Synchronization of Chaotic Systems by Common Random Forcing

We show two examples of noise--induced synchronization. We study a 1-d map and the Lorenz systems, both in the chaotic region. For each system we give numerical evidence that the addition of a (common) random noise, of large enough intensity, to different trajectories which start from different initial conditions, leads eventually to the perfect synchronization of the trajectories. The largest Lyapunov exponent becomes negative due to the presence of the noise terms.Comment: 5 pages, uses aipproc.cls and aipproc.sty (included). Five double figures are provided as ten separate gif files. Version with (large) postscript figures included available from http://www.imedea.uib.es/PhysDept/publicationsDB/date.htm

Analytical and Numerical Studies of Noise-induced Synchronization of Chaotic Systems

We study the effect that the injection of a common source of noise has on the trajectories of chaotic systems, addressing some contradictory results present in the literature. We present particular examples of 1-d maps and the Lorenz system, both in the chaotic region, and give numerical evidence showing that the addition of a common noise to different trajectories, which start from different initial conditions, leads eventually to their perfect synchronization. When synchronization occurs, the largest Lyapunov exponent becomes negative. For a simple map we are able to show this phenomenon analytically. Finally, we analyze the structural stability of the phenomenon.Comment: 10 pages including 12 postscript figures, revtex. Additional work in http://www.imedea.uib.es/Nonlinear . The paper with higher-resolution figures can be obtained from http://www.imedea.uib.es/PhysDept/publicationsDB/date.htm

BATSE Observations of Gamma-Ray Burst Tails

I discuss in this paper the phenomenon of post-burst emission in BATSE gamma-ray bursts at energies traditionally associated with prompt emission. By summing the background-subtracted signals from hundreds of bursts, I find that tails out to hundreds of seconds after the trigger may be a common feature of long events (duration greater than 2s), and perhaps of the shorter bursts at a lower and shorter-lived level. The tail component appears independent of both the duration (within the long GRB sample) and brightness of the prompt burst emission, and may be softer. Some individual bursts have visible tails at gamma-ray energies and the spectrum in at least a few cases is different from that of the prompt emission.Comment: 33 Pages from LaTex including 7 figures, with aastex. To appear in Astrophysical Journa

Fireballs Loading and the Blast Wave Model of Gamma Ray Bursts

A simple function for the spectral power $P(\epsilon,t) \equiv \nu L(\nu)$ is proposed to model, with 9 parameters, the spectral and temporal evolution of the observed nonthermal synchrotron power flux from GRBs in the blast wave model. Here $\epsilon = h\nu/$m$_e$c$^2$ is the observed dimensionless photon energy and $t$ is the observing time. Assumptions and an issue of lack of self-consistency are spelled out. The spectra are found to be most sensitive to the baryon loading, expressed in terms of the initial bulk Lorentz factor $\Gamma_0$, and an equipartition term $q$ which is assumed to be constant in time and independent of $\Gamma_0$. Expressions are given for the peak spectral power $P_p(t) = P(\epsilon_p,t)$ at the photon energy $\epsilon = \epsilon_p(t)$ of the spectral power peak. A general rule is that the total fireball particle kinetic energy $E_0 \sim \Pi_0 t_d$, where $t_d \propto \Gamma_0^{-8/3}$ is the deceleration time scale and $\Pi_0 \equiv P(\epsilon_p,t_d) \propto \Gamma_0^{8/3}$ is the maximum measured bolometric power output in radiation, during which it is carried primarily by photons with energy ${\cal E}_0 = \epsilon_p(t_d) \propto q\Gamma_0^4$.Comment: 26 pages, including 4 figures, uses epsf.sty, rotate.sty; submitted to ApJ; revised version with extended introduction, redrawn figures, and correction

Measurement and control of a mechanical oscillator at its thermal decoherence rate

In real-time quantum feedback protocols, the record of a continuous measurement is used to stabilize a desired quantum state. Recent years have seen highly successful applications in a variety of well-isolated micro-systems, including microwave photons and superconducting qubits. By contrast, the ability to stabilize the quantum state of a tangibly massive object, such as a nanomechanical oscillator, remains a difficult challenge: The main obstacle is environmental decoherence, which places stringent requirements on the timescale in which the state must be measured. Here we describe a position sensor that is capable of resolving the zero-point motion of a solid-state, nanomechanical oscillator in the timescale of its thermal decoherence, a critical requirement for preparing its ground state using feedback. The sensor is based on cavity optomechanical coupling, and realizes a measurement of the oscillator's displacement with an imprecision 40 dB below that at the standard quantum limit, while maintaining an imprecision-back-action product within a factor of 5 of the Heisenberg uncertainty limit. Using the measurement as an error signal and radiation pressure as an actuator, we demonstrate active feedback cooling (cold-damping) of the 4.3 MHz oscillator from a cryogenic bath temperature of 4.4 K to an effective value of 1.1$\pm$0.1 mK, corresponding to a mean phonon number of 5.3$\pm$0.6 (i.e., a ground state probability of 16%). Our results set a new benchmark for the performance of a linear position sensor, and signal the emergence of engineered mechanical oscillators as practical subjects for measurement-based quantum control.Comment: 24 pages, 10 figures; typos corrected in main text and figure

Galactic distribution of merging neutron stars and black holes - prospects for short GRB progenitors and LIGO/VIRGO

We have performed detailed population synthesis on a large number (20 million) of binary systems in order to investigate the properties of massive double degenerate binaries. We have included new important results in our input physics in order to obtain more reliable estimates of the merging timescales and relative formation rates. These improvements include refined treatment of the binding energy in a common envelope, helium star evolution and reduced kicks imparted to newborn black holes. The discovery and observations of GRB afterglows and the identification of host galaxies have allowed comparisons of theoretical distributions of merger sites with the observed distribution of afterglow positions relative to host galaxies. To help investigate the physical nature of short- and long-duration GRBs, we compute the distances of merging neutron stars (NS) and/or black holes (BH) from the centers of their host galaxies, as predicted by their formation scenario combined with motion in galactic potentials. Furthermore, we estimate the formation rate and merging rate of these massive double degenerate binaries. The latter is very important for the prospects of detecting gravitational waves with LIGO/VIRGO. We find that the expected detection rate for LIGO II is ~850 per year for galactic field sources and that this rate is completely dominated by merging BHBH binaries. Even LIGO I may detect such an event (~0.25 per year). Our preferred model estimate the Galactic field NSNS merger rate to be ~1.5*10^(-6) per year. For BHBH systems this model predicts a merger rate of ~9.7*10^{-6} per year. Our studies also reveal an accumulating numerous population of very wide orbit BHBH systems which never merge (t >> t_Hubble).Comment: 17 pages, 14 figures, accepted by MNRA

The Non-Relativistic Evolution of GRBs 980703 and 970508: Beaming-Independent Calorimetry

We use the Sedov-Taylor self-similar solution to model the radio emission from the gamma-ray bursts (GRBs) 980703 and 970508, when the blastwave has decelerated to non-relativistic velocities. This approach allows us to infer the energy independent of jet collimation. We find that for GRB 980703 the kinetic energy at the time of the transition to non-relativistic evolution, t_NR ~ 40 d, is E_ST ~ (1-6)e51 erg. For GRB 970508 we find E_ST ~ 3e51 erg at t_NR ~ 100 d, nearly an order of magnitude higher than the energy derived in Frail, Waxman and Kulkarni (2000). This is due primarily to revised cosmological parameters and partly to the maximum likelihood fit we use here. Taking into account radiative losses prior to t_NR, the inferred energies agree well with those derived from the early, relativistic evolution of the afterglow. Thus, the analysis presented here provides a robust, geometry-independent confirmation that the energy scale of cosmological GRBs is about 5e51 erg, and additionally shows that the central engine in these two bursts did not produce a significant amount of energy in mildly relativistic ejecta at late time. Furthermore, a comparison to the prompt energy release reveals a wide dispersion in the gamma-ray efficiency, strengthening our growing understanding that E_gamma is a not a reliable proxy for the total energy.Comment: Submitted to ApJ; 13 pages, 6 figures, 1 table; high-resolution figures can be found at: http://www.astro.caltech.edu/~ejb/NR

Fe K\alpha emission from photoionized slabs: the impact of the iron abundance

Iron K\alpha emission from photoionized and optically thick material is observed in a variety of astrophysical environments including X-ray binaries, active galactic nuclei, and possibly gamma-ray bursts. This paper presents calculations showing how the equivalent width (EW) of the Fe K line depends on the iron abundance of the illuminated gas and its ionization state -- two variables subject to significant cosmic scatter. Reflection spectra from a constant density slab which is illuminated with a power-law spectrum with photon-index \Gamma are computed using the code of Ross & Fabian. When the Fe K EW is measured from the reflection spectra alone, we find that it can reach values greater than 6 keV if the Fe abundance is about 10 times solar and the illuminated gas is neutral. EWs of about 1 keV are obtained when the gas is ionized. In contrast, when the EW is measured from the incident+reflected spectrum, the largest EWs are ~800 keV and are found when the gas is ionized. When \Gamma is increased, the Fe K line generally weakens, but significant emission can persist to larger ionization parameters. The iron abundance has its greatest impact on the EW when it is less than 5 times solar. When the abundance is further increased, the line strengthens only marginally. Therefore, we conclude that Fe K lines with EWs much greater than 800 eV are unlikely to be produced by gas with a supersolar Fe abundance. These results should be useful in interpreting Fe K emission whenever it arises from optically thick fluorescence.Comment: 5 pages, 5 figures, accepted by MNRAS Letter

Emission Spectra from Internal Shocks in Gamma-Ray-Burst Sources

Unsteady activity of gamma-ray burst sources leads to internal shocks in their emergent relativistic wind. We study the emission spectra from such shocks, assuming that they produce a power-law distribution of relativistic electrons and posses strong magnetic fields. The synchrotron radiation emitted by the accelerated electrons is Compton up-scattered multiple times by the same electrons. A substantial component of the scattered photons acquires high energies and produces e+e- pairs. The pairs transfer back their kinetic energy to the radiation through Compton scattering. The generic spectral signature from pair creation and multiple Compton scattering is highly sensitive to the radius at which the shock dissipation takes place and to the Lorentz factor of the wind. The entire emission spectrum extends over a wide range of photon energies, from the optical regime up to TeV energies. For reasonable values of the wind parameters, the calculated spectrum is found to be in good agreement with the burst spectra observed by BATSE.Comment: 12 pages, latex, 2 figures, submitted to ApJ

The performance of the EU-Rotate_N model in predicting the growth and nitrogen uptake of rotations of field vegetable crops in a Mediterranean environment

The EU-Rotate_N model was developed as a tool to estimate the growth and nitrogen (N) uptake of vegetable crop rotations across a wide range of European climatic conditions and to assess the economic and environmental consequences of alternative management strategies. The model has been evaluated under field conditions in Germany and Norway and under greenhouse conditions in China. The present work evaluated the model using Italian data to evaluate its performance in a warm and dry environment. Data were collected from four 2-year field rotations, which included lettuce (Lactuca sativa L.), fennel (Foeniculum vulgare Mill.), spinach (Spinacia oleracea L.), broccoli (Brassica oleracea L. var. italica Plenck) and white cabbage (B. oleracea convar. capitata var. alba L.); each rotation used three different rates of N fertilizer (average recommended N1, assumed farmer's practice N2=N1+0·3×N1 and a zero control N0). Although the model was not calibrated prior to running the simulations, results for above-ground dry matter biomass, crop residue biomass, crop N concentration and crop N uptake were promising. However, soil mineral N predictions to 0·6 m depth were poor. The main problem with the prediction of the test variables was the poor ability to capture N mineralization in some autumn periods and an inappropriate parameterization of fennel. In conclusion, the model performed well, giving results comparable with other bio-physical process simulation models, but for more complex crop rotations. The model has the potential for application in Mediterranean environments for field vegetable production