Extreme Sub-radiance: Can Quantum Effects Generate Dramatically Longer Atomic Lifetimes?

The prolongation of lifetimes for an excited atom due to the presence of nearby atoms in the ground state is shown to follow simply from unitarity of the time evolution. We also discuss possible approaches to the detection and the overcoming of various technical obstacles.     

Band-gaps in electrostatically controlled dielectric laminates subjected to incremental shear motions

The thickness vibrations of a finitely deformed infinite periodic laminate made out of two layers of dielectric elastomers is studied. The laminate is pre-stretched by inducing a bias electric field perpendicular to the layers. Incremental time-harmonic fields superimposed on the initial finite deformation are considered next. Utilizing the Bloch-Floquet theorem along with the transfer matrix method we determine the dispersion relation which relates the incremental fields frequency and the phase velocity.Ranges of frequencies at which waves cannot propagate are identified whenever the Bloch-parameter is complex. These band-gaps depend on the phases properties, their volume fraction, and most importantly on the electric bias field. Our analysis reveals how these band-gaps can be shifted and their width can be modified by changing the bias electric field. This implies that by controlling the electrostatic bias field desired frequencies can be filtered out. Representative examples of laminates with different combinations of commercially available dielectric elastomers are examined.     

Overcrowded naphthologs of mono-bridged tetraarylethylenes: analogs of bistricyclic aromatic enes

The naphthalogous mono-bridged tetraarylethylenes 9,9′-di-(1-naphthylmethylene)-9H-fluorene (5) and 9,9′-di-(1-naphthylmethylene)-9H-xanthene (6), analogs of bifluorenylidene (1) and bixanthenylidene (2), have been synthesized and their molecular and crystal structures have been determined. Ene 5 has been prepared by two alternative synthetic routes. The molecular structures of 5 and 6 show that each of these enes has very small twist around the central double bond, but the two naphthalene rings in both 5 and 6 are highly twisted. According to the NMR study, 5 and 6 in solution adopt conformations which are similar to those found by X-ray crystal structure analysis. The notable upfield shifts of H¹ and H⁸ (6.11 and 6.83 ppm, respectively) and H² and H⁷ (6.70 and 6.44 ppm, respectively) in 5 and 6 are due to the shielding caused by the nearly orthogonally twisted naphthalene rings. The B3LYP/6-31G(d) calculations of 5, 6, and their 2-naphthyl and phenyl analogs have been performed. In the 1-naphthyl series, the more efficient conjugation between the naphthyl substituents and the central C=C and the overcrowding due to the peri-hydrogen atoms lead to higher twists of the naphthyl groups and to lower twists of the central C=C. In the 2-naphthyl series, the opposite effects are noted. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.

The Radon-split and the Helly-core of a point configuration

We provide a systematic construction of point configurations with incompatible Radon-split and Helly-core. This provides a resolution of problems of Reay and Sierksma, and shows that it is computationally hard to decide the compatibility of the split and core of a configuration. Received 29 June 2000; revised 5 January 2001.     

Positive diagonal scaling of a nonnegative tensor to one with prescribed slice sums

In this paper we give necessary and sufficient conditions on a nonnegative tensor to be diagonally equivalent to a tensor with prescribed slice sums. These conditions are variations of Bapat-Raghavan and Franklin-Lorenz conditions.     

Taming 3-manifolds using scalar curvature

In this paper we address the issue of uniformly positive scalar curvature on noncompact 3-manifolds. In particular we show that the Whitehead manifold lacks such a metric, and in fact that \mathbbR³{\mathbb{R}^3} is the only contractible noncompact 3-manifold with a metric of uniformly positive scalar curvature. We also describe contractible noncompact manifolds of higher dimension exhibiting this curvature phenomenon. Lastly we characterize all connected oriented 3-manifolds with finitely generated fundamental group allowing such a metric.