Matrix exponential-based closures for the turbulent subgrid-scale stress tensor

Two approaches for closing the turbulence subgrid-scale stress tensor in terms of matrix exponentials are introduced and compared. The first approach is based on a formal solution of the stress transport equation in which the production terms can be integrated exactly in terms of matrix exponentials. This formal solution of the subgrid-scale stress transport equation is shown to be useful to explore special cases, such as the response to constant velocity gradient, but neglecting pressure-strain correlations and diffusion effects. The second approach is based on an Eulerian-Lagrangian change of variables, combined with the assumption of isotropy for the conditionally averaged Lagrangian velocity gradient tensor and with the recent fluid deformation approximation. It is shown that both approaches lead to the same basic closure in which the stress tensor is expressed as the matrix exponential of the resolved velocity gradient tensor multiplied by its transpose. Short-time expansions of the matrix exponentials are shown to provide an eddy-viscosity term and particular quadratic terms, and thus allow a reinterpretation of traditional eddy-viscosity and nonlinear stress closures. The basic feasibility of the matrix-exponential closure is illustrated by implementing it successfully in large eddy simulation of forced isotropic turbulence. The matrix-exponential closure employs the drastic approximation of entirely omitting the pressure-strain correlation and other nonlinear scrambling terms. But unlike eddy-viscosity closures, the matrix exponential approach provides a simple and local closure that can be derived directly from the stress transport equation with the production term, and using physically motivated assumptions about Lagrangian decorrelation and upstream isotropy

A powerful intervention: general practitioners' use of sickness certification in depression

<b>Background</b> Depression is frequently cited as the reason for sickness absence, and it is estimated that sickness certificates are issued in one third of consultations for depression. Previous research has considered GP views of sickness certification but not specifically in relation to depression. This study aimed to explore GPs views of sickness certification in relation to depression.<p></p> <b>Methods</b> A purposive sample of GP practices across Scotland was selected to reflect variations in levels of incapacity claimants and antidepressant prescribing. Qualitative interviews were carried out between 2008 and 2009.<p></p> <b>Results</b> A total of 30 GPs were interviewed. A number of common themes emerged including the perceived importance of GP advocacy on behalf of their patients, the tensions between stakeholders involved in the sickness certification system, the need to respond flexibly to patients who present with depression and the therapeutic nature of time away from work as well as the benefits of work. GPs reported that most patients with depression returned to work after a short period of absence and that it was often difficult to predict which patients would struggle to return to work.<p></p> <b>Conclusions</b> GPs reported that dealing with sickness certification and depression presents distinct challenges. Sickness certificates are often viewed as powerful interventions, the effectiveness of time away from work for those with depression should be subject to robust enquiry

Fermi-Walker gauge in 2+1 dimensional gravity.

It is shown that the Fermi-Walker gauge allows the general solution of determining the metric given the sources, in terms of simple quadratures. We treat the general stationary problem providing explicit solving formulas for the metric and explicit support conditions for the energy momentum tensor. The same type of solution is obtained for the time dependent problem with circular symmetry. In both cases the solutions are classified in terms of the invariants of the Wilson loops outside the sources. The Fermi-Walker gauge, due to its physical nature, allows to exploit the weak energy condition and in this connection it is proved that, both for open and closed universes with rotational invariance, the energy condition imply the total absence of closed time like curves. The extension of this theorem to the general stationary problem, in absence of rotational symmetry is considered. At present such extension is subject to some assumptions on the behavior of the determinant of the dreibein in this gauge. PACS number: 0420Comment: 28 pages, RevTex, no figure

A quasi classical approach to electron impact ionization

A quasi classical approximation to quantum mechanical scattering in the Moeller formalism is developed. While keeping the numerical advantage of a standard Classical--Trajectory--Monte--Carlo calculation, our approach is no longer restricted to use stationary initial distributions. This allows one to improve the results by using better suited initial phase space distributions than the microcanonical one and to gain insight into the collision mechanism by studying the influence of different initial distributions on the cross section. A comprehensive account of results for single, double and triple differential cross sections for atomic hydrogen will be given, in comparison with experiment and other theories.Comment: 21 pages, 10 figures, submitted to J Phys

Modeling the pressure Hessian and viscous Laplacian in Turbulence: comparisons with DNS and implications on velocity gradient dynamics

Modeling the velocity gradient tensor A along Lagrangian trajectories in turbulent flow requires closures for the pressure Hessian and viscous Laplacian of A. Based on an Eulerian-Lagrangian change of variables and the so-called Recent Fluid Deformation closure, such models were proposed recently. The resulting stochastic model was shown to reproduce many geometric and anomalous scaling properties of turbulence. In this work, direct comparisons between model predictions and Direct Numerical Simulation (DNS) data are presented. First, statistical properties of A are described using conditional averages of strain skewness, enstrophy production, energy transfer and vorticity alignments, conditioned upon invariants of A. These conditionally averaged quantities are found to be described accurately by the stochastic model. More detailed comparisons that focus directly on the terms being modeled in the closures are also presented. Specifically, conditional statistics associated with the pressure Hessian and the viscous Laplacian are measured from the model and are compared with DNS. Good agreement is found in strain-dominated regions. However, some features of the pressure Hessian linked to rotation dominated regions are not reproduced accurately by the model. Geometric properties such as vorticity alignment with respect to principal axes of the pressure Hessian are mostly predicted well. In particular, the model predicts that an eigenvector of the rate-of-strain will be also an eigenvector of the pressure Hessian, in accord to basic properties of the Euler equations. The analysis identifies under what conditions the Eulerian-Lagrangian change of variables with the Recent Fluid Deformation closure works well, and in which flow regimes it requires further improvements.Comment: 16 pages, 10 figures, minor revisions, final version published in Phys. Fluid

Adiabatic non-equilibrium steady states in the partition free approach

Consider a small sample coupled to a finite number of leads, and assume that the total (continuous) system is at thermal equilibrium in the remote past. We construct a non-equilibrium steady state (NESS) by adiabatically turning on an electrical bias between the leads. The main mathematical challenge is to show that certain adiabatic wave operators exist, and to identify their strong limit when the adiabatic parameter tends to zero. Our NESS is different from, though closely related with the NESS provided by the Jak{\v s}i{\'c}-Pillet-Ruelle approach. Thus we partly settle a question asked by Caroli {\it et al} in 1971 regarding the (non)equivalence between the partitioned and partition-free approaches

We are all one together : peer educators\u27 views about falls prevention education for community-dwelling older adults - a qualitative study

Background: Falls are common in older people. Despite strong evidence for effective falls prevention strategies, there appears to be limited translation of these strategies from research to clinical practice. Use of peers in delivering falls prevention education messages has been proposed to improve uptake of falls prevention strategies and facilitate translation to practice. Volunteer peer educators often deliver educational presentations on falls prevention to community-dwelling older adults. However, research evaluating the effectiveness of peer-led education approaches in falls prevention has been limited and no known study has evaluated such a program from the perspective of peer educators involved in delivering the message. The purpose of this study was to explore peer educators’ perspective about their role in delivering peer-led falls prevention education for community-dwelling older adults. Methods: A two-stage qualitative inductive constant comparative design was used.In stage one (core component) focus group interviews involving a total of eleven participants were conducted. During stage two (supplementary component) semi-structured interviews with two participants were conducted. Data were analysed thematically by two researchers independently. Key themes were identified and findings were displayed in a conceptual framework. Results: Peer educators were motivated to deliver educational presentations and importantly, to reach an optimal peer connection with their audience. Key themes identified included both personal and organisational factors that impact on educators’ capacity to facilitate their peers’ engagement with the message. Personal factors that facilitated message delivery and engagement included peer-to-peer connection and perceived credibility, while barriers included a reluctance to accept the message that they were at risk of falling by some members in the audience. Organisational factors, including ongoing training for peer educators and formative feedback following presentations, were perceived as essential because they affect successful message delivery. Conclusions: Peer educators have the potential to effectively deliver falls prevention education to older adults and influence acceptance of the message as they possess the peer-to-peer connection that facilitates optimal engagement. There is a need to consider incorporating learnings from this research into a formal large scale evaluation of the effectiveness of the peer education approach in reducing falls in older adults