Estimation of time delay by coherence analysis

Using coherence analysis (which is an extensively used method to study the correlations in frequency domain, between two simultaneously measured signals) we estimate the time delay between two signals. This method is suitable for time delay estimation of narrow band coherence signals for which the conventional methods cannot be reliably applied. We show by analysing coupled R\"ossler attractors with a known delay, that the method yields satisfactory results. Then, we apply this method to human pathologic tremor. The delay between simultaneously measured traces of Electroencephalogram (EEG) and Electromyogram (EMG) data of subjects with essential hand tremor is calculated. We find that there is a delay of 11-27 milli-seconds ($ms$) between the tremor correlated parts (cortex) of the brain (EEG) and the trembling hand (EMG) which is in agreement with the experimentally observed delay value of 15 $ms$ for the cortico-muscular conduction time. By surrogate analysis we calculate error-bars of the estimated delay.Comment: 21 pages, 8 figures, elstart.cls file included. Accepted for publication in Physica

Astrometric Positions and Proper Motions of 19 Radio Stars

We have used the Very Large Array, linked with the Pie Town Very Long Baseline Array antenna, to determine astrometric positions of 19 radio stars in the International Celestial Reference Frame (ICRF). The positions of these stars were directly linked to the positions of distant quasars through phase referencing observations. The positions of the ICRF quasars are known to 0.25 mas, thus providing an absolute reference at the angular resolution of our radio observations. Average values for the errors in our derived positions for all sources were 13 mas and 16 mas in R.A. and declination respectively, with accuracies approaching 1-2 mas for some of the stars observed. Differences between the ICRF positions of the 38 quasars, and those measured from our observations showed no systematic offsets, with mean values of -0.3 mas in R.A. and -1.0 mas in declination. Standard deviations of the quasar position differences of 17 mas and 11 mas in R.A. and declination respectively, are consistent with the mean position errors determined for the stars. Our measured positions were combined with previous Very Large Array measurements taken from 1978-1995 to determine the proper motions of 15 of the stars in our list. With mean errors of approximately 1.6 mas/yr, the accuracies of our proper motions approach those derived from Hipparcos, and for a few of the stars in our program, are better than the Hipparcos values. Comparing the positions of our radio stars with the Hipparcos catalog, we find that at the epoch of our observations, the two frames are aligned to within formal errors of approximately 3 mas. This result confirms that the Hipparcos frame is inertial at the expected level.Comment: 20 pages, 9 figures Accepted by the Astronomical Journal, 2003 March 1

Dynamic depletion in a Bose condensate via a sudden increase of the scattering length

We examine the time-dependent quantum depletion of a trapped Bose condensate arising from a rapid increase of the scattering length. Our solution indicates that a significant buildup of incoherent atoms can occur within a characteristic time short compared with the harmonic trap period. We discuss how the depletion density and the characteristic time depend on the physical parameters of the condensate

Weak and Compact Radio Emission in Early High-Mass Star Forming Regions: I. VLA Observations

We present a high sensitivity radio continuum survey at 6 and 1.3$\,$cm using the Karl G. Jansky Very Large Array towards a sample of 58 high-mass star forming regions. Our sample was chosen from dust clumps within infrared dark clouds with and without IR sources (CMC-IRs, CMCs, respectively), and hot molecular cores (HMCs), with no previous, or relatively weak radio continuum detection at the $1\,$mJy level. Due to the improvement in the continuum sensitivity of the VLA, this survey achieved map rms levels of $\sim$ 3-10 $\mu$Jy beam$^{-1}$ at sub-arcsecond angular resolution. We extracted 70 centimeter continuum sources associated with 1.2$\,$mm dust clumps. Most sources are weak, compact, and are prime candidates for high-mass protostars. Detection rates of radio sources associated with the mm dust clumps for CMCs, CMC-IRs and HMCs are 6$\%$, 53$\%$ and 100$\%$, respectively. This result is consistent with increasing high-mass star formation activity from CMCs to HMCs. The radio sources located within HMCs and CMC-IRs occur close to the dust clump centers with a median offset from it of 12,000$\,$AU and 4,000$\,$AU, respectively. We calculated 5 - 25$\,$GHz spectral indices using power law fits and obtain a median value of 0.5 (i.e., flux increasing with frequency), suggestive of thermal emission from ionized jets. In this paper we describe the sample, observations, and detections. The analysis and discussion will be presented in Paper II.Comment: Accepted for publication in the ApJ

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

The extremely collimated bipolar H_2O jet from the NGC 1333-IRAS 4B protostar

We have performed observations of water maser emission towards a sample of low-mass protostars, in order to investigate the properties of jets associated with the earliest stages of star formation and their interaction with the surrounding medium. The main aim is to measure the absolute positions and proper motions of the H_2O spots in order to investigate the kinematics of the region from where the jet is launched. We imaged the protostars in the nearby region NGC 1333-IRAS 4 in the water maser line at 22.2 GHz by using the VLBA in phase-reference mode at the milliarcsecond scale over four epochs, spaced by one month to measure proper motions. Two protostars (A2 and B) were detected in a highly variable H_2O maser emission, with an active phase shorter than four weeks. The H_2O maps allow us to trace the fast jet driven by the B protostar: we observed both the red- and blue-shifted lobes very close to the protostar, =< 35 AU, moving away with projected velocities of ~10-50 km/s. The comparison with the molecular outflow observed at larger scale suggests a jet precession with a 18'/yr rate. By measuring the positional spread of the H_2O spots we estimate a jet width of ~2 AU at a distance of ~12 AU from the driving protostar.Comment: 9 pages, 8 figures, A&A accepte

A highly-collimated SiO jet in the HH212 protostellar outflow

We mapped the HH212 Class 0 outflow in SiO(2--1, 5--4) and continuum using the PdBI in its extended configurations. The unprecedented angular resolution (down to 0.34") allows accurate comparison with a new, deep H2 image obtained at the VLT. The SiO emission is confined to a highly-collimated bipolar jet (width 0.35") along the outflow axis. The jet can be traced down to within 500 AU of the protostar, in a region that is heavily obscured in H2 images. Where both species are detected, SiO shows the same overall kinematics and structure as H2, indicating that both molecules are tracing the same material. We find that the high-velocity SiO gas near the protostar is not tracing a wide-angle wind but is already confined to a flow inside a narrow cone of half-opening angle < 6 deg.Comment: Astronomy and Astrophysics Letter, in pres

PdBI sub-arcsecond study of the SiO microjet in HH212 - Origin and collimation of Class 0 jets

The bipolar HH 212 outflow has been mapped in SiO using the extended configuration of the Plateau de Bure Interferometer (PdBI), revealing a highly collimated SiO jet closely associated with the H2 jet component. We study at unprecedented resolution (0.34" across the jet axis) the properties of the innermost SiO ``microjet'' within 1000 AU of this young Class 0 source, to compare it with atomic microjets from more evolved sources and to constrain its origin. The SiO channel maps are used to investigate the microjet collimation and velocity structure. A large velocity gradient analysis is applied to SiO (2-1), (5-4) and (8-7) data from the PdBI and the Submillimeter Array to constrain the SiO opacity and abundance. The HH212 Class 0 microjet shows striking similarities in collimation and energetic budget with atomic microjets from T Tauri sources. Furthermore, the SiO lines appear optically thick, unlike what is generally assumed. We infer T(kin) ~ 50-500 K and an SiO/H2 abundance greater than 4 10(-8)-6 10(-5) for n(H2) = 10(7)-10(5) cm(-3), i.e. 0.05-90% of the elemental silicon. This similar jet width, regardless of the presence of a dense envelope, definitely rules out jet collimation by external pressure, and favors a common MHD self-collimation (and possibly acceleration) process at all stages of star formation. We propose that the more abundant SiO in Class 0 jets could mainly result from rapid (less than 25 yrs) molecular synthesis at high jet densities

Critical number of atoms in an attractive Bose-Einstein condensate on an optical plus harmonic traps

The stability of an attractive Bose-Einstein condensate on a joint one-dimensional optical lattice and an axially-symmetric harmonic trap is studied using the numerical solution of the time-dependent mean-field Gross-Pitaevskii equation and the critical number of atoms for a stable condensate is calculated. We also calculate this critical number of atoms in a double-well potential which is always greater than that in an axially-symmetric harmonic trap. The critical number of atoms in an optical trap can be made smaller or larger than the corresponding number in the absence of the optical trap by moving a node of the optical lattice potential along the axial direction of the harmonic trap. This variation of the critical number of atoms can be observed experimentally and compared with the present calculation.Comment: Latex with 7 eps figures, Accepted in Journal of Physics

VLA+PT Astrometry of 46 Radio Stars

We have used the Very Large Array (VLA), linked with the Pie Town Very Long Baseline Array antenna, to determine astrometric positions of 46 radio stars in the International Celestial Reference Frame (ICRF). Positions were obtained in the ICRF directly through phase referencing of the stars to nearby ICRF quasars whose positions are accurate at the 0.25 mas level. Radio star positions are estimated to be accurate at the 10 mas level, with position errors approaching a few milli-arcseconds for some of the stars observed. Our measured positions were combined with previous measurements taken from as early as 1978 to obtain proper motion estimates for all 46 stars with average uncertainties of ~1.7 mas/yr. We compared our radio star positions and proper motions with the Hipparcos Catalogue data, and find consistency in the reference frames produced by each data set on the 1-sigma level, with errors of ~2.7 mas per axis for the reference frame orientation angles at our mean epoch of 2003.78. No significant spin is found between our radio data frame and the Hipparcos Celestial Reference Frame (HCRF) with largest rotation rates of +0.55 and -0.41 mas/yr around the x and z axes, respectively, with 1-sigma errors of 0.36 mas/yr. Thus, our results are consistent with a non-rotating Hipparcos frame with respect to the ICRF.Comment: 29 pages, 8 figures, accepted for publication in the Astronomical Journa