25,520 research outputs found
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
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
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
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 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 .
Frequency entrainment and phase ordering are discussed as a function of . 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
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
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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
Scaling laws for rotating Rayleigh-BĂ©nard convection
Numerical simulations of large aspect ratio, three-dimensional rotating Rayleigh-BĂ©nard 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
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