Self-similar solutions to the mean curvature flow in R3\mathbb{R}^{3}

In this paper we make an analysis of self-similar solutions for the mean curvature flow (MCF) by surfaces of revolution and ruled surfaces in $\mathbb{R}^{3}$. We prove that self-similar solutions of the MCF by non-cylindrival surfaces and conical surfaces in $\mathbb{R}^{3}$ are trivial. Moreover, we characterize the self-similar solutions of the MCF by surfaces of revolutions under a homothetic helicoidal motion in $\mathbb{R}^{3}$ in terms of the curvature of the generating curve. Finally, we characterize the self-similar solutions for the MCF by cylindrical surfaces under a homothetic helicoidal motion in $\mathbb{R}^3$. Explicit families of exact solutions for the MCF by cylindrical surfaces in $\mathbb{R}^{3}$ are also given

Fixed Points of the Dissipative Hofstadter Model

The phase diagram of a dissipative particle in a periodic potential and a magnetic field is studied in the weak barrier limit and in the tight-biding regime. For the case of half flux per plaquette, and for a wide range of values of the dissipation, the physics of the model is determined by a non trivial fixed point. A combination of exact and variational results is used to characterize this fixed point. Finally, it is also argued that there is an intermediate energy scale that separates the weak coupling physics from the tight-binding solution.Comment: 4 pages 3 figure

Historical Roots of Histrionic Personality Disorder

Histrionic Personality Disorder is one of the most ambiguous diagnostic categories in psychiatry. Hysteria is a classical term that includes a wide variety of psychopathological states. Ancient Egyptians and Greeks blamed a displaced womb, for many women's afflictions. Several researchers from the 18th and 19th centuries studied this theme, namely, Charcot who defined hysteria as a "neurosis" with an organic basis and Sigmund Freud who redefined "neurosis" as a re-experience of past psychological trauma. Histrionic personality disorder (HPD) made its first official appearance in the Diagnostic and Statistical Manual of Mental Disorders II (DSM-II) and since the DSM-III, HPD is the only disorder that kept the term derived from the old concept of hysteria. The subject of hysteria has reflected positions about health, religion and relationships between the sexes in the last 4000 years, and the discussion is likely to continue

An experimental study on the aerodynamic loads of a floating offshore wind turbine under imposed motions

The rotor of a floating wind turbine is subject to complex aerodynamics due to changes in relative wind speeds at the blades and potential local interactions between blade sections and the rotor near wake. These complex interactions are not yet fully understood. Lab-scale experiments are highly relevant for capturing these phenomena and provide means for the validation of numerical design tools. This paper presents a new wind tunnel experimental setup able to study the aerodynamic response of a wind turbine rotor when subjected to prescribed motions. The present study uses a 1:148 scale model of the DTU 10 MW reference wind turbine mounted on top of a 6 degrees of freedom parallel kinematic robotic platform. Firstly, the thrust variation of the turbine is investigated when single degree of freedom harmonic motions are imposed by the platform, with surge, pitch and yaw being considered in this study. For reduced frequencies greater than 1.2, it is found that the thrust variation is amplified by up to 150 % compared to the quasi-steady value when the turbine is subject to pitch and surge motions, regardless of the amplitude of motion. A similar behaviour is also noticed under yaw motions. Secondly, realistic 6 degrees of freedom motions are imposed by the platform. The motions are derived from FAST simulations performed on the full-scale turbine coupled with the TripleSpar floater, and the tests aim at exploring the thrust force dynamics for different sea states and wind conditions, obtaining reasonable agreement with the simulations. Finally, the work shows the capabilities of an off-the-shelf hexapod to conduct hybrid testing of floating offshore wind turbines in wind tunnels, as well as its limitations in performing such tests.</p

Controller design for model-scale rotors and validation using prescribed motion

Aerodynamic-load calculation in aero-hydro-servo-elastic modeling tools has been recently validated against experiments for low-frequency platform motions but without considering the capability of active wind turbine controls. This work presents a control design framework that allows for including industry-standard wind turbine control functionalities in a model-scale rotor and its application to a 1:100 scaled version of the International Energy Agency (IEA) 15 MW turbine. Wind tunnel tests with a fixed foundation and steady wind show the scaled turbine reproduces the steady-state rotor speed–blade pitch–thrust–torque characteristics of the IEA 15 MW turbine, confirming the controller design method. Tests with a prescribed platform pitch motion are carried out to assess the turbine response and controller modeling in conditions representative of the normal operation of floating wind turbines. The blade element momentum model of OpenFAST is verified against the experiment, showing aerodynamic thrust and torque are predicted with higher accuracy in the below-rated than the above-rated region: in our simulation, the decrease in thrust oscillation amplitude due to blade pitch actuation is underpredicted. This, combined with uncertainty in modeling the blade pitch actuators, complicates the numerical–experimental simulation of the turbine aerodynamic response in above-rated operation.</p