The Berry-Tabor conjecture for spin chains of Haldane-Shastry type

According to a long-standing conjecture of Berry and Tabor, the distribution of the spacings between consecutive levels of a "generic'' integrable model should follow Poisson's law. In contrast, the spacings distribution of chaotic systems typically follows Wigner's law. An important exception to the Berry-Tabor conjecture is the integrable spin chain with long-range interactions introduced by Haldane and Shastry in 1988, whose spacings distribution is neither Poissonian nor of Wigner's type. In this letter we argue that the cumulative spacings distribution of this chain should follow the "square root of a logarithm'' law recently proposed by us as a characteristic feature of all spin chains of Haldane-Shastry type. We also show in detail that the latter law is valid for the rational counterpart of the Haldane-Shastry chain introduced by Polychronakos.Comment: LaTeX with revtex4, 6 pages, 6 figure

The Radio Jet Associated with the Multiple V380 Ori System

The giant Herbig-Haro object 222 extends over $\sim$6$'$ in the plane of the sky, with a bow shock morphology. The identification of its exciting source has remained uncertain over the years. A non-thermal radio source located at the core of the shock structure was proposed to be the exciting source. However, Very Large Array studies showed that the radio source has a clear morphology of radio galaxy and a lack of flux variations or proper motions, favoring an extragalactic origin. Recently, an optical-IR study proposed that this giant HH object is driven by the multiple stellar system V380 Ori, located about 23$'$ to the SE of HH 222. The exciting sources of HH systems are usually detected as weak free-free emitters at centimeter wavelengths. Here we report the detection of an elongated radio source associated with the Herbig Be star or with its close infrared companion in the multiple V380 Ori system. This radio source has the characteristics of a thermal radio jet and is aligned with the direction of the giant outflow defined by HH~222 and its suggested counterpart to the SE, HH~1041. We propose that this radio jet traces the origin of the large scale HH outflow. Assuming that the jet arises from the Herbig Be star, the radio luminosity is a few times smaller than the value expected from the radio-bolometric correlation for radio jets, confirming that this is a more evolved object than those used to establish the correlation.Comment: 13 pages, 3 figure

Moving embedded lattice solitons

It was recently proved that isolated unstable "embedded lattice solitons" (ELS) may exist in discrete systems. The discovery of these ELS gives rise to relevant questions such as the following: are there continuous families of ELS?, can ELS be stable?, is it possible for ELS to move along the lattice?, how do ELS interact?. The present work addresses these questions by showing that a novel differential-difference equation (a discrete version of a complex mKdV equation) has a two-parameter continuous family of exact ELS. The numerical tests reveal that these solitons are stable and robust enough to withstand collisions. The model may apply to the description of a Bose-Einstein condensate with dipole-dipole interactions between the atoms, trapped in a deep optical-lattice potential.Comment: 13 pages, 11 figure

Iterated Nonlinear Control of Ship's Manoeuvring Models

This paper addresses the control design for a nonlinear vessel manoeuvring model. The authors consider a highly nonlinear vessel 4 DOF model. The proposed control algorithm consists of a combination of an iteration technique that approximates the original nonlinear model by a sequence of linear time varying (LTV) equations whose solution converge to the solution of the original nonlinear problem and, a lead compensation design in which for each of the iterated linear time varying systems, the controller is optimized at each time on the interval. The control designed for the last iteration is then applied to the original nonlinear problem. Simulations results show good performance of this approximation methodology and accurate tracking for certain manoeuvring cases under the control of the designed lead controller. The main characteristic of the nonlinear system's response are the reduction of the settling time and the elimination of the steady state error and overshoot

Star Formation Under the Outflow: The Discovery of a Non-Thermal Jet from OMC-2 FIR 3 and its Relationship to the Deeply Embedded FIR 4 Protostar

We carried out multiwavelength (0.7-5 cm), multiepoch (1994-2015) Very Large Array (VLA) observations toward the region enclosing the bright far-IR sources FIR 3 (HOPS 370) and FIR 4 (HOPS 108) in OMC-2. We report the detection of 10 radio sources, seven of them identified as young stellar objects. We image a well-collimated radio jet with a thermal free-free core (VLA 11) associated with the Class I intermediate-mass protostar HOPS 370. The jet presents several knots (VLA 12N, 12C, 12S) of non-thermal radio emission (likely synchrotron from shock-accelerated relativistic electrons) at distances of ~7,500-12,500 au from the protostar, in a region where other shock tracers have been previously identified. These knots are moving away from the HOPS 370 protostar at ~ 100 km/s. The Class 0 protostar HOPS 108, which itself is detected as an independent, kinematically decoupled radio source, falls in the path of these non-thermal radio knots. These results favor the previously proposed scenario where the formation of HOPS 108 has been triggered by the impact of the HOPS 370 outflow with a dense clump. However, HOPS 108 presents a large proper motion velocity of ~ 30 km/s, similar to that of other runaway stars in Orion, whose origin would be puzzling within this scenario. Alternatively, an apparent proper motion could result because of changes in the position of the centroid of the source due to blending with nearby extended emission, variations in the source shape, and /or opacity effects.Comment: 16 pages, 4 figures, accepted for publication in The Astrophysical Journa

TREX-DM: a low background Micromegas-based TPC for low mass WIMP detection

Dark Matter experiments are recently focusing their detection techniques in low-mass WIMPs, which requires the use of light elements and low energy threshold. In this context, we present the TREX-DM experiment, a low background Micromegas-based TPC for low-mass WIMP detection. Its main goal is the operation of an active detection mass $\sim$0.300 kg, with an energy threshold below 0.4 keVee and fully built with previously selected radiopure materials. This article describes the actual setup, the first results of the comissioning in Ar+2\%iC$_4$H$_{10}$ at 1.2 bar and the future updates for a possible physics run at the Canfranc Underground Laboratory in 2016. A first background model is also presented, based on Geant4 simulations and a muon/electron discrimination method. In a conservative scenario, TREX-DM could be sensitive to DAMA/LIBRA and other hints of positive WIMPs signals, with some space for improvement with a neutron/electron discrimination method or the use of other light gases.Comment: Proceedings of the 7th Symposium on Large TPCs for Low-Energy Rare Event Detectio

Proper motions of the HH1 jet

We describe a new method for determining proper motions of extended objects, and a pipeline developed for the application of this method. We then apply this method to an analysis of four epochs of [S~II] HST images of the HH~1 jet (covering a period of $\sim 20$~yr). We determine the proper motions of the knots along the jet, and make a reconstruction of the past ejection velocity time-variability (assuming ballistic knot motions). This reconstruction shows an "acceleration" of the ejection velocities of the jet knots, with higher velocities at more recent times. This acceleration will result in an eventual merging of the knots in $\sim 450$~yr and at a distance of $\sim 80"$ from the outflow source, close to the present-day position of HH~1.Comment: 12 pages, 8 figure