17,117 research outputs found
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
-closed, positive -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 centered at any fixed point is a function of .
Furthermore via a relative monotonicity estimate we obtain a stronger
statement, namely a `positive mass' type result, asserting that if is
not flat, then for any
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
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
A Method for Covert Video Surveillance of a Car or a Pedestrian by an Autonomous Aerial Drone via Trajectory Planning
This paper considers the application of covert video surveillance of a ground mobile target by an autonomous aerial drone. We design a metric to measure the covertness of the drone. Then, we formulate a multi-objective drone trajectory planning problem, which maximizes the drone disguising performance and minimizes its energy consumption. We furthermore propose a forward dynamic programming method to solve the problem online and conduct simulations to verify its effectiveness
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
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