Bispectral and trispectral characterization of transition to chaos in the Duffing oscillator

Higher-order spectral (bispectral and trispectral) analyses of numerical solutions of the Duffing equation with a cubic stiffness are used to isolate the coupling between the triads and quartets, respectively, of nonlinearly interacting Fourier components of the system. The Duffing oscillator follows a period-doubling intermittency catastrophic route to chaos. For period-doubled limit cycles, higher-order spectra indicate that both quadratic and cubic nonlinear interactions are important to the dynamics. However, when the Duffing oscillator becomes chaotic, global behavior of the cubic nonlinearity becomes dominant and quadratic nonlinear interactions are weak, while cubic interactions remain strong. As the nonlinearity of the system is increased, the number of excited Fourier components increases, eventually leading to broad-band power spectra for chaos. The corresponding higher-order spectra indicate that although some individual nonlinear interactions weaken as nonlinearity increases, the number of nonlinearly interacting Fourier modes increases. Trispectra indicate that the cubic interactions gradually evolve from encompassing a few quartets of Fourier components for period-1 motion to encompassing many quartets for chaos. For chaos, all the components within the energetic part of the power spectrum are cubically (but not quadratically) coupled to each other.

Steady state genuine multipartite entanglement in harmonic oscillator ensembles with a common environment

Steady state entanglement in ensembles of harmonic oscillators with a common squeezed reservoir is studied. Under certain conditions the ensemble features genuine multipartite entanglement in the steady state. Several analytic results regarding the bipartite and multipartite entanglement properties of the system are derived. We also discuss a possible experimental implementation which may exhibit steady state genuine multipartite entanglement.

A miniaturised wideband frequency synthesiser

Wideband frequency synthesisers have application in many areas, including test instrumentation and defence electronics. Miniaturisation of these devices provides many advantages to system designers, particularly in applications where extra space and weight are expensive. The purpose of this project was to miniaturise a wideband frequency synthesiser and package it for operation in several different environmental conditions while satisfying demanding technical specifications. The four primary and secondary goals to be achieved were: 1. an operating frequency range from low MHz to greater than 40 GHz, with resolution better than 1 MHz, 2. typical RF output power of +10 dBm, with maximum DC supply of 15 W, 3. synthesiser package of only 150  100  30 mm, and 4. operating temperatures from 20C to +71C, and vibration levels over 7 grms. This task was approached from multiple angles. Electrically, the system is designed to have as few functional blocks as possible. Off the shelf components are used for active functions instead of customised circuits. Mechanically, the synthesiser package is designed for efficient use of the available space. Two identical prototype synthesisers were manufactured to evaluate the design methodology and to show the repeatability of the design. Although further engineering development will improve the synthesiser’s performance, this project has successfully demonstrated a level of miniaturisation which sets a new benchmark for wideband synthesiser design. These synthesisers will meet the demands for smaller, lighter wideband sources. Potential applications include portable test equipment, radar and electronic surveillance systems on unmanned aerial vehicles. They are also useful for reducing the overall weight and power consumption of other systems, even if small dimensions are not essential.

Measurement of anisotropies of the kinetic energy and anharmonicity in pyrolytic graphite by neutron Compton scattering

Neutron Compton scattering (NCS) measurements of the anisotropy of the momentum distribution and the mean Laplacian of the interatomic potential ∇2V have been performed using electron volt neutrons, with wave vector transfers between 24 Å−1 and 98 Å−1. The measured momentum distribution of the atoms displays significantly more anisotropy than a calculation using a model density of states. We have observed anisotropies in ∇2V for the first time. The results suggest that the atomic potential is harmonic within the graphite planes, but anharmonic for vibrations perpendicular to the planes.

Secular series and renormalization group for amplitude equations

We have developed a technique that circumvents the process of elimination of secular terms and reproduces the uniformly valid approximations, amplitude equations, and first integrals. The technique is based on a rearrangement of secular terms and their grouping into the secular series that multiplies the constants of the asymptotic expansion. We illustrate the technique by deriving amplitude equations for standard nonlinear oscillator and boundary-layer problems. © 2008 The American Physical Society.