A conjectural generalization of the n! result to arbitrary groups

The aim of this paper is to formulate a conjecture for an arbitrary simple Lie algebra g in terms of the geometry of principal nilpotent pairs. When g is specialized to sln, this conjecture readily implies the n! result and it is very likely that, in fact, it is equivalent to the n! result in this case. In addition, this conjecture can be thought of as generalizing an old result of Kostant. In another direction, we show that to prove the validity of the n! result for an arbitrary n and an arbitrary partition of n, it suffices to show its validity only for the staircase partitions.     

On the modeling of narrow gaps using the standard boundary element method

Numerical methods based on the Helmholtz integral equation are well suited for solving acoustic scattering and diffraction problems at relatively low frequencies. However, it is well known that the standard method becomes degenerate if the objects that disturb the sound field are very thin. This paper makes use of a standard axisymmetric Helmholtz integral equation formulation and its boundary element method (BEM) implementation to study the behavior of the method on two test cases: a thin rigid disk of variable thickness and two rigid cylinders separated by a gap of variable width. Both problems give rise to the same kind of degeneracy in the method, and modified formulations have been proposed to overcome this difficulty. However, such techniques are better suited for the so-called thin-body problem than for the reciprocal narrow-gap problem, and only the first is usually dealt with in the literature. A simple integration technique that can extend the range of thicknesses/widths tractable by the otherwise unmodified standard formulation is presented and tested. This technique is valid for both cases. The modeling of acoustic transducers like sound intensity probes and condenser microphones has motivated this work, although the proposed technique has a wider range of applications.     

Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models. II. Extended Results for Square-Lattice Chromatic Polynomial

We study the chromatic polynomials for m×n square-lattice strips, of width 9m13 (with periodic boundary conditions) and arbitrary length n (with free boundary conditions). We have used a transfer matrix approach that allowed us also to extract the limiting curves when n. In this limit we have also obtained the isolated limiting points for these square-lattice strips and checked some conjectures related to the Beraha numbers.     

Unusual Corrections to Scaling in the 3-State Potts Antiferromagnet on a Square Lattice

At zero temperature, the 3-state antiferromagnetic Potts model on a square lattice maps exactly onto a point of the 6-vertex model whose long-distance behavior is equivalent to that of a free scalar boson. We point out that at nonzero temperature there are two distinct types of excitation: vortices, which are relevant with renormalization-group eigenvalue 1/2 and non-vortex unsatisfied bonds, which are strictly marginal and serve only to renormalize the stiffness coefficient of the underlying free boson. Together these excitations lead to an unusual form for the corrections to scaling: for example, the correlation length diverges as J/kT according to Ae ² (1+be ^– +···), where b is a nonuniversal constant that may nevertheless be determined independently. A similar result holds for the staggered susceptibility. These results are shown to be consistent with the anomalous behavior found in the Monte Carlo simulations of Ferreira and Sokal.     

Calculation of quantum tunneling for a spatially extended defect: the dislocation kink in copper has a low effective mass

Several experiments indicate that there are atomic tunneling defects in plastically deformed metals. How this is possible has not been clear, given the large mass of the metal atoms. Using a classical molecular-dynamics calculation, we determine the structures, energy barriers, effective masses, and quantum tunneling rates for dislocation kinks and jogs in copper screw dislocations. We find that jogs are unlikely to tunnel, but the kinks should have large quantum fluctuations. The kink motion involves hundreds of atoms each shifting a tiny amount, leading to a small effective mass and tunneling barrier.     

UV absorption spectra of HO2, CH3O2, C2H5O2, and CH3C(O)CH2O2 radicals and mechanism of the reactions of F and Cl atoms with CH3C(O)CH3

Pulse radiolysis techniques were used to measure the gas phase UV absorption spectra of the title peroxy radicals over the range 215–340 nm. By scaling to σ(CH₃O₂)_{240 nm} = (4.24 ± 0.27) × 10^?18, the following absorption cross sections were determined: σ(HO₂)_{240 nm} = 1.29 ± 0.16, σ(C₂H₅O₂)_{240 nm} = 4.71 ± 0.45, σ(CH₃C(O)CH₂O₂)_{240 nm} = 2.03 ± 0.22, σ(CH₃C(O)CH₂O₂)_{230 nm} = 2.94 ± 0.29, and σ(CH₃C(O)CH₂O₂)_{310 nm} = 1.31 ± 0.15 (base e, units of 10^?18 cm² molecule^?1). To support the UV measurements, FTIR‐smog chamber techniques were employed to investigate the reaction of F and Cl atoms with acetone. The F atom reaction proceeds via two channels: the major channel (92% ± 3%) gives CH₃C(O)CH₂ radicals and HF, while the minor channel (8% ± 1%) gives CH₃ radicals and CH₃C(O)F. The majority (>97%) of the Cl atom reaction proceeds via H atom abstraction to give CH₃C(O)CH₂ radicals. The results are discussed with respect to the literature data concerning the UV absorption spectra of CH₃C(O)CH₂O₂ and other peroxy radicals. © 2002 Wiley Periodicals, Inc. Int J Chem Kinet 34: 283–291, 2002     

Towards a synthetic avidin mimic

A series of streptavidin-mimicking molecularly imprinted polymers has been developed and evaluated for their biotin binding characteristics. A combination of molecular dynamics and NMR spectroscopy was used to examine potential polymer systems, in particular with the functional monomers methacrylic acid and 2-acrylamidopyridine. The synthesis of copolymers of ethylene dimethacrylate and one or both of these functional monomers was performed. A combination of radioligand binding studies and surface area analyses demonstrated the presence of selectivity in polymers prepared using methacrylic acid as the functional monomer. This was predicted by the molecular dynamics studies showing the power of this methodology as a prognostic tool for predicting the behavior of molecularly imprinted polymers.

Observation of B Meson decays to b1pi and b1K

We present the results of searches for decays of B mesons to final states with a b1 meson and a charged pion or kaon. The data, collected with the BABAR detector at the Stanford Linear Accelerator Center, represent 382x10(6) BB[over ] pairs produced in e+e- annihilation. The results for the branching fractions are, in units of 10(-6), B(B+-->b1(0)pi+)=6.7+/-1.7+/-1.0, B(B+-->b1(0)K+)=9.1+/-1.7+/-1.0, B(B0-->b1(-/+)pi(+/-))=10.9+/-1.2+/-0.9, and B(B0-->b1(-)K+)=7.4+/-1.0+/-1.0, with the assumption that B(b1-->omega pi)=1. We also measure charge and flavor asymmetries A(ch)(B+-->b1(0)pi+)=0.05+/-0.16+/-0.02, Ach(B+-->b1(0)K+)=-0.46+/-0.20+/-0.02, A(ch)(B0-->b1(-/+)pi(+/-))=-0.05+/-0.10+/-0.02, C(B0-->b1(-/+)pi(+/-))=-0.22+/-0.23+/-0.05, DeltaC(B0-->b1(-/+)pi(+/-))=-1.04+/-0.23+/-0.08, and A(ch)(B0-->b1(-)K+)=-0.07+/-0.12+/-0.02. The first error quoted is statistical, and the second systematic.