Ergodic and non-ergodic clustering of inertial particles

We compute the fractal dimension of clusters of inertial particles in mixing flows at finite values of Kubo (Ku) and Stokes (St) numbers, by a new series expansion in Ku. At small St, the theory includes clustering by Maxey's non-ergodic 'centrifuge' effect. In the limit of St to infinity and Ku to zero (so that Ku^2 St remains finite) it explains clustering in terms of ergodic 'multiplicative amplification'. In this limit, the theory is consistent with the asymptotic perturbation series in [Duncan et al., Phys. Rev. Lett. 95 (2005) 240602]. The new theory allows to analyse how the two clustering mechanisms compete at finite values of St and Ku. For particles suspended in two-dimensional random Gaussian incompressible flows, the theory yields excellent results for Ku < 0.2 for arbitrary values of St; the ergodic mechanism is found to contribute significantly unless St is very small. For higher values of Ku the new series is likely to require resummation. But numerical simulations show that for Ku ~ St ~ 1 too, ergodic 'multiplicative amplification' makes a substantial contribution to the observed clustering.Comment: 4 pages, 2 figure

Advective collisions

Small particles advected in a fluid can collide (and therefore aggregate) due to the stretching or shearing of fluid elements. This effect is usually discussed in terms of a theory due to Saffman and Turner [J. Fluid Mech., 1, 16-30, (1956)]. We show that in complex or random flows the Saffman-Turner theory for the collision rate describes only an initial transient (which we evaluate exactly). We obtain precise expressions for the steady-state collision rate for flows with small Kubo number, including the influence of fractal clustering on the collision rate for compressible flows. For incompressible turbulent flows, where the Kubo number is of order unity, the Saffman-Turner theory is an upper bound.Comment: 4 pages, 1 figur

Staggered Ladder Spectra

We exactly solve a Fokker-Planck equation by determining its eigenvalues and eigenfunctions: we construct nonlinear second-order differential operators which act as raising and lowering operators, generating ladder spectra for the odd and even parity states. These are staggered: the odd-even separation differs from even-odd. The Fokker-Planck equation describes, in the limit of weak damping, a generalised Ornstein-Uhlenbeck process where the random force depends upon position as well as time. Our exact solution exhibits anomalous diffusion at short times and a stationary non-Maxwellian momentum distribution.Comment: 4 pages, 2 figure

Brownian Motion Model of Quantization Ambiguity and Universality in Chaotic Systems

We examine spectral equilibration of quantum chaotic spectra to universal statistics, in the context of the Brownian motion model. Two competing time scales, proportional and inversely proportional to the classical relaxation time, jointly govern the equilibration process. Multiplicity of quantum systems having the same semiclassical limit is not sufficient to obtain equilibration of any spectral modes in two-dimensional systems, while in three-dimensional systems equilibration for some spectral modes is possible if the classical relaxation rate is slow. Connections are made with upper bounds on semiclassical accuracy and with fidelity decay in the presence of a weak perturbation.Comment: 13 pages, 6 figures, submitted to Phys Rev

StochKit-FF: Efficient Systems Biology on Multicore Architectures

The stochastic modelling of biological systems is an informative, and in some cases, very adequate technique, which may however result in being more expensive than other modelling approaches, such as differential equations. We present StochKit-FF, a parallel version of StochKit, a reference toolkit for stochastic simulations. StochKit-FF is based on the FastFlow programming toolkit for multicores and exploits the novel concept of selective memory. We experiment StochKit-FF on a model of HIV infection dynamics, with the aim of extracting information from efficiently run experiments, here in terms of average and variance and, on a longer term, of more structured data.Comment: 14 pages + cover pag

Co‐creating system‐wide improvement for people with traumatic brain injury across one integrated care system in the United Kingdom to initiate a transformation journey through co‐production

Background and Objective There is a need for better integration of services across communities and sectors for people living with traumatic brain injury (TBI) to meet their complex needs. Building on insights gained from earlier pilot work, here we report the outcomes of a participatory workshop that sought to better understand the challenges, barriers and opportunities that currently exist within the care pathway for survivors of TBI. Methods A diverse range of stakeholders from the acute and rehabilitation care pathway and the health and social care system were invited to participate in a 3-h workshop. The participants worked in four mixed subgroups using practice development methodology, which promotes person-centred, inclusive and participatory action. Results Thematic analysis identified shared purposes and values that were used to produce a detailed implementation and impact framework for application at both the level of the care interface and the overarching integrated care system. A variety of enablers were identified that related to collective values and behaviours, case management, team leadership and integrated team working, workforce capability, evidence-based practice and resourcing. The clinical, economic, cultural and social outcomes associated with these enablers were also identified, and included patient safety, independence and well-being, reduced waiting times, re-admission rates, staff retention and professional development. Conclusion The co-produced recommendations made within the implementation and impact framework described here provide a means by which the culture and delivery of health and social care services can be better tailored to meet the needs of people living with TBI. We believe that the recommendations will help shape the formation of new services as well as the development of existing ones. Patient or Public Contribution Patient and public involvement have been established over a 10-year history of relationship building through a joint forum and events involving three charities representing people with TBI, carers, family members, clinicians, service users, researchers and commissioners, culminating in a politically supported event that identified concerns about the needs of people following TBI. These relationships formed the foundation for the interactive workshop, the focus of this publication

The relevance of indigenous technology in curriculum 2005/RNCS with special reference to the technology learning area

In this article it is argued that indigenous technology with its long history cannot be ignored and should be as signed a more prominent place in the Technology Learning Area (TLA) within Curriculum 2005/RNCS Grades R – 9.2 The argument is based on the findings of a study in which the relevance of indigenous technology in the TLA curriculum was investigated. The findings not only pointed to the long history of indigenous technology, but also evidenced the continued use of such technology among indigenous people, especially in the rural contexts. The findings in the study are suggestive of an enhanced recognition of indigenous technology in the TLA curriculum. Therefore, informed by the findings, the authors pose certain recommendations pertaining to the TLA curriculum.The article has as secondary purpose creation of awareness of, and sensitivity for, the cultural heritage of indigenous people in South Africa and context-specific community needs which can be recognised and addressed in learning areas such as the TLA.South African Journal of Education Vol. 26 (4) 2006: pp. 501-51

Structure of purine nucleoside phosphorylase (DeoD) from Bacillus anthracis

Protein structures from the causative agent of anthrax (Bacillus anthracis) are being determined as part of a structural genomics programme. Amongst initial candidates for crystallographic analysis are enzymes involved in nucleotide biosynthesis, since these are recognized as potential targets in antibacterial therapy. Purine nucleoside phosphorylase is a key enzyme in the purine-salvage pathway. The crystal structure of purine nucleoside phosphorylase (DeoD) from B. anthracis has been solved by molecular replacement at 2.24 Å resolution and refined to an R factor of 18.4%. This is the first report of a DeoD structure from a Gram-positive bacterium