A multiple regression model for urban traffic noise in Hong Kong

This article describes the roadside traffic noise surveys conducted in heavily built-up urban areas in Hong Kong. Noise measurements were carried out along 18 major roads in 1999. The measurement data included L10, L50, L90, Leq, Lmax, the number of light vehicles, the number of heavy vehicles, the total traffic flow, and the average speed of vehicles. Statistical analysis using the analysis of variance (ANOVA) and Tukey test (p<0.05) reveals that the total traffic flow and the number of heavy vehicles are the most significant factors of urban traffic noise. Multiple regression was used to derive a set of empirical formulas for predicting L10 noise level due to road traffic. The accuracy of these empirical formulas is quantified and compared to that of another widely used prediction model in Hong Kong--the Calculation of Road Traffic Noise. The applicability of the selected multiple regression model is validated by the noise measurements performed in the winter of 2000.     

Decay Rates and Probability Estimates¶for Massive Dirac Particles¶in the Kerr–Newman Black Hole Geometry

The Cauchy problem is considered for the massive Dirac equation in the non-extreme Kerr–Newman geometry, for smooth initial data with compact support outside the event horizon and bounded angular momentum. We prove that the Dirac wave function decays in at least at the rate t ^−5/6. For generic initial data, this rate of decay is sharp. We derive a formula for the probability p that the Dirac particle escapes to infinity. For various conditions on the initial data, we show that p = 0, 1 or 0 < p < 1. The proofs are based on a refined analysis of the Dirac propagator constructed in [4]. Received: 20 August 2001 / Accepted: 22 January 2002 RID="*" ID="*"Present address: NWF I – Mathematik, Universit?t Regensburg, 93040 Regensburg, Germany.?E-mail: felix.finster@mathematik.uni-regensburg.de RID="**" ID="**"Research supported by NSERC grant # RGPIN 105490-1998. RID="***" ID="***"Research supported in part by the NSF, Grant No. DMS-0103998. RID="****" ID="****"Research supported in part by the NSF, Grant No. 33-585-7510-2-30.     

Fast response self-pumped phase conjugator based on a +c-face incident configuration in a pentagon-shaped BaTiO3 crystal

We propose a novel geometry for a self-pumped phase conjugator that uses a +c-face incident configuration in a photorefractive pentagon-shaped 0°-cut BaTiO₃ crystal for obtaining fast response in phase conjugation. A steady phase-conjugate output with a fast response time 0.4 s is obtained when the incident beam has a 4 W/cm² intensity. The influences of position and angle on the temporal phase-conjugate response are also investigated. The advantage of this phase conjugator using this novel configuration is improved resolution of a phase-distorted image with a value as high as 128 lp/mm.     

A speckle-shearing interferometer: A tool for measuring derivatives of surface displacements

A speckle-shearing interferometer is developed using a sheared Michelson interferometer. The tool, like speckle interferometry, utilizes the speckle effect of coherent light. However, while speckle interferometry measures surface displacements, the speckle-shearing interferometer determines the derivatives of the surface displacements. Hence, it eliminates the necessity of differentiating the measured displacements to obtain strain.     

Derivation of the Euler Equations from Quantum Dynamics

We derive the Euler equations from quantum dynamics for a class of fermionic many-body systems. We make two types of assumptions. The first type are physical assumptions on the solution of the Euler equations for the given initial data. The second type are a number of reasonable conjectures on the statistical mechanics and dynamics of the Fermion Hamiltonian.©2003 B. Nachtergaele and H.-T. Yau. This article may be reproduced in its entirety for non-commercial purposes.Research partially supported by NSF # DMS-0070774.Research partially supported by NSF # DMS-0072098, the Veblen Fund from the Institute for Advanced Study and a Fellowship from the MacArthur Foundation.     

Amphoteric refraction exhibited by anisotropic crystals

Amphoteric refraction of light ray at the interface between isotropic materials and anisotropic materials is analyzed. Depending on the incident angle, the refractive light ray can either refract positively or negatively. This amphoteric refraction phenomenon can be quite prevalent when the difference of the two principal refractive indices is large. The reflectance under various incident angles has also been calculated, and an experimental demonstration with a calcite crystal in air is presented.     

Mutually pumped phase conjugator using a BaTiO3 crystal having two inclined faces

A pentagon-shaped undoped BaTiO₃ crystal was used to construct a high-quality mutually pumped phase conjugator. It yields two very stable phase-conjugate outputs (ǃ.7% fluctuation in intensity) with high reflectivity (the highest ᅝ%) when the two incident beams are of equal intensities. The response time of the conjugator is rather fast (ƻ s) and the tolerance of the acceptance angle is large too (걄°). Fine structures (35 7m) in an image, after passing through a phase aberrator, can be recovered by the conjugate waves yielded by this conjugator.