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

Responding to coronavirus pandemic: human rights movement-building to transform global capitalism

The COVID-19 pandemic makes patently clear the limitations and vulnerabilities of the global capitalist system, portending significant changes in the world economy. Given the long history of divisions in the global Left, is there hope that we might forge the unity needed to transform the global economic order? In this essay I argue that global social movement practices and history reveal human rights as a unifying and transformative framework for organizing across issues and across local-global scales. More localized human rights movements are now well situated to help unite and guide transformative global activism in this moment of crisis, and I provide examples from current Pittsburgh and U.S. national human rights cities organizing

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

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

Cryopreservation studies of an artificial co-culture between the cobalamin-requiring green alga Lobomonas rostrata and the bacterium Mesorhizobium loti

Algal-bacterial co-cultures, rather than cultures of algae alone, are regarded as having the potential to enhance productivity and stability in industrial algal cultivation. As with other inocula in biotechnology, to avoid loss of production strains, it is important to develop preservation methods for the long-term storage of these cultures, and one of the most commonly used approaches is cryopreservation. However, whilst there are many reports of cryopreserved xenic algal cultures, little work has been reported on the intentional preservation of both algae and beneficial bacteria in xenic cultures. Instead, studies have focused on the development of methods to conserve the algal strain(s) present, or to avoid overgrowth of bacteria in xenic isolates during the post-thaw recovery phase. Here, we have established a co-cryopreservation method for the long-term storage of both partners in a unialgal-bacterial co-culture. This is an artificial model mutualism between the alga Lobomonas rostrata and the bacterium Mesorhizobium loti, which provides vitamin B12 (cobalamin) to the alga in return for photosynthate. Using a Planer Kryo 360 controlled-rate cooler, post-thaw viability (PTV) values of 72% were obtained for the co-culture, compared to 91% for the axenic alga. The cultures were successfully revived after 6 months storage in liquid nitrogen, and continued to exhibit mutualism. Furthermore, the alga could be cryopreserved with non-symbiotic bacteria, without bacterial overgrowth occurring. It was also possible to use less controllable passive freezer chambers to cryopreserve the co-cultures, although the PTV was lower. Finally, we demonstrated that an optimised cryopreservation method may be used to prevent the overgrowth potential of non-symbiotic, adventitious bacteria in both axenic and co-cultures of L. rostrata after thawing.John Day and Christian Ridley would like to acknowledge financial support from the EU for the Energetic Algae project ("EnAlgae") a Strategic Initiative of the INTERREG IVB North West Europe (NWE) Programme

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

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

Increases in the abundance of microbial genes encoding halotolerance and photosynthesis along a sediment salinity gradient

Biogeochemical cycles are driven by the metabolic activity of microbial communities, yet the environmental parameters that underpin shifts in the functional potential coded within microbial community genomes are still poorly understood. Salinity is one of the primary determinants of microbial community structure and can vary strongly along gradients within a variety of habitats. To test the hypothesis that shifts in salinity will also alter the bulk biogeochemical potential of aquatic microbial assemblages, we generated four metagenomic DNA sequence libraries from sediment samples taken along a continuous, natural salinity gradient in the Coorong lagoon, Australia, and compared them to physical and chemical parameters. A total of 392483 DNA sequences obtained from four sediment samples were generated and used to compare genomic characteristics along the gradient. The most significant shifts along the salinity gradient were in the genetic potential for halotolerance and photosynthesis, which were more highly represented in hypersaline samples. At these sites, halotolerance was achieved by an increase in genes responsible for the acquisition of compatible solutes-organic chemicals which influence the carbon, nitrogen and methane cycles of sediment. Photosynthesis gene increases were coupled to an increase in genes matching Cyanobacteria, which are responsible for mediating CO2 and nitrogen cycles. These salinity driven shifts in gene abundance will influence nutrient cycles along the gradient, controlling the ecology and biogeochemistry of the entire ecosystem. © 2012 Author(s)