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.     

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.     

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.     

Non-Existence of Black Hole Solutions¶for a Spherically Symmetric, Static Einstein–Dirac–Maxwell System

We consider for j=?, … a spherically symmetric, static system of (2j+1) Dirac particles, each having total angular momentum j. The Dirac particles interact via a classical gravitational and electromagnetic field. The Einstein–Dirac–Maxwell equations for this system are derived. It is shown that, under weak regularity conditions on the form of the horizon, the only black hole solutions of the EDM equations are the Reissner–Nordstr?m solutions. In other words, the spinors must vanish identically. Applied to the gravitational collapse of a “cloud” of spin-?-particles to a black hole, our result indicates that the Dirac particles must eventually disappear inside the event horizon. Received: 2 November 1998 / Accepted: 23 February 1999     

Maximal degeneracy points of GKZ systems

Motivated by mirror symmetry, we study certain integral representations of solutions to the Gel´fand-Kapranov-Zelevinsky (GKZ) hypergeometric system. Some of these solutions arise as period integrals for Calabi-Yau manifolds in mirror symmetry. We prove that for a suitable compactification of the parameter space, there exist certain special boundary points, which we called maximal degeneracy points, at which all solutions but one become singular.

     

Explicit construction of graph invariant for strongly pseudoconvex compact 3-dimensional rational CR manifolds

Let X be a strongly pseudoconvex compact 3-dimensional CR manifolds which bounds a complex variety with isolated singularities in some C^N. The weighted dual graph of the exceptional set of the minimal good resolution of V is a CR invariant of X; in case X has a tranversal holomorphic S¹ action, we show that it is a complete topological invariant of except for two special cases. When X is a rational CR manifolds, we give explicit algebraic algorithms to compute the graph invariant in terms of the ring structure of _k=0 m^k/m^k+1, where m is the maximal ideal of each singularity. An example is computed explicitly to demonstrate how the algorithms work.     

Electrodeposition of Au monolayer on Pt(111) mediated by self-assembled monolayers

In-situ scanning tunneling microscopy (STM), cyclic voltammetry (CV), and infrared reflection-adsorption spectroscopy (IRRAS) have been used to examine the electrodeposition of gold onto Pt(111) electrodes modified with benzenethiol (BT) and benzene-1,2-dithiol (BDT) in 0.1 M HClO4 containing 10 microM HAuCl4. Both BT and BDT were attached to Pt(111) via one sulfur headgroup. STM and IRRAS results indicated that the other SH group of BDT was pendant in the electrolyte. Both BT and BDT formed (2 x 2) structures at the coverage of 0.25, and they were transformed into (square root(3) x square root(3))R30 degrees as the coverage was raised to 0.33. These two organic surface modifiers resulted in 3D and 2D gold islands at BT- and BDT-coated Pt(111) electrodes, respectively. The pendant SH group of BDT could interact specifically with gold adspecies to immobilize gold adatoms on the Pt(111) substrate, which yields a 2D growth of gold deposition. Molecular resolution STM revealed an ordered array of (6 x 2 square root(13)) after a full monolayer of gold was plated on the BDT/Pt(111) electrode. Since BDT was strongly adsorbed on Pt(111), gold adatoms only occupied free sites between BDT admolecules on Pt(111). This is supported by a stripping voltammetric analysis, which reveals no reductive desorption of BDT admolecules at a gold-deposited BDT/Pt(111) electrode. It seems that the BDT adlayer acted as the template for gold deposit on Pt(111). In contrast, a BT adlayer yielded 3D gold deposit on Pt(111). This study demonstrates unambiguously that organic surface modifiers could contribute greatly to the electrodeposition of metal adatoms.     

Coherently Aligned Porphyrin‐Appended Polynorbornenes

You can append on me! Porphyrin‐appended polynorbornenes derived from 5,6‐endo‐fused N‐arylpyrrolidenonorbornenes have been shown to have coherently aligned pendant groups that exhibit exciton coupling and fluorescence quenching in the absorption and emission profiles (see figure).

     

Simultaneous determination of low-molecular-weight organic acids and chlorinated acid herbicides in environmental water by a portable CE system with contactless conductivity detection

This report describes a method to simultaneously determine 11 low-molecular-weight (LMW) organic acids and 16 chlorinated acid herbicides within a single run by a portable CE system with contactless conductivity detection (CCD) in a poly(vinyl alcohol) (PVA)-coated capillary. Under the optimized condition, the LODs of CE-CCD ranged from 0.056 to 0.270 ppm, which were better than for indirect UV (IUV) detection of the 11 LMW organic acids or UV detection of the 16 chlorinated acid herbicides. Combined with an on-line field-amplified sample stacking (FASS) procedure, sensitivity enhancement of 632- to 1078-fold was achieved, with satisfactory reproducibility (RSDs of migration times less than 2.2%, and RSDs of peak areas less than 5.1%). The FASS-CE-CCD method was successfully applied to determine the two groups of acidic pollutants in two kinds of environmental water samples. The portable CE-CCD system shows advantages such as simplicity, cost effectiveness, and miniaturization. Therefore, the method presented in this report has great potential for onsite analysis of various pollutants at the trace level.