On 2017 August 17 a binary neutron star coalescence candidate (later designated GW170817) with merger time 12:41:04 UTC was observed through gravitational waves by the Advanced LIGO and Advanced Virgo detectors. The Fermi Gamma-ray Burst Monitor independently detected a gamma-ray burst (GRB 170817A) with a time delay of $\sim 1.7\,{\rm{s}}$ with respect to the merger time. From the gravitational-wave signal, the source was initially localized to a sky region of 31 deg2 at a luminosity distance of ${40}_{-8}^{+8}$ Mpc and with component masses consistent with neutron stars. The component masses were later measured to be in the range 0.86 to 2.26 $\,{M}_{\odot }$. An extensive observing campaign was launched across the electromagnetic spectrum leading to the discovery of a bright optical transient (SSS17a, now with the IAU identification of AT 2017gfo) in NGC 4993 (at $\sim 40\,{\rm{Mpc}}$) less than 11 hours after the merger by the One-Meter, Two Hemisphere (1M2H) team using the 1 m Swope Telescope. The optical transient was independently detected by multiple teams within an hour. Subsequent observations targeted the object and its environment. Early ultraviolet observations revealed a blue transient that faded within 48 hours. Optical and infrared observations showed a redward evolution over ~10 days. Following early non-detections, X-ray and radio emission were discovered at the transient's position $\sim 9$ and $\sim 16$ days, respectively, after the merger. Both the X-ray and radio emission likely arise from a physical process that is distinct from the one that generates the UV/optical/near-infrared emission. No ultra-high-energy gamma-rays and no neutrino candidates consistent with the source were found in follow-up searches. These observations support the hypothesis that GW170817 was produced by the merger of two neutron stars in NGC 4993 followed by a short gamma-ray burst (GRB 170817A) and a kilonova/macronova powered by the radioactive decay of r-process nuclei synthesized in the ejecta.

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Multi-messenger observations of a binary neutron star merger

This self-contained introduction to the distributed control of robotic networks offers a distinctive blend of computer science and control theory. The book presents a broad set of tools for understanding coordination algorithms, determining their correctness, and assessing their complexity; and it analyzes various cooperative strategies for tasks such as consensus, rendezvous, connectivity maintenance, deployment, and boundary estimation. The unifying theme is a formal model for robotic networks that explicitly incorporates their communication, sensing, control, and processing capabilities--a model that in turn leads to a common formal language to describe and analyze coordination algorithms.Written for first- and second-year graduate students in control and robotics, the book will also be useful to researchers in control theory, robotics, distributed algorithms, and automata theory. The book provides explanations of the basic concepts and main results, as well as numerous examples and exercises.Self-contained exposition of graph-theoretic concepts, distributed algorithms, and complexity measures for processor networks with fixed interconnection topology and for robotic networks with position-dependent interconnection topology Detailed treatment of averaging and consensus algorithms interpreted as linear iterations on synchronous networks Introduction of geometric notions such as partitions, proximity graphs, and multicenter functions Detailed treatment of motion coordination algorithms for deployment, rendezvous, connectivity maintenance, and boundary estimation

/pdf/distributed-control-of-robotic-networks-a-mathematical-1q6nfcvi2l.pdf

Distributed Control of Robotic Networks: A Mathematical Approach to Motion Coordination Algorithms

We summarize our current knowledge of neutron-star masses and radii. Recent instrumentation and computational advances have resulted in a rapid increase in the discovery rate and precise timing of radio pulsars in binaries in the past few years, leading to a large number of mass measurements. These discoveries show that the neutron-star mass distribution is much wider than previously thought, with three known pulsars now firmly in the 1.9–2.0-M⊙ mass range. For radii, large, high-quality data sets from X-ray satellites as well as significant progress in theoretical modeling led to considerable progress in the measurements, placing them in the 10–11.5-km range and shrinking their uncertainties, owing to a better understanding of the sources of systematic errors. The combination of the massive-neutron-star discoveries, the tighter radius measurements, and improved laboratory constraints of the properties of dense matter has already made a substantial impact on our understanding of the composition and bulk p...

Masses, Radii, and the Equation of State of Neutron Stars

Gamma-ray bursts (GRBs) display a bimodal duration distribution with a separation between the short- and long-duration bursts at about 2 s. The progenitors of long GRBs have been identified as massive stars based on their association with Type Ic core-collapse supernovae (SNe), their exclusive location in star-forming galaxies, and their strong correlation with bright UV regions within their host galaxies. Short GRBs have long been suspected on theoretical grounds to arise from compact object binary mergers (neutron star–neutron star or neutron star–black hole). The discovery of short GRB afterglows in 2005 provided the first insight into their energy scale and environments, as well as established a cosmological origin, a mix of host-galaxy types, and an absence of associated SNe. In this review, I summarize nearly a decade of short GRB afterglow and host-galaxy observations and use this information to shed light on the nature and properties of their progenitors, the energy scale and collimation of the relativistic outflow, and the properties of the circumburst environments. The preponderance of the evidence points to compact object binary progenitors, although some open questions remain. On the basis of this association, observations of short GRBs and their afterglows can shed light on the on- and off-axis electromagnetic counterparts of gravitational wave sources from the Advanced LIGO/Virgo experiments.

Short-Duration Gamma-Ray Bursts

Modelling the electromagnetic emission of kilonovae enables the mass, velocity and composition (with some heavy elements) of the ejecta from a neutron-star merger to be derived from the observations. Merging neutron stars are potential sources of gravitational waves and have long been predicted to produce jets of material as part of a low-luminosity transient known as a 'kilonova'. There is growing evidence that neutron-star mergers also give rise to short, hard gamma-ray bursts. A group of papers in this issue report observations of a transient associated with the gravitational-wave event GW170817—a signature of two neutron stars merging and a gamma-ray flash—that was detected in August 2017. The observed gamma-ray, X-ray, optical and infrared radiation signatures support the predictions of an outflow of matter from double neutron-star mergers and present a clear origin for gamma-ray bursts. Previous predictions differ over whether the jet material would combine to form light or heavy elements. These papers now show that the early part of the outflow was associated with lighter elements whereas the later observations can be explained by heavier elements, the origins of which have been uncertain. However, one paper (by Stephen Smartt and colleagues) argues that only light elements are needed for the entire event. Additionally, Eleonora Troja and colleagues report X-ray observations and radio emissions that suggest that the 'kilonova' jet was observed off-axis, which could explain why gamma-ray-burst detections are seen as dim. The cosmic origin of elements heavier than iron has long been uncertain. Theoretical modelling1,2,3,4,5,6,7 shows that the matter that is expelled in the violent merger of two neutron stars can assemble into heavy elements such as gold and platinum in a process known as rapid neutron capture (r-process) nucleosynthesis. The radioactive decay of isotopes of the heavy elements is predicted8,9,10,11,12 to power a distinctive thermal glow (a ‘kilonova’). The discovery of an electromagnetic counterpart to the gravitational-wave source13 GW170817 represents the first opportunity to detect and scrutinize a sample of freshly synthesized r-process elements14,15,16,17,18. Here we report models that predict the electromagnetic emission of kilonovae in detail and enable the mass, velocity and composition of ejecta to be derived from observations. We compare the models to the optical and infrared radiation associated with the GW170817 event to argue that the observed source is a kilonova. We infer the presence of two distinct components of ejecta, one composed primarily of light (atomic mass number less than 140) and one of heavy (atomic mass number greater than 140) r-process elements. The ejected mass and a merger rate inferred from GW170817 imply that such mergers are a dominant mode of r-process production in the Universe.

Origin of the heavy elements in binary neutron-star mergers from a gravitational-wave event

This study considers the problem of vehicle platooning using multiple vehicle look ahead information while utilising a controller based on the constant spacing policy (CSP). First, string instability is shown with a CSP based controller that utilises position, velocity and acceleration information from `r' predecessor vehicles in the presence of parasitic lags in actuation. A novel approach using perturbation analysis is employed to show this result, where the spacing errors are states of a spatially discrete system. Then, an upper bound on the allowable parasitic lag is derived when the CSP controller utilises information from the immediate predecessor vehicle and the leading vehicle; for this controller and a given parasitic lag, a design procedure for selection of the controller gain is also given. Numerical simulations of these two results are provided and discussed.

Vehicle platooning with constant spacing strategies and multiple vehicle look ahead information

Many structures are made of concrete and steel. The response characteristics of such structures that are exposed to the environment change due to its impact such as oxidation due to moisture. Usually the structural element “degrades” in that the load bearing capacity decreases; it also decreases due to “aging”. On the other hand, chemicals are infused into biological systems in order to enhance their strength. Thus far, not much attention has been paid to studying such problems. In this investigation, we study the response of a linearized elastic solid whose material properties change due to the diffusion of a chemical.

Unsteady motions of degrading or aging linearized elastic solids

This paper presents a new method for approximating the set of PID controllers satisfying a class of transient specifications. The problem of designing a controller to satisfy transient specifications such as the maximum allowable overshoot to a given input or the response being required to be within an envelope can be cast as a problem of guaranteeing the impulse response of an appropriate closed loop error transfer function to be non-negative. Stabilizing PID controllers for Linear Time Invariant (LTI) systems can be synthesized as a union of convex polygons in k i − k d space for k p 's lying in a specific range. In this paper, we provide a method to restrict the stabilizing set for LTI systems further by using Widder's theorem and Markov-Lucaks representation for polynomials that are non-negative on the positive real axis. Widder's theorem provides necessary and sufficient conditions for the error response to be non-negative and upon an application of Widder's theorem, we obtain a sequence of polynomials, whose coefficients are polynomial functions of k p , k i and k d to be non-negative. For every polynomial in the sequence and for a specified k p , using Markov-Lucaks theorem and Minkowski's projection, we obtain a polynomial inequality in k i and k d that must be satisfied by every controller satisfying the desired transient specification. We also provide a method to arbitrarily tighten this set of desired controllers.

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Synthesis of PID controllers with guaranteed non-overshooting transient response

Aggregation of a class of interconnected, linear dynamical systems

In this paper, we study the effect of packet losses in Vehicle-to-Vehicle (V2V) communication on string stability of a platoon of vehicles employing a Cooperative Adaptive Cruise Control (CACC) system. Such vehicles employ a Constant Time Headway Policy (CTHP) and utilize communicated information of the acceleration of preceding vehicle in the string. This communication is subject to packet losses in a realistic wireless system and we model the packet loss phenomenon as a binomial random process characterized by a packet reception probability. We assume that the platoon is homogeneous and derive the inverse relationship between the minimum string stable time headway and the packet reception probability. Numerical simulations corroborate the results presented in this paper.

Swaroop Darbha

Papers

Vehicle platooning with constant spacing strategies and multiple vehicle look ahead information

Unsteady motions of degrading or aging linearized elastic solids

Synthesis of PID controllers with guaranteed non-overshooting transient response

Aggregation of a class of interconnected, linear dynamical systems

Reducing Time Headway in Homogeneous CACC Vehicle Platoons in the Presence of Packet Drops