On the Speed of Gravity and the v/cv/c Corrections to the Shapiro Time Delay

Using a relatively simple method, I compute the v/c correction to the gravitational time delay for light passing by a massive object moving with speed v. It turns out that the v/c effects are too small to have been measured in the recent experiment involving Jupiter and quasar J0842+1845 that was used to measure the speed of gravity.Comment: 8 pages, LaTeX (or Latex, etc), one figure, which is also available at http://www-theory.lbl.gov/~samuel/sog_figure.pdf; Revised version is the one to appear in Phys. Rev. Lett

Multifrequency Polarimetry of the Nrao 140 Jet: Possible Detection of a Helical Magnetic Field and Constraints on its Pitch Angle

We present results from multifrequency polarimetry of NRAO 140 using the Very Long Baseline Array. These observations allow us to reveal the distributions of both the polarization position angle and the Faraday rotation measure (RM). These distributions are powerful tools to discern the projected and line-of-sight components of the magnetic field, respectively. We find a systematic gradient in the RM distribution, with its sign being opposite at either side of the jet with respect to the jet axis. The sign of the RM changes only with the direction of the magnetic field component along the line of sight, so this can be explained by the existence of helical magnetic components associated with the jet itself. We derive two constraints for the pitch angle of the helical magnetic field from the distributions of the RM and the projected magnetic field; the RM distribution indicates that the helical fields are tightly wound, while that of the projected magnetic field suggests they are loosely wound around the jet axis. This inconsistency may be explained if the Faraday rotator is not cospatial with theemitting region. Our results may point toward a physical picture in which an ultra-relativistic jet (spine) with a loosely wound helical magnetic field is surrounded by a sub-relativistic wind layer (sheath) with a tightly wound helical magnetic field.Comment: 12 pages, 4 figures, ApJ, in pres

On the jets, kinks, and spheromaks formed by a planar magnetized coaxial gun

Measurements of the various plasma configurations produced by a planar magnetized coaxial gun provide insight into the magnetic topology evolution resulting from magnetic helicity injection. Important features of the experiments are a very simple coaxial gun design so that all observed geometrical complexity is due to the intrinsic physical dynamics rather than the source shape and use of a fast multiple-frame digital camera which provides direct imaging of topologically complex shapes and dynamics. Three key experimental findings were obtained: (1) formation of an axial collimated jet [Hsu and Bellan, Mon. Not. R. Astron. Soc. 334, 257 (2002)] that is consistent with a magnetohydrodynamic description of astrophysical jets, (2) identification of the kink instability when this jet satisfies the Kruskal-Shafranov limit, and (3) the nonlinear properties of the kink instability providing a conversion of toroidal to poloidal flux as required for spheromak formation by a coaxial magnetized source [Hsu and Bellan, Phys. Rev. Lett. 90, 215002 (2003)]. A new interpretation is proposed for how the n=1 central column instability provides flux amplification during spheromak formation and sustainment, and it is shown that jet collimation can occur within one rotation of the background poloidal field.Comment: Physics of Plasmas (accepted

M87 black hole mass and spin estimate through the position of the jet boundary shape break

We propose a new method of estimating a mass of a super massive black hole residing in the center of an active galaxy. The active galaxy M87 offers a convenient test case for the method due to the existence of a large amount of observational data on the jet and ambient environment properties in the central area of the object. We suggest that the observed transition of a jet boundary shape from a parabolic to a conical form is associated with the flow transiting from the magnetically dominated regime to the energy equipartition between plasma bulk motion and magnetic field. By coupling the unique set of observations available for the jet kinematics, environment and boundary profile with our MHD modelling under assumption on the presence of a dynamically important magnetic field in the M87 jet, we estimate the central black hole mass and spin. The method leads us to believe that the M87 super massive black hole has a mass somewhat larger than typically accepted so far.Comment: 10 pages, 1 figure, 3 tables, accepted for publication by MNRA

Learning of Causal Observable Functions for Koopman-DFL Lifting Linearization of Nonlinear Controlled Systems and Its Application to Excavation Automation

Effective and causal observable functions for low-order lifting linearization of nonlinear controlled systems are learned from data by using neural networks. While Koopman operator theory allows us to represent a nonlinear system as a linear system in an infinite-dimensional space of observables, exact linearization is guaranteed only for autonomous systems with no input, and finding effective observable functions for approximation with a low-order linear system remains an open question. Dual Faceted Linearization uses a set of effective observables for low-order lifting linearization, but the method requires knowledge of the physical structure of the nonlinear system. Here, a data-driven method is presented for generating a set of nonlinear observable functions that can accurately approximate a nonlinear control system to a low-order linear control system. A caveat in using data of measured variables as observables is that the measured variables may contain input to the system, which incurs a causality contradiction when lifting the system, i.e. taking derivatives of the observables. The current work presents a method for eliminating such anti-causal components of the observables and lifting the system using only causal observables. The method is applied to excavation automation, a complex nonlinear dynamical system, to obtain a low-order lifted linear model for control design

The wave front set of oscillatory integrals with inhomogeneous phase function

A generalized notion of oscillatory integrals that allows for inhomogeneous phase functions of arbitrary positive order is introduced. The wave front set of the resulting distributions is characterized in a way that generalizes the well-known result for phase functions that are homogeneous of order one.Comment: 12 pages, published versio