Polariton induced transparency at low light level: polymer chains dispersed in a monomer single crystal

Excitons of polydiacetylene chains, diluted in a 3BCMU monomer single crystal, turn at very low light intensity into a nonabsorbing polariton state once the polymer concentration exceeds 10{-4} in weight. The transition is evident from a Lorentzian absorption peak which is truncated at an optical density OD approximately 2 and is consistent with polariton coupling of light to eigenstates of the solid while Rabi coupling of individual chains to light is excluded. The saturated absorption is nearly independent of polymer content and crystal thickness and defines a surface region where photons are converted into polaritons, the corresponding electromagnetic eigenmodes of matter.     

Kinetics and mechanism of proton transport across membrane nanopores

We use computer simulations to study the kinetics and mechanism of proton passage through a narrow-pore carbon-nanotube membrane separating reservoirs of liquid water. Free energy and rate constant calculations show that protons move across the membrane diffusively along single-file chains of hydrogen-bonded water molecules. Proton passage through the membrane is opposed by a high barrier in the effective potential, reflecting the large electrostatic penalty for desolvation and reminiscent of charge exclusion in biological water channels. At neutral pH, we estimate a translocation rate of about 1 proton per hour and tube.     

Cycloaddition Reactions of an Active Cyclic Phosphane/Borane Pair with Alkenes,Alkynes, and Carbon Dioxide

The active six-membered cyclo-FLP 6 undergoes a rapid P/B addition reaction to carbon dioxide. At elevated temperature, the resulting heterobicyclo[2.2.2]octane derived product 7 undergoes ring opening and equilibrates with the cyclotetramer (7)₄ . In the large macrocyclic structure, four monomeric six-membered cyclo-FLP units are connected by four CO₂ molecules to form the supramolecular ring system. The P/B cyclo-FLP 6 undergoes a variety of additional cycloaddition reactions.     

On Reflection Subgroups of Finite Coxeter Groups

Let W be a finite Coxeter group. We classify the reflection subgroups of W up to conjugacy and give necessary and sufficient conditions for the map that assigns to a reflection subgroup R of W the conjugacy class of its Coxeter elements to be injective, up to conjugacy.     

A hybrid Arnoldi-Faber iterative method for nonsymmetric systems of linear equations

Summary We present here a new hybrid method for the iterative solution of large sparse nonsymmetric systems of linear equations, say of the formAx=b, whereA ^{N, N} , withA nonsingular, andb ^N are given. This hybrid method begins with a limited number of steps of the Arnoldi method to obtain some information on the location of the spectrum ofA, and then switches to a Richardson iterative method based on Faber polynomials. For a polygonal domain, the Faber polynomials can be constructed recursively from the parameters in the Schwarz-Christoffel mapping function. In four specific numerical examples of non-normal matrices, we show that this hybrid algorithm converges quite well and is approximately as fast or faster than the hybrid GMRES or restarted versions of the GMRES algorithm. It is, however, sensitive (as other hybrid methods also are) to the amount of information on the spectrum ofA acquired during the first (Arnoldi) phase of this procedure.     

Internal rotation and chlorine nuclear quadrupole coupling of o-chlorotoluene studied by microwave spectroscopy and ab initio calculations

The microwave spectrum of o-chlorotoluene has been reinvestigated using molecular beam Fourier transform microwave (MB-FTMW) spectrometers in the frequency range of 4–23 GHz. Due to the high resolution of this molecular beam technique the analysis yielded improved rotational constants, centrifugal distortion constants, and, for the first time, the complete chlorine nuclear quadrupole coupling tensor. From the torsional fine structure the barrier to internal rotation of the methyl group was found to be 5.5798(52) kJ mol⁻¹. Experimental results and ab initio calculations are compared.     

Bootstrap approximation of nearest neighbor regression function estimates

Let (X, Y) be a random vector in the plane and denote by m(x) = (Y|X = x) the corresponding regression function. We show that the bootstrap approximation for the distribution of a smoothed nearest neighbor estimate of m(x) is valid. Also we compare, by Monte Carlo, confidence intervals which are obtained from both the normal and the bootstrap approximation.