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Feb 12

Drift surface solver for runaway electron current dominant equilibria during the Current Quench

Runaway electron current generated during the Current Quench phase of tokamak disruptions could result in severe damage to future high performance devices. To control and mitigate such runaway electron current, it is important to accurately describe the runaway electron current dominated equilibrium, based on which further stability analysis could be carried out. In this paper, we derive a Grad-Shafranov-like equation solving for the axisymmetric drift surfaces of the runaway electrons for the simple case that all runaway electron share the same parallel momentum. This new equilibrium equation is then numerically solved with simple rectangular wall with ITER-like and MAST-like geometry parameters. The deviation between the drift surfaces and the flux surfaces is readily obtained, and runaway electrons is found to be well confined even in regions with open field lines. The change of the runaway electron parallel momentum is found to result in a horizontal current center displacement without any changes in the total current or the external field. The runaway current density profile is found to affect the susceptibility of such displacement, with flatter profiles result in more displacement by the same momentum change. With up-down asymmetry in the external poloidal field, such displacement is accompanied by a vertical displacement of runaway electron current. It is found that this effect is more pronounced in smaller, compact device and weaker poloidal field cases. The above results demonstrate the dynamics of current center displacement caused by the momentum space change in the runaway electrons, and pave way for future, more sophisticated runaway current equilibrium theory with more realistic consideration on the runaway electron momentum distribution. This new equilibrium theory also provides foundation for future stability analysis of the runaway electron current.

  • 2 authors
·
Mar 2, 2023

Size and shape of terrestrial animals

Natural selection for terrestrial locomotion has yielded unifying patterns in the body shape of legged animals, often manifesting as scaling laws. One such pattern appears in the frontal aspect ratio. Smaller animals like insects typically adopt a landscape frontal aspect ratio, with a wider side-to-side base of support than center of mass height. Larger animals like elephants, however, are taller than wide with a portrait aspect ratio. Known explanations for postural scaling are restricted to animal groups with similar anatomical and behavioural motifs, but the trend in frontal aspect ratio transcends such commonalities. Here we show that vertebrates and invertebrates with diverse body plans, ranging in mass from 28 mg to 22000 kg, exhibit size-dependent scaling of the frontal aspect ratio driven by the need for lateral stability on uneven natural terrain. Because natural terrain exhibit scale-dependent unevenness, and the frontal aspect ratio is important for lateral stability during locomotion, smaller animals need a wider aspect ratio for stability. This prediction is based on the fractal property of natural terrain unevenness, requires no anatomical or behavioural parameters, and agrees with the measured scaling despite vast anatomical and behavioural differences. Furthermore, a statistical phylogenetic comparative analysis found that shared ancestry and random trait evolution cannot explain the measured scaling. Thus, our findings reveal that terrain roughness, acting through natural selection for stability, likely drove the macroevolution of frontal shape in terrestrial animals.

  • 2 authors
·
Jan 31

A review of path following control strategies for autonomous robotic vehicles: theory, simulations, and experiments

This article presents an in-depth review of the topic of path following for autonomous robotic vehicles, with a specific focus on vehicle motion in two dimensional space (2D). From a control system standpoint, path following can be formulated as the problem of stabilizing a path following error system that describes the dynamics of position and possibly orientation errors of a vehicle with respect to a path, with the errors defined in an appropriate reference frame. In spite of the large variety of path following methods described in the literature we show that, in principle, most of them can be categorized in two groups: stabilization of the path following error system expressed either in the vehicle's body frame or in a frame attached to a "reference point" moving along the path, such as a Frenet-Serret (F-S) frame or a Parallel Transport (P-T) frame. With this observation, we provide a unified formulation that is simple but general enough to cover many methods available in the literature. We then discuss the advantages and disadvantages of each method, comparing them from the design and implementation standpoint. We further show experimental results of the path following methods obtained from field trials testing with under-actuated and fully-actuated autonomous marine vehicles. In addition, we introduce open-source Matlab and Gazebo/ROS simulation toolboxes that are helpful in testing path following methods prior to their integration in the combined guidance, navigation, and control systems of autonomous vehicles.

  • 9 authors
·
Apr 14, 2022