Curvature contraction flows in the sphere

We show that convex surfaces in an ambient three-sphere contract to round points in finite time under fully nonlinear, degree one homogeneous curvature flows, with no concavity condition on the speed. The result extends to convex axially symmetric hypersurfaces of the (n+1)-dimensional sphere. Using a different pinching function we also obtain the analogous results for contraction by Gauss curvature

Brushless Direct Current Motor Control for Inspired Flight

Brushless direct current motors have become a very common part of many modern electronics. Although they are more expensive and less robust than conventional brushed direct current motors, they provide large advantages in control, power output, longevity as well as efficiency. To make these motors run, they need more than just power. Each motor needs a separate motor controller that is responsible for taking in a signal for what speed/torque to run the motor at, and then managing the current flow to the motor to keep it spinning while fitting within these boundaries. Brushless direct current motors have a set of pairs of poles that act as electromagnets that need to be turned on and off at very certain times to start and then spin the motor. There are a variety of control strategies, each with their benefits and shortcomings, to facilitate startup and operation. This paper will examine fixed as well as dynamic startup strategies, as well as six step and field oriented motor control strategies with code samples to show implementations. Fixed startup is easier to implement as it just runs a startup script over and over again until there is readable feedback from the motor, but dynamic can allow for a more controlled and faster startup that rarely has to reset entirely. Once spinning, field oriented control provides the most control but requires extra hardware and/or more processing power than six step alternatives but can be challenging to set up on a new motor. For drone applications, a combination of fixed startup scripts with field oriented control makes for the best control strategy by balancing complexity with improved control when you really need it

The physical properties of magnetic inks

The magnetic particle inspection (MPI) method is a widely used non destructive testing (NDT) technique for ferrous structures. Magnetic inks used in MPI are suspensions of fine ferro/ferrimagnetic particles which, when applied to a magnetized test specimen, delineate surface flaws. This work is an investigation of some of the properties of magnetic ink systems and some aspects of their interaction with defect leakage flux. Reviews of magnetism, the MPI method and leakage flux at defects are given. The construction, characterization and automation of a 1.2 T electromagnet vibrating sample magnetometer, used for magnetic measurements on the inks, is described. The instrument has a resolution of better than l0(^-9) JT(^-1) . A 2D model of indication formation in MPI, based upon the simulation of many particles in the neighbourhood of a defect, is presented. Results of the role of several of the model parameters are given. Results indicate that carrier coefficients of viscosity at the lower end of the range investigated (η = 0.3 mPas) are optimum. The size and contrast of an indication increases with defect size. The contrast and rate of formation of contrast increase with defect aspect ratio. The effect of the contrast paint layer thickness indicates that the recommendation of the British Standard, BS 5044 (1973), is qualitatively correct. Experimental observations of particles in field gradients reveals a discrepancy between theoretical and observed behaviour which is attributed, in particular, to unobservable voids in the particles. Detailed characterization of the particles shows them to be aggregates of 20 - 200 nm crystallites which are probably single domain particles. The morphology of larger aggregates is related to measurements of the low field susceptibility. Evidence from intensive magnetic measurements supports the relationship between magnetic properties and aggregate characteristics. A 'In t' magnetic viscosity effect is reported. At 77 K, the coefficient of magnetic viscosity has a maximum near the coercivity field