The polyharmonic heat flow of closed plane curves

In this paper we consider the polyharmonic heat flow of a closed curve in the plane. Our main result is that closed initial data with initially small normalised oscillation of curvature and isoperimetric defect flows exponentially fast in the C^infty-topology to a simple circle. Our results yield a characterisation of the total amount of time during which the flow is not strictly convex, quantifying in a sense the failure of the maximum principle.Comment: 23 page

A novel continuously adjustable hydrodynamic bearing

A novel form of adjustable fluid film bearing has been devised whereby the hydrodynamic conditions can be changed in a continuously controlled manner during operation. The principle can be applied to conventionally orientated journal bearings, i.e. a shaft rotating within a stationary bearing housing; to inverse orientations, i.e. a rotor on a stationary shaft; and to thrust bearings. A theoretical model and computerised solution technique were developed in which the fluid film profile, temperature, viscosity and pressure fields were simultaneously solved. Experiments were conducted on journal bearing versions for which recently developed measurement techniques demonstrated stable operation at zero eccentricity, and the ability to move the rotational centre whilst in operation. Performance characteristics predicted by the computer model have been demonstrated in practice. The novel bearing has shown significant improvements over conventional designs in tems of stiffness, damping, rotational accuracy, power losses and temperature rise

Dynamical quantum phase transitions in the dissipative Lipkin-Meshkov-Glick model and proposed realization in optical cavity QED

We present an optical cavity QED configuration that is described by a dissipative version of the Lipkin-Meshkov-Glick model of an infinitely coordinated spin system. This open quantum system exhibits both first- and second-order non-equilibrium quantum phase transitions as a single, effective field parameter is varied. Light emitted from the cavity offers measurable signatures of the critical behavior, including that of the spin-spin entanglement.Comment: 4 pages, 4 figures, typos corrected and other minor change