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

Does "thin client" mean "energy efficient"?

The thick client –a personal computer with integral disk storage and local processing capability, which also has access to data and other resources via a network connection – is accepted as the model for providing computing resource in most office environments. The Further and Higher Education sector is no exception to that, and therefore most academic and administrative offices are equipped with desktop computers of this form to support users in their day to day tasks. This system structure has a number of advantages: there is a reduced reliance on network resources; users access a system appropriate to their needs, and may customise “their” system to meet their own personal requirements and working patterns. However it also has disadvantages: some are outside the scope of this project, but of most relevance to the green IT agenda is the fact that relatively complex and expensive (in first cost and in running cost) desktop systems and servers are underutilised – especially in respect of processing power. While some savings are achieved through use of “sleep” modes and similar power reducing mechanisms, in most configurations only a small portion of the overall total available processor resource is utilised. This realisation has led to the promotion of an alternative paradigm, the thin client. In a thin client system, the desktop is shorn of most of its local processing and data storage capability, and essentially acts as a terminal to the server, which now takes on responsibility for data storage and processing. The energy benefit is derived through resource sharing: the processor of the server does the work, and because that processor is shared by all users, a number of users are supported by a single system. Therefore – according to proponents of thin client – the total energy required to support a user group is reduced, since a shared physical resource is used more efficiently. These claims are widely reported: indeed there are a number of estimation tools which show these savings can be achieved; however there appears to be little or no actual measured data to confirm this. The community does not appear to have access to measured data comparing thin and thick client systems in operation in the same situation, allowing direct comparisons to be drawn. This is the main goal of this project. One specific question relates to the overall power use, while it would seem to be obvious that the thin client would require less electricity, what of the server? Two other variations are also considered: it is not uncommon for thin client deployments to continue to use their existing PCs as thin client workstations, with or without modification. Also, attempts by PC makers to reduce the power requirements of their products have given rise to a further variation: the incorporation of low power features in otherwise standard PC technology, working as thick clients. This project was devised to conduct actual measurements in use in a typical university environment. We identified a test area: a mixed administrative and academic office location which supported a range of users, and we made a direct replacement of the current thick client systems with thin client equivalents; in addition, we exchanged a number of PCs operating in thin and thick client mode with devices specifically branded as “low power” PCs and measured their power requirements in both thin and thick modes. We measured the energy consumption at each desktop for the duration of our experiments, and also measured the energy draw of the server designated to supporting the thin client setup, giving us the opportunity to determine the power per user of each technology. Our results show a significant difference in power use between the various candidate technologies, and that a configuration of low power PC in thick client mode returned the lowest power use during our study. We were also aware of other factors surrounding a change such as this: we have addressed the technical issues of implementation and management, and the non-technical or human factors of acceptance and use: all are reported within this document. Finally, our project is necessarily limited to a set of experiments carried out in a particular situation, therefore we use estimation methods to draw wider conclusions and make general observations which should allow others to select appropriate thick or thin client solutions in their situation

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

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

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

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