Distributed Optimal Frequency Control Considering a Nonlinear Network-Preserving Model

This paper addresses the distributed optimal frequency control of power systems considering a network-preserving model with nonlinear power flows and excitation voltage dynamics. Salient features of the proposed distributed control strategy are fourfold: i) nonlinearity is considered to cope with large disturbances; ii) only a part of generators are controllable; iii) no load measurement is required; iv) communication connectivity is required only for the controllable generators. To this end, benefiting from the concept of 'virtual load demand', we first design the distributed controller for the controllable generators by leveraging the primal-dual decomposition technique. We then propose a method to estimate the virtual load demand of each controllable generator based on local frequencies. We derive incremental passivity conditions for the uncontrollable generators. Finally, we prove that the closed-loop system is asymptotically stable and its equilibrium attains the optimal solution to the associated economic dispatch problem. Simulations, including small and large-disturbance scenarios, are carried on the New England system, demonstrating the effectiveness of our design

World-line Quantisation of a Reciprocally Invariant System

We present the world-line quantisation of a system invariant under the symmetries of reciprocal relativity (pseudo-unitary transformations on ``phase space coordinates" $(x^\mu(\tau),p^\mu(\tau))$ which preserve the Minkowski metric and the symplectic form, and global shifts in these coordinates, together with coordinate dependent transformations of an additional compact phase coordinate, $\theta(\tau)$). The action is that of free motion over the corresponding Weyl-Heisenberg group. Imposition of the first class constraint, the generator of local time reparametrisations, on physical states enforces identification of the world-line cosmological constant with a fixed value of the quadratic Casimir of the quaplectic symmetry group $Q(D-1,1)\cong U(D-1,1)\ltimes H(D)$, the semi-direct product of the pseudo-unitary group with the Weyl-Heisenberg group (the central extension of the global translation group, with central extension associated to the phase variable $\theta(\tau)$). The spacetime spectrum of physical states is identified. Even though for an appropriate range of values the restriction enforced by the cosmological constant projects out negative norm states from the physical spectrum, leaving over spin zero states only, the mass-squared spectrum is continuous over the entire real line and thus includes a tachyonic branch as well

On the rate of black hole binary mergers in galactic nuclei due to dynamical hardening

We assess the contribution of dynamical hardening by direct three-body scattering interactions to the rate of stellar-mass black hole binary (BHB) mergers in galactic nuclei. We derive an analytic model for the single-binary encounter rate in a nucleus with spherical and disk components hosting a super-massive black hole (SMBH). We determine the total number of encounters $N_{\rm GW}$ needed to harden a BHB to the point that inspiral due to gravitational wave emission occurs before the next three-body scattering event. This is done independently for both the spherical and disk components. Using a Monte Carlo approach, we refine our calculations for $N_{\rm GW}$ to include gravitational wave emission between scattering events. For astrophysically plausible models we find that typically $N_{\rm GW} \lesssim$ 10. We find two separate regimes for the efficient dynamical hardening of BHBs: (1) spherical star clusters with high central densities, low velocity dispersions and no significant Keplerian component; and (2) migration traps in disks around SMBHs lacking any significant spherical stellar component in the vicinity of the migration trap, which is expected due to effective orbital inclination reduction of any spherical population by the disk. We also find a weak correlation between the ratio of the second-order velocity moment to velocity dispersion in galactic nuclei and the rate of BHB mergers, where this ratio is a proxy for the ratio between the rotation- and dispersion-supported components. Because disks enforce planar interactions that are efficient in hardening BHBs, particularly in migration traps, they have high merger rates that can contribute significantly to the rate of BHB mergers detected by the advanced Laser Interferometer Gravitational-Wave Observatory.Comment: 13 pages, 9 figures, accepted for publication in MNRA

NICMOS Imaging of the Nuclei of Arp 220

We report high resolution imaging of the ultraluminous infrared galaxy Arp 220 at 1.1, 1.6, and 2.22 microns with NICMOS on the HST. The diffraction-limited images at 0.1--0.2 arcsecond resolution clearly resolve both nuclei of the merging galaxy system and reveal for the first time a number of luminous star clusters in the circumnuclear envelope. The morphologies of both nuclei are strongly affected by dust obscuration, even at 2.2 microns : the primary nucleus (west) presents a crescent shape, concave to the south and the secondary (eastern) nucleus is bifurcated by a dust lane with the southern component being very reddened. In the western nucleus, the morphology of the 2.2 micron emission is most likely the result of obscuration by an opaque disk embedded within the nuclear star cluster. The morphology of the central starburst-cluster in the western nucleus is consistent with either a circumnuclear ring of star formation or a spherical cluster with the bottom half obscured by the embedded dust disk. Comparison of cm-wave radio continuum maps with the near-infrared images suggests that the radio nuclei lie in the dust disk on the west and near the highly reddened southern component of the eastern complex. The radio nuclei are separated by 0.98 arcseconds (corresponding to 364 pc at 77 Mpc) and the half-widths of the infrared nuclei are approximately 0.2-0.5 arcseconds. At least 8, unresolved infrared sources -- probably globular clusters -- are also seen in the circumnuclear envelope at radii 2-7 arcseconds . Their near-infrared colors do not significantly constrain their ages.Comment: LaTex, 15 pages with 1 gif figure and 5 postscript figures. ApJL accepte

Factorization Properties of Soft Graviton Amplitudes

We apply recently developed path integral resummation methods to perturbative quantum gravity. In particular, we provide supporting evidence that eikonal graviton amplitudes factorize into hard and soft parts, and confirm a recent hypothesis that soft gravitons are modelled by vacuum expectation values of products of certain Wilson line operators, which differ for massless and massive particles. We also investigate terms which break this factorization, and find that they are subleading with respect to the eikonal amplitude. The results may help in understanding the connections between gravity and gauge theories in more detail, as well as in studying gravitational radiation beyond the eikonal approximation.Comment: 35 pages, 5 figure

Sunspot rotation, filament, and flare: The event on 2000 February 10

We find that a sunspot with positive polarity had an obvious counter-clockwise rotation and resulted in the formation and eruption of an inverse S-shaped filament in NOAA active region (AR) 08858 from 2000 February 9 to 10. The sunspot had two umbrae which rotated around each other by 195 degrees within about twenty-four hours. The average rotation rate was nearly 8 degrees per hour. The fastest rotation in the photosphere took place during 14:00UT to 22:01UT on February 9, with the rotation rate of nearly 16 degrees per hour. The fastest rotation in the chromosphere and the corona took place during 15:28UT to 19:00UT on February 9, with the rotation rate of nearly 20 degrees per hour. Interestingly, the rapid increase of the positive magnetic flux just occurred during the fastest rotation of the rotating sunspot, the bright loop-shaped structure and the filament. During the sunspot rotation, the inverse S-shaped filament gradually formed in the EUV filament channel. The filament experienced two eruptions. In the first eruption, the filament rose quickly and then the filament loops carrying the cool and the hot material were seen to spiral into the sunspot counterclockwise. About ten minutes later, the filament became active and finally erupted. The filament eruption was accompanied with a C-class flare and a halo coronal mass ejection (CME). These results provide evidence that sunspot rotation plays an important role in the formation and eruption of the sigmoidal active-region filament.Comment: 20 pages, 9 figures, Accepted for publication in Ap

Sum Rule Description of Color Transparency

The assumption that a small point-like configuration does not interact with nucleons leads to a new set of sum rules that are interpreted as models of the baryon-nucleon interaction. These models are rendered semi-realistic by requiring consistency with data for cross section fluctuations in proton-proton diffractive collisions.Comment: 22 pages + 3 postscript figures attache

Multiple-Scattering Series For Color Transparency

Color transparency CT depends on the formation of a wavepacket of small spatial extent. It is useful to interpret experimental searches for CT with a multiple scattering scattering series based on wavepacket-nucleon scattering instead of the standard one using nucleon-nucleon scattering. We develop several new techniques which are valid for differing ranges of energy. These techniques are applied to verify some early approximations; study new forms of the wave-packet-nucleon interaction; examine effects of treating wave packets of non-zero size; and predict the production of $N^*$'s in electron scattering experiments.Comment: 26 pages, U.Wa. preprint 40427-23-N9

Higgs After the Discovery: A Status Report

Recently, the ATLAS and CMS collaborations have announced the discovery of a 125 GeV particle, commensurable with the Higgs boson. We analyze the 2011 and 2012 LHC and Tevatron Higgs data in the context of simplified new physics models, paying close attention to models which can enhance the diphoton rate and allow for a natural weak-scale theory. Combining the available LHC and Tevatron data in the ZZ* 4-lepton, WW* 2-lepton, diphoton, and b-bbar channels, we derive constraints on the effective low-energy theory of the Higgs boson. We map several simplified scenarios to the effective theory, capturing numerous new physics models such as supersymmetry, composite Higgs, dilaton. We further study models with extended Higgs sectors which can naturally enhance the diphoton rate. We find that the current Higgs data are consistent with the Standard Model Higgs boson and, consequently, the parameter space in all models which go beyond the Standard Model is highly constrained.Comment: 37 pages; v2: ATLAS dijet-tag diphoton channel added, dilaton and doublet-singlet bugs corrected, references added; v3: ATLAS WW channel included, comments and references adde