Stability borders of feedback control of delayed measured systems

When stabilization of unstable periodic orbits or fixed points by the method given by Ott, Grebogi and Yorke (OGY) has to be based on a measurement delayed by $\tau$ orbit lengths, the performance of unmodified OGY method is expected to decline. For experimental considerations, it is desired to know the range of stability with minimal knowledge of the system. We find that unmodified OGY control fails beyond a maximal Ljapunov number of $\lambda_{max}=1+\frac{1}{\tau}$. In this paper the area of stability is investigated both for OGY control of known fixed points and for difference control of unknown or inaccurately known fixed points. An estimated value of the control gain is given. Finally we outline what extensions have to be considered if one wants to stabilize fixed points with Ljapunov numbers above $\lambda_{max}$.Comment: 5 pages LaTeX using revtex and epsfig (4 figs included). Revised versio

Enhanced Dimer Relaxation in an Atomic/Molecular BEC

We derive a universal formula for the rate constant \beta for relaxation of a shallow dimer into deeply-bound diatomic molecules in the case of atoms with a large scattering length a. We show that \beta is determined by a and by two 3-body parameters that also determine the binding energies and widths of Efimov states. The rate constant \beta scales like \hbar a/m near the resonance, but the coefficient is a periodic function of ln(a) that may have resonant enhancement at values of a that differ by multiples of 22.7.Comment: 5 pages, revtex4, 2 PS figures, title changed, final versio

The Sizes of 1720 MHz OH Masers: VLBA and MERLIN Observations of the Supernova Remnants W44 and W28

We have used the NRAO Very Long Baseline Array (VLBA) to image OH(1720 MHz) masers in the supernova remnants W28 and W44 at a resolution of 40 mas. We also used MERLIN to observe the same OH(1720 MHz) masers in W44 at a resolution of 290 x 165 mas. All the masers are resolved by these VLBA and MERLIN observations. The measured sizes range from 50 to 180 mas and yield brightness temperature estimates from 0.3--20 x 10**8 K. We investigate whether these measured angular sizes are intrinsic and hence originate as a result of the physical conditions in the supernova remnant shock, or whether they are scatter broadened sizes produced by the turbulent ionized gas along the line of sight. While the current data on the temporal and angular broadening of pulsars, masers and extragalactic soures toward W44 and W28 can be understood in terms of scattering, we cannot rule out that these large sizes are intrinsic. Recent theoretical modeling by Lockett et al. suggests that the physical parameters in the shocked region are indicative of densities and OH abundances which lead to estimates of sizes as large as what we measure. If the sizes and structure are intrinsic, then the OH(1720 MHz) masrs may be more like the OH(1612 MHz) masers in circumstellar shells than OH masers associated with HII regions. At two locations in W28 we observe the classical S-shapes in the Stokes V profiles caused by Zeeman splitting and use it to infer magnetic fields of order 2 milliGauss.Comment: 24 pages, 6 figures, accepted by Ap

Stochastic differential equations for evolutionary dynamics with demographic noise and mutations

We present a general framework to describe the evolutionary dynamics of an arbitrary number of types in finite populations based on stochastic differential equations (SDE). For large, but finite populations this allows to include demographic noise without requiring explicit simulations. Instead, the population size only rescales the amplitude of the noise. Moreover, this framework admits the inclusion of mutations between different types, provided that mutation rates, $\mu$, are not too small compared to the inverse population size 1/N. This ensures that all types are almost always represented in the population and that the occasional extinction of one type does not result in an extended absence of that type. For $\mu N\ll1$ this limits the use of SDE's, but in this case there are well established alternative approximations based on time scale separation. We illustrate our approach by a Rock-Scissors-Paper game with mutations, where we demonstrate excellent agreement with simulation based results for sufficiently large populations. In the absence of mutations the excellent agreement extends to small population sizes.Comment: 8 pages, 2 figures, accepted for publication in Physical Review

Database management and analysis of fisheries in Illinois: Final report, 1 March 1999-28 February 2002

Issued May 2002; F-69-RReport issued on: May 200