Dynamical properties of a particle in a wave packet: scaling invariance and boundary crisis

Some dynamical properties present in a problem concerning the acceleration of particles in a wave packet are studied. The dynamics of the model is described in terms of a two-dimensional area preserving map. We show that the phase space is mixed in the sense that there are regular and chaotic regions coexisting. We use a connection with the standard map in order to find the position of the first invariant spanning curve which borders the chaotic sea. We find that the position of the first invariant spanning curve increases as a power of the control parameter with the exponent 2/3. The standard deviation of the kinetic energy of an ensemble of initial conditions obeys a power law as a function of time, and saturates after some crossover. Scaling formalism is used in order to characterize the chaotic region close to the transition from integrability to nonintegrability and a relationship between the power law exponents is derived. The formalism can be applied in many different systems with mixed phase space. Then, dissipation is introduced into the model and therefore the property of area preservation is broken, and consequently attractors are observed. We show that after a small change of the dissipation, the chaotic attractor as well as its basin of attraction are destroyed, thus leading the system to experience a boundary crisis. The transient after the crisis follows a power law with exponent -2.Comment: Chaos, Solitons & Fractals, 201

A flowing plasma model to describe drift waves in a cylindrical helicon discharge

A two-fluid model developed originally to describe wave oscillations in the vacuum arc centrifuge, a cylindrical, rapidly rotating, low temperature and confined plasma column, is applied to interpret plasma oscillations in a RF generated linear magnetised plasma (WOMBAT), with similar density and field strength. Compared to typical centrifuge plasmas, WOMBAT plasmas have slower normalised rotation frequency, lower temperature and lower axial velocity. Despite these differences, the two-fluid model provides a consistent description of the WOMBAT plasma configuration and yields qualitative agreement between measured and predicted wave oscillation frequencies with axial field strength. In addition, the radial profile of the density perturbation predicted by this model is consistent with the data. Parameter scans show that the dispersion curve is sensitive to the axial field strength and the electron temperature, and the dependence of oscillation frequency with electron temperature matches the experiment. These results consolidate earlier claims that the density and floating potential oscillations are a resistive drift mode, driven by the density gradient. To our knowledge, this is the first detailed physics model of flowing plasmas in the diffusion region away from the RF source. Possible extensions to the model, including temperature non-uniformity and magnetic field oscillations, are also discussed

Deck the Walls with Anisotropic Colloids in Nematic Liquid Crystals.

Nematic liquid crystals (NLCs) offer remarkable opportunities to direct colloids to form complex structures. The elastic energy field that dictates colloid interactions is determined by the NLC director field, which is sensitive to and can be controlled by boundaries including vessel walls and colloid surfaces. By molding the director field via liquid-crystal alignment on these surfaces, elastic energy landscapes can be defined to drive structure formation. We focus on colloids in otherwise defect-free director fields formed near undulating walls. Colloids can be driven along prescribed paths and directed to well-defined docking sites on such wavy boundaries. Colloids that impose strong alignment generate topologically required companion defects. Configurations for homeotropic colloids include a dipolar structure formed by the colloid and its companion hedgehog defect or a quadrupolar structure formed by the colloid and its companion Saturn ring. Adjacent to wavy walls with wavelengths larger than the colloid diameter, spherical particles are attracted to locations along the wall with distortions in the nematic director field that complement those from the colloid. This is the basis of lock-and-key interactions. Here, we study ellipsoidal colloids with homeotropic anchoring near complex undulating walls. The walls impose distortions that decay with distance from the wall to a uniform director in the far field. Ellipsoids form dipolar defect configurations with the colloid's major axis aligned with the far field director. Two distinct quadrupolar defect structures also form, stabilized by confinement; these include the Saturn I configuration with the ellipsoid's major axis aligned with the far field director and the Saturn II configuration with the major axis perpendicular to the far field director. The ellipsoid orientation varies only weakly in bulk and near undulating walls. All configurations are attracted to walls with long, shallow waves. However, for walls with wavelengths that are small compared to the colloid length, Saturn II is repelled, allowing selective docking of aligned objects. Deep, narrow wells prompt the insertion of a vertical ellipsoid. By introducing an opening at the bottom of such a deep well, we study colloids within pores that connect two domains. Ellipsoids with different aspect ratios find different equilibrium positions. An ellipsoid of the right dimension and aspect ratio can plug the pore, creating a class of 2D selective membranes

Pair plasma cushions in the hole-boring scenario

Pulses from a 10 PW laser are predicted to produce large numbers of gamma-rays and electron-positron pairs on hitting a solid target. However, a pair plasma, if it accumulates in front of the target, may partially shield it from the pulse. Using stationary, one-dimensional solutions of the two-fluid (electron-positron) and Maxwell equations, including a classical radiation reaction term, we examine this effect in the hole-boring scenario. We find the collective effects of a pair plasma "cushion" substantially reduce the reflectivity, converting the absorbed flux into high-energy gamma-rays. There is also a modest increase in the laser intensity needed to achieve threshold for a non-linear pair cascade.Comment: 17 pages, 5 figures. Accepted for publication in Plasma Physics and Controlled Fusion. Typos corrected, reference update

Chaotification as a Means of Broadband Vibration Energy Harvesting with Piezoelectric Materials

Computing advances and component miniaturization in circuits coupled with stagnating battery technology have fueled growth in the development of high efficiency energy harvesters. Vibration-to-electricity energy harvesting techniques have been investigated extensively for use in sensors embedded in structures or in hard-to-reach locations like turbomachinery, surgical implants, and GPS animal trackers. Piezoelectric materials are commonly used in harvesters as they possess the ability to convert strain energy directly into electrical energy and can work concurrently as actuators for damping applications. The prototypical harvesting system places two piezoelectric patches on both sides of the location of maximum strain on a cantilever beam. While efficient around resonance, performance drops dramatically should the driving frequency drift away from the beam\u27s fundamental frequency. To date, researchers have worked to improve harvesting capability by modifying material properties, using alternative geometries, creating more efficient harvesting circuits, and inducing nonlinearities. These techniques have partially mitigated the resonance excitation dependence for vibration-based harvesting, but much work remains. In this dissertation, an induced nonlinearity destabilizes a central equilibrium point, resulting in a bistable potential function governing the cantilever beam system. Depending on the environment, multiple stable solutions are possible and can coexist. Typically, researchers neglect chaos and assume that with enough energy in the ambient environment, large displacement trajectories can exist uniquely. When subjected to disturbances a system can fall to coexistent lower energy solutions including aperiodic, chaotic oscillations. Treating chaotic motion as a desirable behavior of the system allows frequency content away from resonance to produce motion about a theoretically infinite number of unstable periodic orbits that can be stabilized through control. The extreme sensitivity to initial conditions exhibited by chaotic systems paired with a pole placement control strategy pioneered by Ott, Grebogi, and Yorke permits small perturbations to an accessible system parameter to alter the system response dramatically. Periodic perturbation of the system trajectories in the vicinity of isolated unstable orbit points can therefore stabilize low-energy chaotic oscillations onto larger trajectory orbits more suitable for energy harvesting. The periodic perturbation-based control method rids the need of a system model. It only requires discrete displacement, velocity, or voltage time series data of the chaotic system driven by harmonic excitation. While the analysis techniques are not fundamentally limited to harmonic excitation, this condition permits the use of standard discrete mapping techniques to isolate periodic orbits of interest. Local linear model fits characterize the orbit and admit the necessary control perturbation calculations from the time series data. This work discusses the feasibility of such a method for vibration energy harvesting, displays stable solutions under various control algorithms, and implements a hybrid bench-top experiment using MATLAB and LabVIEW FPGA. In conclusion, this work discusses the limitations for wide-scale use and addresses areas of further work; both with respect to chaotic energy harvesting and parallel advances required within the field as a whole