Vortex sheet dynamics and turbulence

The nonlinear evolution of a vortex sheet driven by the Kelvin--Helmholtz instability is characterized by the formation of a spiral possessing complex stretching and intensity patterns. We show that the power energy spectrum of a single two-dimensional vortex sheet tends to the usual fluid turbulent spectrum, with an exponent of -3. Using numerical simulations and asymptotic methods, we demonstrate the relation between this power law and the singularities in the geometry and vorticity distribution of the sheet.Comment: Submitted to Phys. Rev. Letters, the Dynamique des vortex Collaboratio

High-speed spiral imaging technique for an atomic force microscope using a linear quadratic Gaussian controller

This paper demonstrates a high-speed spiral imaging technique for an atomic force microscope (AFM). As an alternative to traditional raster scanning, an approach of gradient pulsing using a spiral line is implemented and spirals are generated by applying single-frequency cosine and sine waves of slowly varying amplitudes to the X and Y-axes of the AFM's piezoelectric tube scanner (PTS). Due to these single-frequency sinusoidal input signals, the scanning process can be faster than that of conventional raster scanning. A linear quadratic Gaussian controller is designed to track the reference sinusoid and a vibration compensator is combined to damp the resonant mode of the PTS. An internal model of the reference sinusoidal signal is included in the plant model and an integrator for the system error is introduced in the proposed control scheme. As a result, the phase error between the input and output sinusoids from the X and Y-PTSs is reduced. The spirals produced have particularly narrow-band frequency measures which change slowly over time, thereby making it possible for the scanner to achieve improved tracking and continuous high-speed scanning rather than being restricted to the back and forth motion of raster scanning. As part of the post-processing of the experimental data, a fifth-order Butterworth filter is used to filter noises in the signals emanating from the position sensors and a Gaussian image filter is used to filter the images. A comparison of images scanned using the proposed controller (spiral) and the AFM PI controller (raster) shows improvement in the scanning rate using the proposed method

Detection of a Corrugated Velocity Pattern in the Spiral Galaxy NGC 5427

Here we report the detection, in Halpha emission, of a radial corrugation in the velocity field of the spiral galaxy NGC 5427. The central velocity of the Halpha line displays coherent, wavy-like variations in the vicinity of the spiral arms. The spectra along three different arm segments show that the maximum amplitude of the sinusoidal line variations are displaced some 500 pc from the central part of the spiral arms. The peak blueshifted velocities appear some 500 pc upstream the arm, whereas the peak redshifted velocities are located some 500 pc downstream the arm. This kinematical behavior is similar to the one expected in a galactic bore generated by the interaction of a spiral density wave with a thick gaseous disk, as recently modeled by Martos & Cox (1998).Comment: Accepted for publication in Ap

Controlling Tensegrity Robots Through Evolution

Tensegrity structures (built from interconnected rods and cables) have the potential to offer a revolutionary new robotic design that is light-weight, energy-efficient, robust to failures, capable of unique modes of locomotion, impact tolerant, and compliant (reducing damage between the robot and its environment). Unfortunately robots built from tensegrity structures are difficult to control with traditional methods due to their oscillatory nature, nonlinear coupling between components and overall complexity. Fortunately this formidable control challenge can be overcome through the use of evolutionary algorithms. In this paper we show that evolutionary algorithms can be used to efficiently control a ball-shaped tensegrity robot. Experimental results performed with a variety of evolutionary algorithms in a detailed soft-body physics simulator show that a centralized evolutionary algorithm performs 400 percent better than a hand-coded solution, while the multi-agent evolution performs 800 percent better. In addition, evolution is able to discover diverse control solutions (both crawling and rolling) that are robust against structural failures and can be adapted to a wide range of energy and actuation constraints. These successful controls will form the basis for building high-performance tensegrity robots in the near future

An Analysis of Harmonic Airloads Acting on Helicopter Rotor Blades

Rotary wing aircrafts in any flight conditions suffer from excessive vibration which makes the passengers feel uncomfortable and causes fatigue failure in the structure. The main sources of vibration are the rotor harmonic airloads which originate primarily from the rapid variation of flow around the blade due to the vortex wake. In this thesis, a mathematical model is developed for rotor blades to compute the harmonic airloads at rotor blades for two flight conditions vertical takeoff and landing, and forward flight. The sectional lift, drag, and pitching moment are computed at a radial blade station for both flight conditions. The lift at a particular radial station is computed considering trailing and shed vortices and summing over each blade. The results for airloads are obtained after considering zeroth, first, and second harmonics. The calculated results for airloads are compared to the experimental flight-test data