490 research outputs found
Attractiveness of periodic orbits in parametrically forced systemswith time-increasing friction
We consider dissipative one-dimensional systems subject to a periodic force
and study numerically how a time-varying friction affects the dynamics. As a
model system, particularly suited for numerical analysis, we investigate the
driven cubic oscillator in the presence of friction. We find that, if the
damping coefficient increases in time up to a final constant value, then the
basins of attraction of the leading resonances are larger than they would have
been if the coefficient had been fixed at that value since the beginning. From
a quantitative point of view, the scenario depends both on the final value and
the growth rate of the damping coefficient. The relevance of the results for
the spin-orbit model are discussed in some detail.Comment: 30 pages, 6 figure
Canonical phase space approach to the noisy Burgers equation: Probability distributions
We present a canonical phase space approach to stochastic systems described
by Langevin equations driven by white noise. Mapping the associated
Fokker-Planck equation to a Hamilton-Jacobi equation in the nonperturbative
weak noise limit we invoke a {\em principle of least action} for the
determination of the probability distributions. We apply the scheme to the
noisy Burgers and KPZ equations and discuss the time-dependent and stationary
probability distributions. In one dimension we derive the long-time skew
distribution approaching the symmetric stationary Gaussian distribution. In the
short-time region we discuss heuristically the nonlinear soliton contributions
and derive an expression for the distribution in accordance with the directed
polymer-replica and asymmetric exclusion model results. We also comment on the
distribution in higher dimensions.Comment: 18 pages Revtex file, including 8 eps-figures, submitted to Phys.
Rev.
Parametric resonance in tunable superconducting cavities
We develop a theory of parametric resonance in tunable superconducting
cavities. The nonlinearity introduced by the SQUID attached to the cavity, and
damping due to connection of the cavity to a transmission line are taken into
consideration. We study in detail the nonlinear classical dynamics of the
cavity field below and above the parametric threshold for the degenerate
parametric resonance, featuring regimes of multistability and parametric
radiation. We investigate the phase-sensitive amplification of external signals
on resonance, as well as amplification of detuned signals, and relate the
amplifier performance to that of linear parametric amplifiers. We also discuss
applications of the device for dispersive qubit readout. Beyond the classical
response of the cavity, we investigate small quantum fluctuations around the
amplified classical signals. We evaluate the noise power spectrum both for the
internal field in the cavity and the output field. Other quantum statistical
properties of the noise are addressed such as squeezing spectra, second order
coherence, and two-mode entanglement.Comment: 25 pages, 17 figure
Influence of dissipation on extreme oscillations of a forced anharmonic oscillator
Dynamics of a periodically forced anharmonic oscillator (AO) with cubic
nonlinearity, linear damping, and nonlinear damping, is studied. To begin with,
the authors examine the dynamics of an AO. Due to this symmetric nature, the
system has two neutrally stable elliptic equilibrium points in positive and
negative potential-wells. Hence, the unforced system can exhibit both
single-well and double-well periodic oscillations depending on the initial
conditions. Next, the authors include nonlinear damping into the system. Then,
the symmetry of the system is broken instantly and the stability of the two
elliptic points is altered to result in stable focus and unstable focus in the
positive and negative potential-wells, respectively. Consequently, the system
is dual-natured and is either non-dissipative or dissipative, depending on
location in the phase space. Furthermore, when one includes a periodic external
forcing with suitable parameter values into the nonlinearly damped AO system
and starts to increase the damping strength, the symmetry of the system is not
broken right away, but it occurs after the damping reaches a threshold value.
As a result, the system undergoes a transition from double-well chaotic
oscillations to single-well chaos mediated through extreme events (EEs).
Furthermore, it is found that the large-amplitude oscillations developed in the
system are completely eliminated if one incorporates linear damping into the
system. The numerically calculated results are in good agreement with the
theoretically obtained results on the basis of Melnikov's function. Further, it
is demonstrated that when one includes linear damping into the system, this
system has a dissipative nature throughout the entire phase space of the
system. This is believed to be the key to the elimination of EEs.Comment: 15 pages, 9 figures. Accepted for publications in International
Journal of Non-Linear Mechanic
Phase Diagrams for Sonoluminescing Bubbles
Sound driven gas bubbles in water can emit light pulses. This phenomenon is
called sonoluminescence (SL). Two different phases of single bubble SL have
been proposed: diffusively stable and diffusively unstable SL. We present phase
diagrams in the gas concentration vs forcing pressure state space and also in
the ambient radius vs gas concentration and vs forcing pressure state spaces.
These phase diagrams are based on the thresholds for energy focusing in the
bubble and two kinds of instabilities, namely (i) shape instabilities and (ii)
diffusive instabilities. Stable SL only occurs in a tiny parameter window of
large forcing pressure amplitude atm and low gas
concentration of less than of the saturation. The upper concentration
threshold becomes smaller with increasing forcing. Our results quantitatively
agree with experimental results of Putterman's UCLA group on argon, but not on
air. However, air bubbles and other gas mixtures can also successfully be
treated in this approach if in addition (iii) chemical instabilities are
considered. -- All statements are based on the Rayleigh-Plesset ODE
approximation of the bubble dynamics, extended in an adiabatic approximation to
include mass diffusion effects. This approximation is the only way to explore
considerable portions of parameter space, as solving the full PDEs is
numerically too expensive. Therefore, we checked the adiabatic approximation by
comparison with the full numerical solution of the advection diffusion PDE and
find good agreement.Comment: Phys. Fluids, in press; latex; 46 pages, 16 eps-figures, small
figures tarred and gzipped and uuencoded; large ones replaced by dummies;
full version can by obtained from: http://staff-www.uni-marburg.de/~lohse
- …