Travelling waves in two-dimensional plane Poiseuille flow

The asymptotic structure of laminar modulated travelling waves in two-dimensional high-Reynolds-number plane Poiseuille flow is investigated on the upper-energy branch. A finite set of independent slowly varying parameters are identified which parameterize the solution of the Navier–Stokes equations in this subset of the phase space. Our parameterization of the weakly stable modes describes an attracting manifold of maximum-entropy configurations. The complementary modes, which have been neglected in this parameterization, are strongly damped. In order to seek a closure, a countably infinite number of modulation equations are derived on the long viscous time scale: a single equation for averaged kinetic energy and momentum; and the remaining equations for averaged powers of vorticity. Only a finite number of these vorticity modulation equations are required to determine the finite number of unknowns. The new results show that the evolution of the slowly varying amplitude parameters is determined by the vorticity field and that the phase velocity responds to these changes in the amplitude in accordance with the kinetic energy and momentum. The new results also show that the most crucial physical mechanism in the production of vorticity is the interaction between vorticity and kinetic energy, this interaction being responsible for the existence of the attractor

Parameterization of travelling waves in plane Poiseuille flow

© The authors 2012. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved. This is a pre-copyedited, author-produced PDF of an article accepted for publication in [IMA Journal of Applied Mathematics ] following peer review. The version of record [ IMA Journal of Applied Mathematics (2014) 79(1): 22-32.] is available online at: http://imamat.oxfordjournals.org/content/79/1/22The first finite-dimensional parameterization of a subset of the phase space of the Navier-Stokes equations is presented. Travelling waves in two-dimensional plane Poiseuille flow are numerically shown to approximate maximum-entropy configurations. In a coordinate system moving with the phase velocity, the enclosed body of the flow exhibits a hyperbolic sinusoidal relationship between the vorticity and stream function. The phase velocity and two-amplitude parameters describe the stable manifold on the slow viscous time scale. This original parameterization provides a valuable visualization of this subset of the phase space of the Navier-Stokes equations. These new results provide physical insight into an important intermediate stage in the instability process of plane Poiseuille flow

Neutrophil responses to CRP are not dependent on polymorphism of human FcgammaRIIA (R131H).

IgG2a mediated in vitro phagocytosis is less effective for individuals homozygous for Fcgamma RIIaR131 allele and such individuals are also more susceptible to certain infections. It has been reported that CRP binds to Fcgamma RIIaR131 but not Fcgamma RIIaH131 and since Fcgamma RIIa is also a major Fc receptor on neutrophils it would be expected that normal healthy donors who did not have at least one copy of Fcgamma RIIaR131 would not respond to CRP. We examined responses reported to be dependent on FcgammaRIIa but no difference between groups was observed in CRP mediated phagocytosis of S. pneumoniae, reactive oxygen production, or IL-8 synthesis. This suggests that either neutrophil receptors other than Fcgamma RIIa are responsible for CRP mediated responses or differences in CRP binding to the forms of Fcgamma RIIa are comparatively minor

What is the impact of psychiatric decision units on mental health crisis care pathways? Protocol for an interrupted time series analysis with a synthetic control study

Background The UK mental health system is stretched to breaking point. Individuals presenting with mental health problems wait longer at the ED than those presenting with physical concerns and finding a bed when needed is difficult – 91% of psychiatric wards are operating at above the recommended occupancy rate. To address the pressure, a new type of facility – psychiatric decision units (also known as mental health decision units) – have been introduced in some areas. These are short-stay facilities, available upon referral, targeted to help individuals who may be able to avoid an inpatient admission or lengthy ED visit. To advance knowledge about the effectiveness of this service for this purpose, we will examine the effect of the service on the mental health crisis care pathway over a 4-year time period; the 2 years proceeding and following the introduction of the service. We use aggregate service level data of key indicators of the performance of this pathway. Methods Data from four mental health Trusts in England will be analysed using an interrupted time series (ITS) design with the primary outcomes of the rate of (i) ED psychiatric presentations and (ii) voluntary admissions to mental health wards. This will be supplemented with a synthetic control study with the same primary outcomes, in which a comparable control group is generated for each outcome using a donor pool of suitable National Health Service Trusts in England. The methods are well suited to an evaluation of an intervention at a service delivery level targeting population-level health outcome and the randomisation or ‘trialability’ of the intervention is limited. The synthetic control study controls for national trends over time, increasing our confidence in the results. The study has been designed and will be carried out with the involvement of service users and carers. Discussion This will be the first formal evaluation of psychiatric decision units in England. The analysis will provide estimates of the effect of the decision units on a number of important service use indicators, providing much-needed information for those designing service pathways

A summary of the BARREL campaigns: Technique for studying electron precipitation.

BARREL observed electron precipitation over wide range of energy and timescalesPrecipitating electron distribution is determined using spectroscopy for 19 January 2013 eventBARREL timing data has accuracy within sampling interval of 0.05 s

Korn's second inequality and geometric rigidity with mixed growth conditions

Geometric rigidity states that a gradient field which is $L^p$-close to the set of proper rotations is necessarily $L^p$-close to a fixed rotation, and is one key estimate in nonlinear elasticity. In several applications, as for example in the theory of plasticity, energy densities with mixed growth appear. We show here that geometric rigidity holds also in $L^p+L^q$ and in $L^{p,q}$ interpolation spaces. As a first step we prove the corresponding linear inequality, which generalizes Korn's inequality to these spaces

The impact of mental health services at outreach clinics and non-clinic sites on the attendance of Deaf children and young people and families

Deaf children show high rates of mental health disorders, with difficulties getting access to appropriate health care. The National Deaf Child and Adolescent Mental Health Service (ND-CAMHS) was set up to provide specialist mental health care to Deaf young people and hearing children of Deaf adults in the UK. This study retrospectively examined the impact of the introduction of ND-CAMHS at outreach clinics and non-clinic sites on attendance rates at clients and carers’ first and follow-up appointments over a three-and-a-half-year period. In all, 4177 appointments, 372 first and 3805 follow-up, associated with 369 clients were considered for analyses. First appointments were much more likely to be clinic-based than follow-up appointments (78.2% versus 34.3%, p < 0.001), which were administered in a variety of sites, most frequently at the client’s school or home. The overall attendance rates for first and follow-up appointments were 68.5% and 79.2%, respectively. There was no significant effect of appointment location on attendance rates for first appointments. However, multivariate analyses indicated that clients at follow-up appointments were more likely to attend when appointments occurred at non-clinic sites compared with clinic-based appointments (81.9% versus 74.1%; odds ratio (OR) = 1.39, 95% confidence interval (CI) 1.17, 1.65). Improved attendance rates were a function of significant decreases in ‘did not attends’ (DNA) and client/carer cancellations at non-clinic sites. There was also an increased attendance rate for follow-up appointments held in outreach clinics relative to hospital-based sites (79.0% versus 72.2%), although this failed to achieve significance after adjusting for other relevant factors (OR = 1.27, 95% CI 0.93, 1.73). The findings indicate that providing specialised mental health services for Deaf children and young people into schools and other locations that are easier to access can improve service accessibility and continuity of care

The role of cardiac troponin T quantity and function in cardiac development and dilated cardiomyopathy

Background: Hypertrophic (HCM) and dilated (DCM) cardiomyopathies results from sarcomeric protein mutations, including cardiac troponin T (cTnT, TNNT2). We determined whether TNNT2 mutations cause cardiomyopathies by altering cTnT function or quantity; whether the severity of DCM is related to the ratio of mutant to wildtype cTnT; whether Ca2+ desensitization occurs in DCM; and whether absence of cTnT impairs early embryonic cardiogenesis. Methods and Findings: We ablated Tnnt2 to produce heterozygous Tnnt2+/ mice, and crossbreeding produced homozygous null Tnnt2-/-embryos. We also generated transgenic mice overexpressing wildtype (TGWT) or DCM mutant (TGK210Δ) Tnnt2. Crossbreeding produced mice lacking one allele of Tnnt2, but carrying wildtype (Tnnt2+/-/TGWT) or mutant (Tnnt2+/-/TGK210Δ) transgenes. Tnnt2+/-mice relative to wildtype had significantly reduced transcript (0.82 ± 0.06 [SD] vs. 1.00 ± 0.12 arbitrary units; p = 0.025), but not protein (1.01 ± 0.20 vs. 1.00 ± 0.13 arbitrary units; p = 0.44). Tnnt2+/-mice had normal hearts (histology, mass, left ventricular end diastolic diameter [LVEDD], fractional shortening [FS]). Moreover, whereas Tnnt2+/-/ TGK210Δ mice had severe DCM, TGK210Δ mice had only mild DCM (FS 18 ± 4 vs. 29 ± 7%; p < 0.01). The difference in severity of DCM may be attributable to a greater ratio of mutant to wildtype Tnnt2 transcript in Tnnt2+/-/TGK210Δ relative to TGK210Δ mice (2.42±0.08, p = 0.03). Tnnt2+/-/TGK210Δ muscle showed Ca2+ desensitization (pCa50 = 5.34 ± 0.08 vs. 5.58 ± 0.03 at sarcomere length 1.9 μm. p<0.01), but no difference in maximum force generation. Day 9.5 Tnnt2-/-embryos had normally looped hearts, but thin ventricular walls, large pericardial effusions, noncontractile hearts, and severely disorganized sarcomeres. Conclusions: Absence of one Tnnt2 allele leads to a mild deficit in transcript but not protein, leading to a normal cardiac phenotype. DCM results from abnormal function of a mutant protein, which is associated with myocyte Ca2+ desensitization. The severity of DCM depends on the ratio of mutant to wildtype Tnnt2 transcript. cTnT is essential for sarcomere formation, but normal embryonic heart looping occurs without contractile activity. © 2008 Ahmad et al

A mathematical modelling study of an athlete's sprint time when towing a weighted sled

This is the author's accepted manuscript. The final publication is available at Springer via http://dx.doi.org/10.1007/s12283-013-0114-2.This study used a mathematical model to examine the effects of the sled, the running surface, and the athlete on sprint time when towing a weighted sled. Simulations showed that ratio scaling is an appropriate method of normalising the weight of the sled for athletes of different body size. The relationship between sprint time and the weight of the sled was almost linear, as long as the sled was not excessively heavy. The athlete’s sprint time and rate of increase in sprint time were greater on running surfaces with a greater coefficient of friction, and on any given running surface an athlete with a greater power-to-weight ratio had a lower rate of increase in sprint time. The angle of the tow cord did not have a substantial effect on an athlete’s sprint time. This greater understanding should help coaches set the training intensity experienced by an athlete when performing a sled-towing exercise

The development of path integration: combining estimations of distance and heading

Efficient daily navigation is underpinned by path integration, the mechanism by which we use self-movement information to update our position in space. This process is well-understood in adulthood, but there has been relatively little study of path integration in childhood, leading to an underrepresentation in accounts of navigational development. Previous research has shown that calculation of distance and heading both tend to be less accurate in children as they are in adults, although there have been no studies of the combined calculation of distance and heading that typifies naturalistic path integration. In the present study 5-year-olds and 7-year-olds took part in a triangle-completion task, where they were required to return to the startpoint of a multi-element path using only idiothetic information. Performance was compared to a sample of adult participants, who were found to be more accurate than children on measures of landing error, heading error, and distance error. 7-year-olds were significantly more accurate than 5-year-olds on measures of landing error and heading error, although the difference between groups was much smaller for distance error. All measures were reliably correlated with age, demonstrating a clear development of path integration abilities within the age range tested. Taken together, these data make a strong case for the inclusion of path integration within developmental models of spatial navigational processing