On the stability of periodic 2D Euler-alpha flows

An explicit expression is obtained for the sectional curvature in the plane spanned by two stationary flows, cos(k, x) and cos(l, x). It is shown that for certain values of the wave vectors k and l the curvature becomes positive for alpha > alpha_0, where 0 < alpha_0 < 1 is of the order 1/k. This suggests that the flow corresponding to such geodesics becomes more stable as one goes from usual Eulerian description to the Euler-alpha model

Abstract mechanical connection and Abelian reconstruction for almost Kähler manifolds

When the phase space P of a Hamiltonian G-system (P,ω,G,J,H) has an almost Kähler structure a preferred connection, called abstract mechanical connection, can be defined by declaring horizontal spaces at each point to be metric orthogonal to the tangent to the group orbit. Explicit formulas for the corresponding connection one-form. A are derived in terms of the momentum map, symplectic and complex structures. Such connection can play the role of the reconstruction connection (see A. Blaom, Reconstruction phases via Poisson reduction. Diff. Geom. Appl., 12:231{252, 2000.), thus signicantly simplifying computations of the corresponding dynamic and geometric phases for an Abelian group G. These ideas are illustrated using the example of the resonant three-wave interaction. Explicit formulas for the connection one-form and the phases are given together with some new results on the symmetry reduction of the Poisson structure

Point vortices on a sphere: Stability of relative equilibria

In this paper we analyze the dynamics of N point vortices moving on a sphere from the point of view of geometric mechanics. The formalism is developed for the general case of N vortices, and the details are worked out for the (integrable) case of three vortices. The system under consideration is SO(3) invariant; the associated momentum map generated by this SO(3) symmetry is equivariant and corresponds to the moment of vorticity. Poisson reduction corresponding to this symmetry is performed; the quotient space is constructed and its Poisson bracket structure and symplectic leaves are found explicitly. The stability of relative equilibria is analyzed by the energy-momentum method. Explicit criteria for stability of different configurations with generic and nongeneric momenta are obtained. In each case a group of transformations is specified, modulo which one has stability in the original (unreduced) phase space. Special attention is given to the distinction between the cases when the relative equilibrium is a nongreat circle equilateral triangle and when the vortices line up on a great circle

Symmetry reduction of discrete Lagrangian mechanics on Lie groups

For a discrete mechanical system on a Lie group $G$ determined by a (reduced) Lagrangian $\ell$ we define a Poisson structure via the pull-back of the Lie-Poisson structure on the dual of the Lie algebra ${\mathfrak g}^*$ by the corresponding Legendre transform. The main result shown in this paper is that this structure coincides with the reduction under the symmetry group $G$ of the canonical discrete Lagrange 2-form $\omega_\mathbb{L}$ on $G \times G$. Its symplectic leaves then become dynamically invariant manifolds for the reduced discrete system. Links between our approach and that of groupoids and algebroids as well as the reduced Hamilton-Jacobi equation are made. The rigid body is discussed as an example

Discrete Euler-Poincar\'{e} and Lie-Poisson Equations

In this paper, discrete analogues of Euler-Poincar\'{e} and Lie-Poisson reduction theory are developed for systems on finite dimensional Lie groups $G$ with Lagrangians $L:TG \to {\mathbb R}$ that are $G$-invariant. These discrete equations provide ``reduced'' numerical algorithms which manifestly preserve the symplectic structure. The manifold $G \times G$ is used as an approximation of $TG$, and a discrete Langragian ${\mathbb L}:G \times G \to {\mathbb R}$ is construced in such a way that the $G$-invariance property is preserved. Reduction by $G$ results in new ``variational'' principle for the reduced Lagrangian $\ell:G \to {\mathbb R}$, and provides the discrete Euler-Poincar\'{e} (DEP) equations. Reconstruction of these equations recovers the discrete Euler-Lagrange equations developed in \cite{MPS,WM} which are naturally symplectic-momentum algorithms. Furthermore, the solution of the DEP algorithm immediately leads to a discrete Lie-Poisson (DLP) algorithm. It is shown that when $G=\text{SO} (n)$, the DEP and DLP algorithms for a particular choice of the discrete Lagrangian ${\mathbb L}$ are equivalent to the Moser-Veselov scheme for the generalized rigid body. %As an application, a reduced symplectic integrator for two dimensional %hydrodynamics is constructed using the SU$(n)$ approximation to the volume %preserving diffeomorphism group of ${\mathbb T}^2$

Stability of Relative Equilibria of Point Vortices on a Sphere and Symplectic Integrators

This paper analyzes the dynamics of N point vortices moving on a sphere from the point of view of geometric mechanics. The formalism is developed for the general case of N vortices, and the details are provided for the (integrable) case N = 3. Stability of relative equilibria is analyzed by the energy-momentum method. Explicit criteria for stability of different configurations with generic and non-generic momenta are obtained. In each case, a group of transformations is specied, such that motion in the original (unreduced) phase space is stable modulo this group. Finally, we outline the construction of a symplectic-momentum integrator for vortex dynamics on a sphere

Fundholding: learning from the past and looking to the future

The document attached has been archived with permission from the editor of the Medical Journal of Australia (26 April 2007). An external link to the publisher’s copy is included.Australian trials of healthcare initiatives that included fundholding models have not produced convincing quantitative evidence of health gains, but there is qualitative evidence of improved patient well-being and significant changes in service mix, which may produce longer-term health gains. Fundholding is most likely to improve patient outcomes when implemented within a broader healthcare initiative that has the potential to be more effective if financed outside existing funding structures. The most appropriate fundholder organisation depends on the nature of the initiative and the type of stakeholder engagement required, but technical and organisational skills will always be needed for balancing financial viability and additional patient services. Stakeholders’ willingness to engage in fundholding depends on the anticipated budget impact, how they will use the savings generated, and whether workforce needs will be fulfilled. Before including fundholding in healthcare initiatives, there must be realistic prospective analyses and community debate. Monitoring and evaluation frameworks must also be in place to provide ongoing evidence of quality of care, health and well-being outcomes and financial implications for fund contributors.Justin J Beilby and Brita Pekarsk

Cost analysis of ambulatory blood pressure monitoring in initiating antihypertensive drug treatment in Australian general practice

The document attached has been archived with permission from the editor of the Medical Journal of Australia. An external link to the publisher’s copy is included.Objective: To compare the cost of ambulatory blood pressure monitoring (ABPM) with the putative savings made through treatment avoided by identification and non-treatment of those with "white coat" hypertension. Design: A cost analysis based on a model of four alternative strategies (no ABPM, yearly, two-yearly, or three-yearly monitoring) over a seven-year period applied to a case series from Australian general practice. Participants: 62 patients newly diagnosed by their GPs as having hypertension and requiring drug treatment. Main outcome measures: The proportion of patients shown to not need treatment. The discounted costs to the Pharmaceutical Benefits Scheme, Medical Benefits Scheme and patients. Results: 16 of 62 patients (26%; 95% CI, 15%–37%) were normotensive on ABPM and did not require treatment. All monitoring strategies are more expensive in the first year, but the initial costs are offset by year 3 and the monitoring strategies are cost saving thereafter. Sensitivity analysis shows that this result holds across a range of costs of pharmacotherapy and proportion of patients with white coat hypertension. Conclusion: The additional costs of 24-hour ABPM in the first year are offset by savings associated with patients with white coat hypertension who would otherwise have been treated.Ben Ewald and Brita Pekarsk