From Switching Arcs to Ball Lightning to Curing Cancer!

Previous modelling of switching has been through calculation of reductions in temperature of the arc at "current zero". "Enthalpy density" as a function of temperature is found to be an important property. New calculations now include an account of non-equilibrium electron density as a function of time through current zero and it is found that electron attachment rates, which are very large for SF6, could be a dominant property. Modelling discharges is having other successes, for example in explaining "ball lightning" observations inside of houses and aircraft, which suddenly appear, usually at glass windows. Discharge modelling suggests these observations might be explained by the production of "singlet delta" metastable molecules of oxygen in electrical discharges in air. If metastable densities are sufficient, electrons can be produced from the detachment of negative ions to produce radiation and explain ball lightning. An exciting new development is that plasmas from electric corona in air have been found to reduce the size of cancer tumours. These excited oxygen molecules have also been proposed as having a role in this remarkable interchange between classical electrical engineering and medical science

Tractable Quantification of Metastability for Robust Bipedal Locomotion

This work develops tools to quantify and optimize performance metrics for bipedal walking, toward enabling improved practical and autonomous operation of two-legged robots in real-world environments. While speed and energy efficiency of legged locomotion are both useful and straightforward to quantify, measuring robustness is arguably more challenging and at least as critical for obtaining practical autonomy in variable or otherwise uncertain environmental conditions, including rough terrain. The intuitive and meaningful robustness quantification adopted in this thesis begins by stochastic modeling of disturbances such as terrain variations, and conservatively defining what a failure is, for example falling down, slippage, scuffing, stance foot rotation, or a combination of such events. After discretizing the disturbance and state sets by meshing, step-to-step dynamics are studied to treat the system as a Markov chain. Then, failure rates can be easily quantified by calculating the expected number of steps before failure. Once robustness is measured, other performance metrics can also be easily incorporated into the cost function for optimization.For high performance and autonomous operation under variations, we adopt a capacious framework, exploiting a hierarchical control structure. The low-level controllers, which use only proprioceptive (internal state) information, are optimized by a derivative-free method without any constraints. For practicability of this process, developing an algorithm for fast and accurate computation of our robustness metric was a crucial and necessary step. While the outcome of optimization depends on capabilities of the controller scheme employed, the convenient and time-invariant parameterization presented in this thesis ensures accommodating large terrain variations. In addition, given environment estimation and state information, the high-level control is a behavioral policy to choose the right low-level controller at each step. In this thesis, optimal switching policies are determined by applying dynamic programming tools on Markov decision processes obtained through discretization. For desirable performance in practice from policies that are formed using meshing-based approximation to the true dynamics, robustness of high-level control to environment estimation and discretization errors are ensured by modeling stochastic noise in the terrain information and belief state while solving for behavioral policies

Robustness: a new SLIP model based criterion for gait transitions in bipedal locomotion

Bipedal locomotion is a phenomenon that still eludes a fundamental and concise mathematical understanding. Conceptual models that capture some relevant aspects of the process exist but their full explanatory power is not yet exhausted. In the current study, we introduce the robustness criterion which defines the conditions for stable locomotion when steps are taken with imprecise angle of attack. Intuitively, the necessity of a higher precision indicates the difficulty to continue moving with a given gait. We show that the spring-loaded inverted pendulum model, under the robustness criterion, is consistent with previously reported findings on attentional demand during human locomotion. This criterion allows transitions between running and walking, many of which conserve forward speed. Simulations of transitions predict Froude numbers below the ones observed in humans, nevertheless the model satisfactorily reproduces several biomechanical indicators such as hip excursion, gait duty factor and vertical ground reaction force profiles. Furthermore, we identify reversible robust walk-run transitions, which allow the system to execute a robust version of the hopping gait. These findings foster the spring-loaded inverted pendulum model as the unifying framework for the understanding of bipedal locomotion.Comment: unpublished, in preparatio