An Optimal Control Formulation for Inviscid Incompressible Ideal Fluid Flow

In this paper we consider the Hamiltonian formulation of the equations of incompressible ideal fluid flow from the point of view of optimal control theory. The equations are compared to the finite symmetric rigid body equations analyzed earlier by the authors. We discuss various aspects of the Hamiltonian structure of the Euler equations and show in particular that the optimal control approach leads to a standard formulation of the Euler equations -- the so-called impulse equations in their Lagrangian form. We discuss various other aspects of the Euler equations from a pedagogical point of view. We show that the Hamiltonian in the maximum principle is given by the pairing of the Eulerian impulse density with the velocity. We provide a comparative discussion of the flow equations in their Eulerian and Lagrangian form and describe how these forms occur naturally in the context of optimal control. We demonstrate that the extremal equations corresponding to the optimal control problem for the flow have a natural canonical symplectic structure.Comment: 6 pages, no figures. To appear in Proceedings of the 39th IEEEE Conference on Decision and Contro

Development of a long life thermal cell Final report

Development of long life thermal cells, environmental and electrochemical performance tests to evaluate their capability and reproductibilit

Aerodynamic test results of bicycle helmets in different configurations: Towards a responsive design

© IMechE 2019. Within the sport of cycling, aerodynamic efficiency is a fundamental criterion for equipment such as bicycle frames, wheels, clothing and helmets. Emerging technologies continually challenge the rules governing the sport as designers, engineers, sports scientists and athletes attempt to gain the edge on their competition. This study compares three-dimensional (3D) printed bicycle helmet prototypes with three commercially available helmets via aerodynamic testing in a wind tunnel. One 3D printed helmet featured a mechanical mechanism allowing two states of ventilation closure to be examined for aerodynamic efficiency, while the other featured electronically adjustable ventilation openings tested at five different states of ventilation closure. Data were collected using an anthropometrically accurate mannequin sitting atop a bicycle in a road-cycling position. The results found that the mechanically controlled prototype offered a 4.1% increase in overall drag experienced by the mannequin with ventilation in the open position compared to the closed position. The electronic prototype showed an increase in drag as ventilation openings increased through the five states, with an overall difference in drag of 3.7% between closed and the maximum opening. These experimental findings indicate that the responsive helmet prototypes can significantly affect the drag force on a cyclist between their closed and open positions and, when understood as being adaptable using sensors and automated controls, may provide new opportunities to modify athlete performance throughout varying stages of training and competition

Regeneration of Old Ungrazed Old Man Saltbush (\u3ci\u3eAtriplex nummularia\u3c/i\u3e) Stands in South-West Australia

Many old man saltbush (Atriplex nummularia) stands were sown in the grainbelt of Western Australia for soil regeneration and salinity management up to 25 years ago, but have not been effectively grazed subsequently, such that the main feed available for sheep is above grazing height. The aim of the study was therefore to see if it was possible to return the old man saltbush stands to a productive grazing stand. Two sites were chosen that had been sown up to 25 years previously in Goomalling and Corrigin, in the south-west of Western Australia. The sites were split into four treatments that would reduce the height of the stands and bring all grazing material back to less than 1.2 m (the maximum grazing height for sheep in Australia); cutting to 0.5 m, cutting to 1 m, rolling to ground level, and a uncut control. Available feed above and below 1.2 m was assessed before cutting or rolling and then four times over the next two years. The results found that all three treatments removed feed above 1.2 m and that after 2 years the amount of feed below 1.2 m was increasing. The greatest feed available below 1.2 m was in the rolled treatment, followed by cutting to 0.5 m. Cutting old man saltbush stands to 1 m provides greater feed on the plants after cutting, but within one year of cutting some of the new feed is already above grazing height. It is concluded there is potential to return old established stands of old man saltbush to a productive grazing stand

Development of a long life thermal cell Status report no. 1

Quality control program and cell construction flow chart for development of 50 ampere hour thermal cell with copper oxide cathod

Sublinear Estimation of Weighted Matchings in Dynamic Data Streams

This paper presents an algorithm for estimating the weight of a maximum weighted matching by augmenting any estimation routine for the size of an unweighted matching. The algorithm is implementable in any streaming model including dynamic graph streams. We also give the first constant estimation for the maximum matching size in a dynamic graph stream for planar graphs (or any graph with bounded arboricity) using $\tilde{O}(n^{4/5})$ space which also extends to weighted matching. Using previous results by Kapralov, Khanna, and Sudan (2014) we obtain a $\mathrm{polylog}(n)$ approximation for general graphs using $\mathrm{polylog}(n)$ space in random order streams, respectively. In addition, we give a space lower bound of $\Omega(n^{1-\varepsilon})$ for any randomized algorithm estimating the size of a maximum matching up to a $1+O(\varepsilon)$ factor for adversarial streams

Detection of Coulomb Charging around an Antidot in the Quantum Hall Regime

We have detected oscillations of the charge around a potential hill (antidot) in a two-dimensional electron gas as a function of a large magnetic field B. The field confines electrons around the antidot in closed orbits, the areas of which are quantised through the Aharonov-Bohm effect. Increasing B reduces each state's area, pushing electrons closer to the centre, until enough charge builds up for an electron to tunnel out. This is a new form of the Coulomb blockade seen in electrostatically confined dots. Addition and excitation spectra in DC bias confirm the Coulomb blockade of tunnelling.Comment: 4 pages, 4 Postscript figure

A variational problem on Stiefel manifolds

In their paper on discrete analogues of some classical systems such as the rigid body and the geodesic flow on an ellipsoid, Moser and Veselov introduced their analysis in the general context of flows on Stiefel manifolds. We consider here a general class of continuous time, quadratic cost, optimal control problems on Stiefel manifolds, which in the extreme dimensions again yield these classical physical geodesic flows. We have already shown that this optimal control setting gives a new symmetric representation of the rigid body flow and in this paper we extend this representation to the geodesic flow on the ellipsoid and the more general Stiefel manifold case. The metric we choose on the Stiefel manifolds is the same as that used in the symmetric representation of the rigid body flow and that used by Moser and Veselov. In the extreme cases of the ellipsoid and the rigid body, the geodesic flows are known to be integrable. We obtain the extremal flows using both variational and optimal control approaches and elucidate the structure of the flows on general Stiefel manifolds.Comment: 30 page

NEXUS/Physics: An interdisciplinary repurposing of physics for biologists

In response to increasing calls for the reform of the undergraduate science curriculum for life science majors and pre-medical students (Bio2010, Scientific Foundations for Future Physicians, Vision & Change), an interdisciplinary team has created NEXUS/Physics: a repurposing of an introductory physics curriculum for the life sciences. The curriculum interacts strongly and supportively with introductory biology and chemistry courses taken by life sciences students, with the goal of helping students build general, multi-discipline scientific competencies. In order to do this, our two-semester NEXUS/Physics course sequence is positioned as a second year course so students will have had some exposure to basic concepts in biology and chemistry. NEXUS/Physics stresses interdisciplinary examples and the content differs markedly from traditional introductory physics to facilitate this. It extends the discussion of energy to include interatomic potentials and chemical reactions, the discussion of thermodynamics to include enthalpy and Gibbs free energy, and includes a serious discussion of random vs. coherent motion including diffusion. The development of instructional materials is coordinated with careful education research. Both the new content and the results of the research are described in a series of papers for which this paper serves as an overview and context.Comment: 12 page