Nonaxisymmetric, multi-region relaxed magnetohydrodynamic equilibrium solutions

We describe a magnetohydrodynamic (MHD) constrained energy functional for equilibrium calculations that combines the topological constraints of ideal MHD with elements of Taylor relaxation. Extremizing states allow for partially chaotic magnetic fields and non-trivial pressure profiles supported by a discrete set of ideal interfaces with irrational rotational transforms. Numerical solutions are computed using the Stepped Pressure Equilibrium Code, SPEC, and benchmarks and convergence calculations are presented.Comment: Submitted to Plasma Physics and Controlled Fusion for publication with a cluster of papers associated with workshop: Stability and Nonlinear Dynamics of Plasmas, October 31, 2009 Atlanta, GA on occasion of 65th birthday of R.L. Dewar. V2 is revised for referee

Hamilton--Jacobi theory for continuation of magnetic field across a toroidal surface supporting a plasma pressure discontinuity

The vanishing of the divergence of the total stress tensor (magnetic plus kinetic) in a neighborhood of an equilibrium plasma containing a toroidal surface of discontinuity gives boundary and jump conditions that strongly constrain allowable continuations of the magnetic field across the surface. The boundary conditions allow the magnetic fields on either side of the discontinuity surface to be described by surface magnetic potentials, reducing the continuation problem to that of solving a Hamilton--Jacobi equation. The characteristics of this equation obey Hamiltonian equations of motion, and a necessary condition for the existence of a continued field across a general toroidal surface is that there exist invariant tori in the phase space of this Hamiltonian system. It is argued from the Birkhoff theorem that existence of such an invariant torus is also, in general, sufficient for continuation to be possible. An important corollary is that the rotational transform of the continued field on a surface of discontinuity must, generically, be irrational.Comment: Prepared for submission to Phys. Letts.

Relaxed plasma equilibria and entropy-related plasma self-organization principles

The concept of plasma relaxation as a constrained energy minimization is reviewed. Recent work by the authors on generalizing this approach to partially relaxed threedimensional plasma systems in a way consistent with chaos theory is discussed, with a view to clarifying the thermodynamic aspects of the variational approach used. Other entropy-related approaches to finding long-time steady states of turbulent or chaotic plasma systems are also briefly reviewed

BIOMECHANICAL GOLF SWING ANALYSIS

The Biomechanics Laboratory of the Australian Institute of Sport has spent eight years developing a comprehensive golf swing analysis system. The system is designed to assist the golfer and professional golf coach in identifying problems within the goWs swing and enable corrections to be made so that the golfer may reach full potential. Correct weight transference is a major component of the perfect swing. The Golf Analysis System measures changes in the centre of pressure of the golfer during the swing which provides a measure of the golfer's weight transference pattern. The path the club follows during the swing is directly related to the quality of the swing. An automatic digitising system is used in the Golf Analysis System to capture the location of the club shaft every one two-hundredths of the second during the swing. This path is then reconstructed by computer, plotted on paper and animated on video for review purposes. Views from the front, side and above the club path plane are reconstructed in relation to the movement of the leading shoulder for examination. The absolute velocity of the club's head is obtained and plotted out for 0.1 sec. before impact to 0.1 seconds after impact. The velocity components of the club head in the forward, crosswise and vertical direction are also plotted out which provides information as to the direction the club head is moving at the time of ball contact. A graph of the angle that the club is making to the desired ball path is also graphed out from 0.02 seconds before impact to 0.02 seconds after impact. A split vision video image of the golf swing is f h e d during the swing. This is captured by way of two shuttered S-VHS video cameras located directly above and to the open side of the golfer. The video provides a complete visual image of each entire golf swing analyzed. The position of the golf club head during ball contact phase has a direct relationship to the path the ball will follow after ball contact. In the Golf Analysis System the path of the golf club head is captured by a high speed video camera (400 frames per second) several frames before ball contact to several frames after contact. Sensors in the tee-off platform provide immediate feedback on the velocity of the club head immediately before impact and velocity of the ball immediately after impact. The direction and elevation of ball flight is also measured by sensors. A printout of this information together with where the ball would have landed as a d tof the swing is also provided in printouts. The Golf Analysis System provides valuable information about the golfefs swing which if used properly can produce drastic improvement in the goWs game. To be most effective a professional golf coach should be utilised to eliminate faults which are disclosed by Golf Analysis System. The swing analysis of 65 third year apprentices in the Australian P.G.A. professional coaching course has come up with some interesting information. This information will be presented at the ISBS 1995 Symposium

Architecture, physical activity and a capability evaluative framework: satisfaction is not enough

Despite recognition that building design can contribute to human health by facilitating increased incidental physical activity, knowledge of how building design can enable this is underdeveloped. Further, there is evidence that design features introduced to support routine physical activity and improve occupant satisfaction may not necessarily lead to increases in actual physical activity. Evaluative frameworks encompassing a range of individual, organisational and built environment factors that contribute to shaping occupant behaviour may provide insight into how buildings can support greater levels of routine physical activity. This paper argues that capability theory can inform our understandings of the dynamic interrelationship between building design and building use. In this paper we describe our approach to developing a framework for capabilities-based evaluation of buildings and building occupant physical activity. Based on a capability perspective we consider the intersection of building ‘domains’ and ‘functionings’ that influence occupant physical activity; and question how such evaluations could account for a range of occupants. The research is of relevance to those engaged in the production of architectural environments and evaluation tools that support physical activity—inclusive of building designers, procurers, managers and occupants

Computation of multi-region relaxed magnetohydrodynamic equilibria

We describe the construction of stepped-pressure equilibria as extrema of a multi-region, relaxed magnetohydrodynamic (MHD) energy functional that combines elements of ideal MHD and Taylor relaxation, and which we call MRXMHD. The model is compatible with Hamiltonian chaos theory and allows the three-dimensional MHD equilibrium problem to be formulated in a well-posed manner suitable for computation. The energy-functional is discretized using a mixed finite-element, Fourier representation for the magnetic vector potential and the equilibrium geometry; and numerical solutions are constructed using the stepped-pressure equilibrium code, SPEC. Convergence studies with respect to radial and Fourier resolution are presented.The authors gratefully acknowledge support of the U.S. Department of Energy and the Australian Research Council, through Grants DP0452728, FT0991899, and DP110102881

Ectopic models for endochondral ossification: comparing pellet and alginate bead culture methods

Key aspects of native endochondral bone development and fracture healing can be mimicked in mesenchymal stem cells (MSCs) through standard in vitro chondrogenic induction. Exploiting this phenomenon has recently emerged as an attractive technique to engineer bone tissue, however, relatively little is known about the best conditions for doing so. The objective of the present study was to compare the bone-forming capacity and angiogenic induction of hypertrophic cell constructs containing human adipose-derived stem cells (hASCs) primed for chondrogenesis in two different culture systems: high-density pellets and alginate bead hydrogels. The hASC constructs were subjected to 4 weeks of identical chondrogenic induction in vitro, encapsulated in an agarose carrier, and then implanted subcutaneously in immune-compromised mice for 8 weeks to evaluate their endochondral potential. At the time of implantation, both pellets and beads expressed aggrecan and type II collagen, as well as alkaline phosphatase (ALP) and type X collagen. Interestingly, ASCs in pellets formed a matrix containing higher glycosaminoglycan and collagen contents than that in beads, and ALP activity per cell was higher in pellets. However, after 8 weeks in vivo, pellets and beads induced an equivalent volume of mineralized tissue and a comparable level of vascularization. Although osteocalcin and osteopontin-positive osteogenic tissue and new vascular growth was found within both types of constructs, all appeared to be better distributed throughout the hydrogel beads. The results of this ectopic model indicate that hydrogel culture may be an attractive alternative to cell pellets for bone tissue engineering via the endochondral pathway

Genipin crosslinking decreases the mechanical wear and biochemical degradation of impacted cartilage in vitro

High energy trauma to cartilage causes surface fissures and microstructural damage, but the degree to which this damage renders the tissue more susceptible to wear and contributes to the progression of post-traumatic osteoarthritis (PTOA) is unknown. Additionally, no treatments are currently available to strengthen cartilage after joint trauma and to protect the tissue from subsequent degradation and wear. The purposes of this study were to investigate the role of mechanical damage in the degradation and wear of cartilage, to evaluate the effects of impact and subsequent genipin crosslinking on the changes in the viscoelastic parameters of articular cartilage, and to test the hypothesis that genipin crosslinking is an effective treatment to enhance the resistance to biochemical degradation and mechanical wear. Results demonstrate that cartilage stiffness decreases after impact loading, likely due to the formation of fissures and microarchitectural damage, and is partially or fully restored by crosslinking. The wear resistance of impacted articular cartilage was diminished compared to undamaged cartilage, suggesting that mechanical damage that is directly induced by the impact may contribute to the progression of PTOA. However, the decrease in wear resistance was completely reversed by the crosslinking treatments. Additionally, the crosslinking treatments improved the resistance to collagenase digestion at the impact-damaged articular surface. These results highlight the potential therapeutic value of collagen crosslinking via genipin in the prevention of cartilage degeneration after traumatic injury

Automated analysis of atrial late gadolinium enhancement imaging that correlates with endocardial voltage and clinical outcomes: A 2-center study

This work was supported by the British Heart Foundation PG/10/37/28347, RG/10/11/28457, NIHR Biomedical Research Centre funding, and the ElectroCardioMaths Programme of the Imperial BHF Centre of Research Excellence