Domain Coarsening in Systems Far from Equilibrium

The growth of domains of stripes evolving from random initial conditions is studied in numerical simulations of models of systems far from equilibrium such as Rayleigh-Benard convection. The scaling of the size of the domains deduced from the inverse width of the Fourier spectrum is studied for both potential and nonpotential models. The morphology of the domains and the defect structures are however quite different in the two cases, and evidence is presented for a second length scale in the nonpotential case.Comment: 11 pages, RevTeX; 3 uufiles encoded postscript figures appende

The challenges and potential benefits of perennial organic cropping systems-example of organic top fruit

Of all the organic food sectors in the UK, top fruit production is one of the least developed. Despite strong consumer demand and high prices for organic fruit, UK production remains small and 90% of supplies are imported. Current methods of production are unsatisfactory with low yields and erratic quality, with resulting variable economic performance. Pest and disease problems are one of the main reasons for this poor performance, with current varieties being unable to provide sufficient resistance. New varieties and an improved pest and disease management programme, identified as part of a HORTLINK project, offer new hope to the sector. There are now opportunities for the sector to grow and provide greater UK supplies of top fruit, in addition to widening the proven benefits to biodiversity of organic orchards

Scaling laws for rotating Rayleigh-Bénard convection

Numerical simulations of large aspect ratio, three-dimensional rotating Rayleigh-Bénard convection for no-slip boundary conditions have been performed in both cylinders and periodic boxes. We have focused near the threshold for the supercritical bifurcation from the conducting state to a convecting state exhibiting domain chaos. A detailed analysis of these simulations has been carried out and is compared with experimental results, as well as predictions from multiple scale perturbation theory. We find that the time scaling law agrees with the theoretical prediction, which is in contradiction to experimental results. We also have looked at the scaling of defect lengths and defect glide velocities. We find a separation of scales in defect diameters perpendicular and parallel to the rolls as expected, but the scaling laws for the two different lengths are in contradiction to theory. The defect velocity scaling law agrees with our theoretical prediction from multiple scale perturbation theory

Lyapunov exponents for small aspect ratio Rayleigh-Bénard convection

Leading order Lyapunov exponents and their corresponding eigenvectors have been computed numerically for small aspect ratio, three-dimensional Rayleigh-Benard convection cells with no-slip boundary conditions. The parameters are the same as those used by Ahlers and Behringer [Phys. Rev. Lett. 40, 712 (1978)] and Gollub and Benson [J. Fluid Mech. 100, 449 (1980)] in their work on a periodic time dependence in Rayleigh-Benard convection cells. Our work confirms that the dynamics in these cells truly are chaotic as defined by a positive Lyapunov exponent. The time evolution of the leading order Lyapunov eigenvector in the chaotic regime will also be discussed. In addition we study the contributions to the leading order Lyapunov exponent for both time periodic and aperiodic states and find that while repeated dynamical events such as dislocation creation/annihilation and roll compression do contribute to the short time Lyapunov exponent dynamics, they do not contribute to the long time Lyapunov exponent. We find instead that nonrepeated events provide the most significant contribution to the long time leading order Lyapunov exponent

Chaotic Quivering of Micron-Scaled On-Chip Resonators Excited by Centrifugal Optical Pressure

Opto-mechanical chaotic oscillation of an on-chip resonator is excited by the radiation-pressure nonlinearity. Continuous optical input, with no external feedback or modulation, excites chaotic vibrations in very different geometries of the cavity (both tori and spheres) and shows that opto-mechanical chaotic oscillations are an intrinsic property of optical microcavities. Measured phenomena include period doubling, a spectral continuum, aperiodic oscillations, and complex trajectories. The rate of exponential divergence from a perturbed initial condition (Lyapunov exponent) is calculated. Continuous improvements in cavities mean that such chaotic oscillations can be expected in the future with many other platforms, geometries, and frequency spans

Opto-Mechanical Chaotic Behaviour of Micron-Scaled On-Chip Resonators

Opto-mechanical vibration of an on-chip oscillator is experimentally excited by radiation-pressure nonlinearity to a regime where oscillation is chaotic. Period-doubling and broad power spectra are measured in spherical and toroidal-resonators

The Sure Start Mellow Valley area Through the lens of a camera

This report gives an account of a participatory evaluation conducted using photography within the Sure Start Mellow Valley area. Information about the current status of the Sure Start programme and the plans for the future are first provided. The report then describes the research that was undertaken and presents and discusses the findings

Defect Dynamics for Spiral Chaos in Rayleigh-Benard Convection

A theory of the novel spiral chaos state recently observed in Rayleigh-Benard convection is proposed in terms of the importance of invasive defects i.e defects that through their intrinsic dynamics expand to take over the system. The motion of the spiral defects is shown to be dominated by wave vector frustration, rather than a rotational motion driven by a vertical vorticity field. This leads to a continuum of spiral frequencies, and a spiral may rotate in either sense depending on the wave vector of its local environment. Results of extensive numerical work on equations modelling the convection system provide some confirmation of these ideas.Comment: Revtex (15 pages) with 4 encoded Postscript figures appende

Synchronization by Reactive Coupling and Nonlinear Frequency Pulling

We present a detailed analysis of a model for the synchronization of nonlinear oscillators due to reactive coupling and nonlinear frequency pulling. We study the model for the mean field case of all-to-all coupling, deriving results for the initial onset of synchronization as the coupling or nonlinearity increase, and conditions for the existence of the completely synchronized state when all the oscillators evolve with the same frequency. Explicit results are derived for Lorentzian, triangular, and top-hat distributions of oscillator frequencies. Numerical simulations are used to construct complete phase diagrams for these distributions

Structure of Stochastic Dynamics near Fixed Points

We analyze the structure of stochastic dynamics near either a stable or unstable fixed point, where force can be approximated by linearization. We find that a cost function that determines a Boltzmann-like stationary distribution can always be defined near it. Such a stationary distribution does not need to satisfy the usual detailed balance condition, but might have instead a divergence-free probability current. In the linear case the force can be split into two parts, one of which gives detailed balance with the diffusive motion, while the other induces cyclic motion on surfaces of constant cost function. Using the Jordan transformation for the force matrix, we find an explicit construction of the cost function. We discuss singularities of the transformation and their consequences for the stationary distribution. This Boltzmann-like distribution may be not unique, and nonlinear effects and boundary conditions may change the distribution and induce additional currents even in the neighborhood of a fixed point.Comment: 7 page