Concentration and exact convergence rates for expected Brownian signatures

The signature of a dd-dimensional Brownian motion is a sequence of iterated Stratonovich integrals along the Brownian paths, an object taking values in the tensor algebra over RdRd. In this article, we derive the exact rate of convergence for the expected signatures of piecewise linear approximations to Brownian motion. The computation is based on the identification of the set of words whose coefficients are of the leading order, and the convergence is concentrated on this subset of words. Moreover, under the choice of l1l1 tensor norm, we give the explicit value of the leading term constant

Ellipsometry noise spectrum, suspension transfer function measurement and closed-loop control of the suspension system in the Q & A experiment

The Q & A experiment, aiming at the detection of vacuum birefringence predicted by quantum electrodynamics, consists mainly of a suspended 3.5 m Fabry-Perot cavity, a rotating permanent dipole magnet and an ellipsometer. The 2.3 T magnet can rotate up to 10 rev/s, introducing an ellipticity signal at twice the rotation frequency. The X-pendulum gives a good isolation ratio for seismic noise above its main resonant frequency 0.3 Hz. At present, the ellipsometry noise decreases with frequency, from 1*10^{-5} rad Hz^{-1/2} at 5 Hz, 2*10^{-6} rad Hz^{-1/2} at 20 Hz to 5*10^{-7} rad Hz^{-1/2} at 40 Hz. The shape of the noise spectrum indicates possible improvement can be made by further reducing the movement between the cavity mirrors. From the preliminary result of yaw motion alignment control, it can be seen that some peaks due to yaw motion of the cavity mirror was suppressed. In this paper, we first give a schematic view of the Q & A experiment, and then present the measurement of transfer function of the compound X-pendulum-double pendulum suspension. A closed-loop control was carried out to verify the validity of the measured transfer functions. The ellipsometry noise spectra with and without yaw alignment control and the newest improvement is presented.Comment: 7 pages, 5 figures, presented in 6th Edoardo Amaldi Conference on Gravitational Waves, June 2005, Okinawa Japan and submitted to Journal of Physics: Conference Series. Some modifications are made according to the referee's comments: mainly to explain the relation between the displacement of cavity mirror and the ellipticity noise spectru

Acceleration disturbances due to local gravity gradients in ASTROD I

The Astrodynamical Space Test of Relativity using Optical Devices (ASTROD) mission consists of three spacecraft in separate solar orbits and carries out laser interferometric ranging. ASTROD aims at testing relativistic gravity, measuring the solar system and detecting gravitational waves. Because of the larger arm length, the sensitivity of ASTROD to gravitational waves is estimated to be about 30 times better than Laser Interferometer Space Antenna (LISA) in the frequency range lower than about 0.1 mHz. ASTROD I is a simple version of ASTROD, employing one spacecraft in a solar orbit. It is the first step for ASTROD and serves as a technology demonstration mission for ASTROD. In addition, several scientific results are expected in the ASTROD I experiment. The required acceleration noise level of ASTROD I is 10^-13 m s^-2 Hz^{-1/2} at the frequency of 0.1 mHz. In this paper, we focus on local gravity gradient noise that could be one of the largest acceleration disturbances in the ASTROD I experiment. We have carried out gravitational modelling for the current test-mass design and simplified configurations of ASTROD I by using an analytical method and the Monte Carlo method. Our analyses can be applied to figure out the optimal designs of the test mass and the constructing materials of the spacecraft, and the configuration of compensation mass to reduce local gravity gradients.Comment: 6 pages, presented at the 6th Edoardo Amaldi Conference (Okinawa Japan, June 2005); to be published in Journal of Physics: Conference Serie

Rotation, Equivalence Principle, and GP-B Experiment

The ultra-precise Gravity Probe B experiment measured the frame-dragging effect and geodetic precession on four quartz gyros. We use this result to test WEP II (Weak Equivalence Principle II) which includes rotation in the universal free-fall motion. The free-fall E\"otv\"os parameter eta for rotating body is < = 10**(-11) with four-order improvement over previous results. The anomalous torque per unit angular momentum parameter lambda is constrained to (-0.05 +- 3.67) \times 10**(-15) s-1, (0.24 +- 0.98) \times 10**(-15) s-1, and (0 +- 3.6) \times 10**(-13) s-1 respectively in the directions of geodetic effect, frame-dragging effect and angular momentum axis; the dimensionless frequency-dependence parameter {\kappa} is constrained to (1.75 +- 4.96) \times 10**(-17), (1.80 +- 1.34) \times 10**(-17), and (0 +- 3) \times 10**(-14) respectively.Comment: 9 pages, 2 figures, 3 table

An optimal gap theorem

By solving the Cauchy problem for the Hodge-Laplace heat equation for $d$-closed, positive $(1, 1)$-forms, we prove an optimal gap theorem for K\"ahler manifolds with nonnegative bisectional curvature which asserts that the manifold is flat if the average of the scalar curvature over balls of radius $r$ centered at any fixed point $o$ is a function of $o(r^{-2})$. Furthermore via a relative monotonicity estimate we obtain a stronger statement, namely a `positive mass' type result, asserting that if $(M, g)$ is not flat, then $\liminf_{r\to \infty} \frac{r^2}{V_o(r)}\int_{B_o(r)}\mathcal{S}(y)\, d\mu(y)>0$ for any $o\in M$

Non-minimal coupling of photons and axions

We establish a new self-consistent system of equations accounting for a non-minimal interaction of gravitational, electromagnetic and axion fields. The procedure is based on a non-minimal extension of the standard Einstein-Maxwell-axion action. The general properties of a ten-parameter family of non-minimal linear models are discussed. We apply this theory to the models with pp-wave symmetry and consider propagation of electromagnetic waves non-minimally coupled to the gravitational and axion fields. We focus on exact solutions of electrodynamic equations, which describe quasi-minimal and non-minimal optical activity induced by the axion field. We also discuss empirical constraints on coupling parameters from astrophysical birefringence and polarization rotation observations.Comment: 31 pages, 2 Tables; replaced with the final version published in Classical and Quantum Gravit

Kalman filter based estimation of neutral-axis position of bridge deck sections using strain monitoring data

The neutral-axis position has been recognized as a damage indicator for bridge deck assessment because of its high sensitivity to local damage on deck sections. It can be estimated when strain responses at the top and bottom of a deck cross-section under traffic loading are measured. However, the accuracy of neutral-axis position estimation directly using the measured strain responses might be significantly distorted in the presence of measurement noise and varying traffic load patterns. In this study, a Kalman filter (KF) estimator is formulated to locate the neutral-axis position from measured strain responses under traffic loading. Its capability for consistently locating the neutral-axis position under varying traffic load patterns is verified using the field monitoring data of traffic-induced strain responses acquired from the suspension Tsing Ma Bridge under diverse load scenarios (highway traffic, railway traffic, and their combination). The results indicate that the proposed KF estimator gives rise to consistent neutral-axis position estimation results which are independent of load conditions and patterns

Online UAV Trajectory Planning for Covert Video Surveillance of Mobile Targets

This article considers the use of an unmanned aerial vehicle (UAV) for covert video surveillance of a mobile target on the ground and presents a new online UAV trajectory planning technique with a balanced consideration of the energy efficiency, covertness, and aeronautic maneuverability of the UAV. Specifically, a new metric is designed to quantify the covertness of the UAV, based on which a multiobjective UAV trajectory planning problem is formulated to maximize the disguising performance and minimize the trajectory length of the UAV. A forward dynamic programming method is put forth to solve the problem online and plan the trajectory for the foreseeable future. In addition, the kinematic model of the UAV is considered in the planning process so that it can be tracked without any later adjustment. Extensive computer simulations are conducted to demonstrate the effectiveness of the proposed technique. Note to Practitioners - The 'Follow Me' flight mode is available in many unmanned aerial vehicle (UAV) products, and this technique enables a UAV to automatically follow a target. However, this flight mode may make the UAV noticeable to the target and compromise the video surveillance missions of the UAV. Inspired by some security surveillance applications where UAV surveillance is conducted so that a target would not take actions to avoid being monitored, we propose an efficient method to construct the trajectory for the UAV. The proposed method considers the visual covertness and the battery capacity limitation of the UAV, and it can produce a trajectory online for the UAV. The proposed method and scenario can potentially extend the 'Follow Me' flight mode and generate new applications and market for UAVs

Decentralized Navigation of a UAV Team for Collaborative Covert Eavesdropping on a Group of Mobile Ground Nodes

Unmanned aerial vehicles (UAVs) are increasingly applied to surveillance tasks, thanks to their excellent mobility and flexibility. Different from existing works using UAVs for video surveillance, this paper employs a UAV team to carry out collaborative radio surveillance on ground moving nodes and disguise the purpose of surveillance. We consider two aspects of disguise. The first is that the UAVs do not communicate with each other (or the ground nodes can notice), and each UAV plans its trajectory in a decentralized way. The other aspect of disguise is that the UAVs avoid being noticed by the nodes for which a metric quantifying the disguising performance is adopted. We present a new decentralized method for the online trajectory planning of the UAVs, which maximizes the disguising metric while maintaining uninterrupted surveillance and avoiding UAV collisions. Based on the model predictive control (MPC) technique, our method allows each UAV to separately estimate the locations of the UAVs and the ground nodes, and decide its trajectory accordingly. The impact of potential estimation errors is mitigated by incorporating the error bounds into the online trajectory planning, hence achieving a robust control of the trajectories. Computer-based simulation results demonstrate that the developed strategy ensures the surveillance requirement without losing disguising performance, and outperforms existing alternatives. Note to Practitioners - The paper is motivated by the covertness requirement in the radio surveillance (also called eavesdropping) by UAVs. In some situations, the UAV user (such as the police department) wishes to disguise the surveillance intention from the targets, and the trajectories of UAVs play a significant role in the disguising. However, the typical UAV trajectories such as standoff tracking and orbiting can easily be noticed by the targets. Considering this gap, we focus on how to plan the UAVs' trajectories so that they are less noticeable while conducting effective eavesdropping. We formulate a path planning problem aiming at maximizing a disguising metric, which measures the magnitude of the relative position change between a UAV and a target. A decentralized method is proposed for the online trajectory planning of the UAVs based on MPC, and its robust version is also presented to account for the uncertainty in the estimation and prediction of the nodes' states