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

Pattern formation with trapped ions

Ion traps are a versatile tool to study nonequilibrium statistical physics, due to the tunability of dissipation and nonlinearity. We propose an experiment with a chain of trapped ions, where dissipation is provided by laser heating and cooling, while nonlinearity is provided by trap anharmonicity and beam shaping. The collective dynamics are governed by an equation similar to the complex Ginzburg-Landau equation, except that the reactive nature of the coupling leads to qualitatively different behavior. The system has the unusual feature of being both oscillatory and excitable at the same time. We account for noise from spontaneous emission and find that the patterns are observable for realistic experimental parameters. Our scheme also allows controllable experiments with noise and quenched disorder.Comment: 4 pages + appendi

Stability of the aligned state of ^3He-A in a superflow

The stability of the equilibrium orientation of l parallel or antiparallel to a counterflow is studied both dynamically and statically. In contrast to the recent work of Hall and Hook (1977) - who, it is shown, use incorrect dynamical equations - the equilibrium is found to be stable in the Ginzburg-Landau regime. At lower temperatures an instability should develop

Synchronization of oscillators with long range power law interactions

We present analytical calculations and numerical simulations for the synchronization of oscillators interacting via a long range power law interaction on a one dimensional lattice. We have identified the critical value of the power law exponent $\alpha_c$ across which a transition from a synchronized to an unsynchronized state takes place for a sufficiently strong but finite coupling strength in the large system limit. We find $\alpha_c=3/2$. Frequency entrainment and phase ordering are discussed as a function of $\alpha \geq 1$. The calculations are performed using an expansion about the aligned phase state (spin-wave approximation) and a coarse graining approach. We also generalize the spin-wave results to the {\it d}-dimensional problem.Comment: Final published versio

Numerical bifurcation diagram for the two-dimensional boundary-fed chlorine-dioxide–iodine–malonic-acid system

We present a numerical solution of the chlorine-dioxide–iodine–malonic-acid reaction-diffusion system in two dimensions in a boundary-fed system using a realistic model. The bifurcation diagram for the transition from nonsymmetry-breaking structures along boundary feed gradients to transverse symmetry-breaking patterns in a single layer is numerically determined. We find this transition to be discontinuous. We make a connection with earlier results and discuss prospects for future work

Frequency Precision of Oscillators Based on High-Q Resonators

We present a method for analyzing the phase noise of oscillators based on feedback driven high quality factor resonators. Our approach is to derive the phase drift of the oscillator by projecting the stochastic oscillator dynamics onto a slow time scale corresponding physically to the long relaxation time of the resonator. We derive general expressions for the phase drift generated by noise sources in the electronic feedback loop of the oscillator. These are mixed with the signal through the nonlinear amplifier, which makes them {cyclostationary}. We also consider noise sources acting directly on the resonator. The expressions allow us to investigate reducing the oscillator phase noise thereby improving the frequency precision using resonator nonlinearity by tuning to special operating points. We illustrate the approach giving explicit results for a phenomenological amplifier model. We also propose a scheme for measuring the slow feedback noise generated by the feedback components in an open-loop driven configuration in experiment or using circuit simulators, which enables the calculation of the closed-loop oscillator phase noise in practical systems

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

A vertex-based finite volume method applied to non-linear material problems in computational solid mechanics

A vertex-based finite volume (FV) method is presented for the computational solution of quasi-static solid mechanics problems involving material non-linearity and infinitesimal strains. The problems are analysed numerically with fully unstructured meshes that consist of a variety of two- and three-dimensional element types. A detailed comparison between the vertex-based FV and the standard Galerkin FE methods is provided with regard to discretization, solution accuracy and computational efficiency. For some problem classes a direct equivalence of the two methods is demonstrated, both theoretically and numerically. However, for other problems some interesting advantages and disadvantages of the FV formulation over the Galerkin FE method are highlighted

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