51,456 research outputs found
Concentration of the distance between points in the unit ball
No full textWe prove that in every finite dimensional normed space, for “most” pairs (x, y) of points in the unit ball, ║x − y║ is more than √2(1 − ε). As a consequence, we obtain a result proved by Bourgain, using QS-decomposition, that guarantees an exponentially large number of points in the unit ball any two of which are separated by more than √2(1 − ε)
Stability of a spherical flame ball in a porous medium
No full textGaseous flame balls and their stability to symmetric disturbances are studied numerically and asymptotically, for large activation temperature, within a porous medium that serves only to exchange heat with the gas. Heat losses to a distant ambient environment, affecting only the gas, are taken to be radiative in nature and are represented using two alternative models. One of these treats the heat loss as being constant in the burnt gases and linearizes the radiative law in the unburnt gas (as has been studied elsewhere without the presence of a solid). The other does not distinguish between burnt and unburnt gas and is a continuous dimensionless form of Stefan's law, having a linear part that dominates close to ambient temperatures and a fourth power that dominates at higher temperatures.Numerical results are found to require unusually large activation temperatures in order to approach the asymptotic results. The latter involve two branches of solution, a smaller and a larger flame ball, provided heat losses are not too high. The two radiative heat loss models give completely analogous steady asymptotic solutions, to leading order, that are also unaffected by the presence of the solid which therefore only influences their stability. For moderate values of the dimensionless heat-transfer time between the solid and gas all flame balls are unstable for Lewis numbers greater than unity. At Lewis numbers less than unity, part of the branch of larger flame balls becomes stable, solutions with the continuous radiative law being stable over a narrower range of parameters. In both cases, for moderate heat-transfer times, the stable region is increased by the heat capacity of the solid in a way that amounts, simply, to decreasing an effective Lewis number for determining stability, just as if the heat-transfer time was zero
Generating ball trajectory in soccer video sequences
No full textThis paper demonstrates innovative techniques for estimating the trajectory of a soccer ball, using fixed cameras with constant calibration parameters. In contrast with broadcast coverage, for fixed camera data, the ball is often rendered with poor resolution away from the image centre. The rapidly moving ball is subject to motion-blur, caused by finite shutter speeds and interlaced fields, resulting in variable shape, size and colour. The velocity estimated from Kalman tracking is used in both normalising ball size and filtering the ball from false alarms. Furthermore, occlusion-reasoning and tracking-back methods are utilized to estimate its position when it is occluded, and also to remove false alarms. Finally, temporal hysteresis based thresholding of the ball likelihood is applied for trajectory filtering to improve the robustness and continuity of the tracked ball. Promising experimental results from several long sequences are reported
Tracking the soccer ball using multiple fixed cameras
No full textThis paper demonstrates innovative techniques for estimating the trajectory of a soccer ball from multiple fixed cameras. Since the ball is nearly always moving and frequently occluded, its size and shape appearance varies over time and between cameras. Knowledge about the soccer domain is utilized and expressed in terms of field, object and motion models to distinguish the ball from other movements in the tracking and matching processes. Using ground plane velocity, longevity, normalized size and color features, each of the tracks obtained from a Kalman filter is assigned with a likelihood measure that represents the ball. This measure is further refined by reasoning through occlusions and back-tracking in the track history. This can be demonstrated to improve the accuracy and continuity of the results. Finally, a simple 3D trajectory model is presented, and the estimated 3D ball positions are fed back to constrain the 2D processing for more efficient and robust detection and tracking. Experimental results with quantitative evaluations from several long sequences are reported
The specific selection function effect on clinker grinding efficiency in a dry batch ball mill
No full textDry grinding experiments on cement clinker were carried out using a laboratory batch ball mill equipped with a torque measurement. The influence of the ball size distribution on the specific selection function can be approached by laboratory runs using mono-size balls. The breakage is more efficient with maximal specific selection functions at the initial size reduction stage. But, in terms of cement finish grinding all stages of grinding are determinant for the production of a required Blaine surface area (3500 cm2/g). So, the choice of ball size according to a maximal specific selection function leads to an increase of the energy consumption. In addition, investigations on the mono-sized fractions and on the crude material (size minus 2.8 mm) demonstrate that the energy efficiency factor can be optimized using ball size corresponding to relatively low specific selection function
The 2010 regulations on golf groove design: impact on ball flight characteristics during a controlled shot.
No full textThe purpose of this study was to investigate the difference in the amount of spin that can be generated during a controlled golf shot, as a result of the 2010 rule change regarding restrictions applied to the design of the grooves on the clubface implemented by the United States Golf Association and the Royal & Ancient Golf Club. Ten experienced golfers (mean ± SD; age, 23.0 ± 0.67 yr; playing experience, 13.2 ± 1.6 yr; handicap, 1.6 ± 1.4) were required to play a total of 120 shots inside a state of the art golf simulator with 3 clubs consisting of ‘old’ pre 2010 U-groove design and ‘new’ post 2010 V-groove design. With the U and V grooved clubs, participants played 10 shots from a fairway mat and 10 shots from a rough mat using a 9 iron, PW and SW. Backspin (RPM) and, as a measure of accuracy, distance landed from the pin (yds) were recorded. Compared to the U-grooves, the newer V-groove design imparted significantly less backspin from both the fairway and rough surfaces (P < 0.05), additionally, shots with all clubs were consistently further away from the pin (P < 0.05). The newer groove design does not enable players to impart as much backspin on the ball as they previously could and our data suggest that the recent change in golf club design might therefore reward driving accuracy
Parametric impact characterisation of a solid sports ball, WITH a view to developing a standard core for the GAA Sliotar
No full textThe main aim of this research was to characterise the dynamic impact behaviour of the sliotar core. Viscoelastic characterisation of the balls was conducted for a range of impact speeds. Modern polymer balls exhibited strain and strain-rate sensitivity while traditional multi-compositional balls exhibited strain dependency. The non-linear viscoelastic response was defined by two values of stiffness, initial and bulk stiffness.
Traditional balls were up to 2.5 times stiffer than the modern types, with this magnitude being rate-dependent. The greater rate of increase of traditional ball stiffness produced a more non-linear COR velocity-dependence compared to modern balls. The dynamic stiffness results demonstrated limited applicability of quasi-static testing and springtheory equations. Analysis of ball deformation behaviour demonstrated that centre-of mass displacement and diameter compression values were not consistently equivalent for all ball types. The contribution of manufacturing conditions to ball performance was investigated by conducting extensive prototyping experiments. Manufacturing parameters of temperature, pressure and material composition were varied to produce a range of balls. Polymer hardness affected stiffness but not energy dissipation, with increased hardness increasing ball stiffness. The nucleating additive influenced ball COR, with increased additive tending to reduce ball COR, but this effect was sensitive to polymer grade. The impact response of the ball was simulated using three mathematical models. The first model was shown to replicate ball behaviour to only a limited degree, despite being used previously with reported success for other ball types. The second model exhibited a reasonable representation of ball impact response that was universally applicable to all tested ball types; however, the accuracy in terms of predicting force-displacement response was not as high as required for broad range implementation. The third model exhibited significantly better accuracy in simulating ball response. The force values generated from this model exhibited up to 95% agreement with experimental data
A novel eccentric lapping machine for finishing advanced ceramic balls
No full textAdvanced ceramic balls are used extensively in hybrid precision ball bearings and show advantages in high speed, high temperature, high load and hostile environment. Finishing these balls with high quality, good efficiency and low cost is critical to their widespread application. A brief review of the methods for finishing ceramic balls is presented. The design of a novel eccentric lapping machine for finishing advanced ceramic balls is described. The kinematics of eccentric lapping is analysed and discussed, the symbolic expressions for the ball spin angular speed, omega (b), ball spin angle, beta, and ball circulation angular speed, omega (c), are derived and numerical solutions are plotted. Two kinds of hot isostatically pressed (HIPed) silicon nitride ball blanks (13.25-13.50 mm in diameter) were lapped and polished to 12.700 mm using this machine. A maximum material removal rate of 68 mum/h was achieved at the lapping step, which is much higher than by the traditional concentric lapping method. The polished ball surface roughness, R-a, value is 0.003 mum, and the ball roundness is 0.08-0.09 mum, which is above grade 5 and close to grade 3 of the precision bearing ball specification. This machine can be used as a prototype to develop a larger-scale machine for production
The collapse of single bubbles and approximation of the far-field acoustic emissions for cavitation induced by shock wave lithotripsy
No full textRecent clinical trials have shown the efficacy of a passive acoustic device used during shock wave lithotripsy (SWL) treatment. The device uses the far-field acoustic emissions resulting from the interaction of the therapeutic shock waves with the tissue and kidney stone to diagnose the effectiveness of each shock in contributing to stone fragmentation. This paper details simulations that supported the development of that device by extending computational fluid dynamics (CFD) simulations of the flow and near-field pressures associated with shock-induced bubble collapse to allow estimation of those far-field acoustic emissions. This is a required stage in the development of the device, because current computational resources are not sufficient to simulate the far-field emissions to ranges of O(10 cm) using CFD. Similarly, they are insufficient to cover the duration of the entire cavitation event, and here simulate only the first part of the interaction of the bubble with the lithotripter shock wave in order to demonstrate the methods by which the far-field acoustic emissions resulting from the interaction can be estimated. A free-Lagrange method (FLM) is used to simulate the collapse of initially stable air bubbles in water as a result of their interaction with a planar lithotripter shock. To estimate the far-field acoustic emissions from the interaction, this paper developed two numerical codes using the Kirchhoff and Ffowcs William–Hawkings (FW-H) formulations. When coupled to the FLM code, they can be used to estimate the far-field acoustic emissions of cavitation events. The limitation of the technique is that it assumes that no significant nonlinear acoustic propagation occurs outside the control surface. Methods are outlined for ameliorating this problem if, as here, computational resources cannot compute the flow field to sufficient distance, although for the clinical situation discussed, this limitation is tempered by the effect of tissue absorption, which here is incorporated through the standard derating procedure. This approach allowed identification of the sources of, and explanation of trends seen in, the characteristics of the far-field emissions observed in clinic, to an extent that was sufficient for the development of this clinical device
"Closing the R&D Gap, Evaluating the Sources of R&D Spending"
No full textBoth spending and tax policies have been implemented in the United States with the goal of stimulating private sector research and development (R&D). Karier questions whether current R&D policy, especially the research and experimentation tax credit, can contribute to closing the gap between nondefense expenditures on R&D in the United States and such expenditures in other countries, such as Japan and Germany. He also explores possible changes to our current R&D policy to make it more effective.
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