was undertaken by two independent reviewers according to the preferred reporting items for systematic reviews and meta-analyses (PRISMA) and the recommendations of the Cochrane Musculoskeletal Review Group. Six electronic databases (Medline, CINAHL, PsychINFO, PEDro, Sport DISCUS and the Cochrane Central Register of Controlled Trials) were searched for relevant papers published up to January 2010 using MeSH terms. All randomised or non-randomised studies published in full were considered for inclusion. Studies were required to include adults aged 18 years or over with a diagnosis of chronic low back pain, osteoarthritis or fibromyalgia. Studies were excluded if they involved peri-operative or post-operative interventions or did not include a comparative, non exercise or non-walking exercise control group. The U.S. Preventative Services Task Force system was used to assess methodological quality. Data for pain and self-reported function were extracted and converted to a score out of 100.Analysis: Data were pooled and analyzed using RevMan (v.5.0.24). Statistical heterogeneity was assessed using the X2 and I2 test statistics. A random effects model was used to calculate the mean differences and 95% CIs. Data were analyzed by length of final follow-up which was categorized as short (≤8 weeks post randomisation), mid (2-12 months) or long-term (>12 months).Results: A total of 4324 articles were identified and twenty studies (1852 participants) meeting the inclusion criteria were included in the review. Overall, studies were judged to be of at least fair methodological quality. The most common sources of likely bias were identified as lack of concealed allocation and failure to adequately address incomplete data. Data from 12 studies were suitable for meta-analysis. Walking led to reductions in pain at short (<8 weeks post randomisation) (-8.44 [-14.54, -2.33]) and mid-term (>8 weeks - 12 month) follow-up (-9.28 [-16.34, -2.22]). No effect was observed for long-term (>12 month) data (-2.49 [-7.62, 2.65]). For function, between group differences were observed for short (-11.57 [-16.06, -7.08]) and mid-term data (-13.26 [-16.91, -9.62]). A smaller effect was also observed at long-term follow-up (-5.60 [-7.70, -3.50]).Conclusions: Walking interventions were associated with statistically significant improvements in pain and function at short and mid-term follow-up. Long-term data were limited but indicated that these effects do not appear to be maintained beyond twelve months.Implications: Walking may be an effective form of exercise for individuals with chronic musculoskeletal pain. However, further research is required which examines longer term follow-up and dose-response issues in this population.Key-words: 1. Walking exercise 2. Musculoskeletal pain 3. Systematic reviewFunding acknowledgements: Department of Employment and Learning, Northern Ireland.Ethics approval: Not applicable.

On the statistics of transverse permeability of randomly distributed fibers

An RVE–based stochastic numerical model is used to calculate the permeability of randomly generated porous media at different values of the fiber volume fraction for the case of transverse flow in a unidirectional ply. Analysis of the numerical results shows that the permeability is not normally distributed. With the aim of proposing a new understanding on this particular topic, permeability data are fitted using both a mixture model and a unimodal distribution. Our findings suggest that permeability can be fitted well using a mixture model based on the lognormal and power law distributions. In case of a unimodal distribution, it is found, using the maximum-likelihood estimation method (MLE), that the generalized extreme value (GEV) distribution represents the best fit. Finally, an expression of the permeability as a function of the fiber volume fraction based on the GEV distribution is discussed in light of the previous results.