Delayed feedback as a means of control of noise-induced motion

Time--delayed feedback is exploited for controlling noise--induced motion in coherence resonance oscillators. Namely, under the proper choice of time delay, one can either increase or decrease the regularity of motion. It is shown that in an excitable system, delayed feedback can stabilize the frequency of oscillations against variation of noise strength. Also, for fixed noise intensity, the phenomenon of entrainment of the basic oscillation period by the delayed feedback occurs. This allows one to steer the timescales of noise-induced motion by changing the time delay.Comment: 4 pages, 4 figures. In the replacement file Fig. 2 and Fig. 4(b),(d) were amended. The reason is numerical error found, that affected the quantitative estimates of correlation time, but did not affect the main messag

Exponential decay for the damped wave equation in unbounded domains

We study the decay of the semigroup generated by the damped wave equation in an unbounded domain. We first prove under the natural geometric control condition the exponential decay of the semigroup. Then we prove under a weaker condition the logarithmic decay of the solutions (assuming that the initial data are smoother). As corollaries, we obtain several extensions of previous results of stabilisation and control

Twisted and Nontwisted Bifurcations Induced by Diffusion

We discuss a diffusively perturbed predator-prey system. Freedman and Wolkowicz showed that the corresponding ODE can have a periodic solution that bifurcates from a homoclinic loop. When the diffusion coefficients are large, this solution represents a stable, spatially homogeneous time-periodic solution of the PDE. We show that when the diffusion coefficients become small, the spatially homogeneous periodic solution becomes unstable and bifurcates into spatially nonhomogeneous periodic solutions. The nature of the bifurcation is determined by the twistedness of an equilibrium/homoclinic bifurcation that occurs as the diffusion coefficients decrease. In the nontwisted case two spatially nonhomogeneous simple periodic solutions of equal period are generated, while in the twisted case a unique spatially nonhomogeneous double periodic solution is generated through period-doubling. Key Words: Reaction-diffusion equations; predator-prey systems; homoclinic bifurcations; periodic solutions.Comment: 42 pages in a tar.gz file. Use ``latex2e twisted.tex'' on the tex files. Hard copy of figures available on request from [email protected]

Memory Effects and Scaling Laws in Slowly Driven Systems

This article deals with dynamical systems depending on a slowly varying parameter. We present several physical examples illustrating memory effects, such as metastability and hysteresis, which frequently appear in these systems. A mathematical theory is outlined, which allows to show existence of hysteresis cycles, and determine related scaling laws.Comment: 28 pages (AMS-LaTeX), 18 PS figure

Scattering and Iron Fluorescence Revealed During Absorption Dips in Circinus X-1

We show that dramatic spectral evolution associated with dips occurring near phase zero in RXTE observations of Cir X-1 is well-fit by variable and at times heavy absorption (N_H > 10^24 cm^-2) of a bright component, plus an underlying faint component which is not attenuated by the variable column and whose flux is ~10% of that of the unabsorbed bright component. A prominent Fe emission line at ~6.5 keV is evident during the dips. The absolute line flux outside the dips is similar to that during the dips, indicating that the line is associated with the faint component. These results are consistent with a model in which the bright component is radiation received directly from a compact source while the faint component may be attributed to scattered radiation. Our results are also generally consistent with those of Brandt et al., who found that a partial- covering model could explain ASCA spectra of a low-to-high transition in Cir X-1. The relative brightness of the two components in our model requires a column density of ~2*10^23 cm^-2 if the faint component is due to Thomson scattering in material that mostly surrounds the source. We find that illumination of such a scattering cloud by the observed direct component would produce an Fe K-alpha fluorescence flux that is in rough agreement with the flux of the observed emission line. We also conclude that if the scattering medium is not highly ionized, our line of sight to the compact source does not pass through it. Finally, we discuss simple pictures of the absorbers responsible for the dips themselves.Comment: Accepted for publication in The Astrophysical Journal (23 pages, including 11 figures

Collective modes of coupled phase oscillators with delayed coupling

We study the effects of delayed coupling on timing and pattern formation in spatially extended systems of dynamic oscillators. Starting from a discrete lattice of coupled oscillators, we derive a generic continuum theory for collective modes of long wavelength. We use this approach to study spatial phase profiles of cellular oscillators in the segmentation clock, a dynamic patterning system of vertebrate embryos. Collective wave patterns result from the interplay of coupling delays and moving boundary conditions. We show that the phase profiles of collective modes depend on coupling delays.Comment: 5 pages, 2 figure

Localization of shadow poles by complex scaling

Through numerical examples we show that the complex scaling method is suited to explore the pole structure in multichannel scattering problems. All poles lying on the multisheeted Riemann energy surface, including shadow poles, can be revealed and the Riemann sheets on which they reside can be identified.Comment: 6 pages, Latex with Revtex, 3 figures (not included) available on reques

Influence of shock wave propagation on dielectric barrier discharge plasma actuator performance

Interest in plasma actuators as active flow control devices is growing rapidly due to their lack of mechanical parts, light weight and high response frequency. Although the flow induced by these actuators has received much attention, the effect that the external flow has on the performance of the actuator itself must also be considered, especially the influence of unsteady high-speed flows which are fast becoming a norm in the operating flight envelopes. The primary objective of this study is to examine the characteristics of a dielectric barrier discharge (DBD) plasma actuator when exposed to an unsteady flow generated by a shock tube. This type of flow, which is often used in different studies, contains a range of flow regimes from sudden pressure and density changes to relatively uniform high-speed flow regions. A small circular shock tube is employed along with the schlieren photography technique to visualize the flow. The voltage and current traces of the plasma actuator are monitored throughout, and using the well-established shock tube theory the change in the actuator characteristics are related to the physical processes which occur inside the shock tube. The results show that not only is the shear layer outside of the shock tube affected by the plasma but the passage of the shock front and high-speed flow behind it also greatly influences the properties of the plasma