Microcavity-controlled single-molecule fluorescence.

We present for the first time cavity-controlled fluorescence spectra and decay curves of single dipole emitters interacting at room temperature with the first longitudinal mode of a Fabry-Perot microcavity offering a lambda/2-spacing between its silver mirrors. The spontaneous emission rate of individual dye molecules was found to be enhanced by the Purcell effect by up to three times compared to the rate in free space, in agreement with theoretical predictions. Moreover, our new microcavity design was found to provide long-term stability and single-molecule sensitivity under ambient conditions for several months without noticeable reduction of the cavity-Q value. We consider this as a significant advance for single-photon sources operating at room temperature.     

Hydrogen‐bonding patterns in six derivatives of 2,4‐dimethyl­pyrrole

The crystal and mol­ecular structures of 4‐ethyl‐3,5‐dimethyl­pyrrole‐2‐carbaldehyde, C₁₀H₁₅NO, (I), benzyl 3,5‐dimethyl­pyrrole‐2‐carboxyl­ate, C₁₄H₁₅NO₂, (II), benzyl 4‐acetyl‐3,5‐dimethyl­pyrrole‐2‐carboxyl­ate, C₁₆H₁₇NO₃, (III), dimethyl 3,5‐dimethyl­pyrrole‐2,4‐dicarboxyl­ate, C₁₀H₁₃NO₄, (IV), 4‐ethyl‐3,5‐dimethyl‐2‐(p‐tos­ylacet­yl)pyrrole, C₁₇H₂₁NO₃S, (V), and ethyl 4‐(2‐ethoxy­carbonyl‐2‐hydroxy­acrylo­yl)‐3,5‐dimethyl­pyrrole‐2‐carboxyl­ate, C₁₅H₁₉NO₆, (VI), were determined at 130 K. Compounds (I), (II), (IV), (V) and (VI) form hydrogen‐bonded dimers [N—H⋯O=C = 1.97 (2)–2.03 (3) Å]. Four dimers, viz. (I) and (IV)–(VI), have inversion symmetry, while the dimer of (II) has twofold symmetry. Only (III) forms polymeric chains involving hydrogen bonds between the pyrrole H atom and the acetyl carbonyl group [H⋯O = 1.97 (2) Å] and is further stabilized by CH₃⋯O inter­actions (C—H⋯O = 2.28–2.49 Å). Compound (VI) was found to occur as the enol ether in the crystal.     

On equivariant self-similar wave maps

By variational methods, we establish the existence of an infinite number of self-similar wave maps which evolve from smooth, compactly supported data and develop a singularity in finite time.     

On contact tops and integrable tops

In this paper, we introduce a geometric structure called top, which is a trivialized bundle of plane pencils over a Riemannian 3-manifold, defined as the set of kernels of a circle of l-forms (e.g., of contact and integrable forms) with particular properties with respect to the metric. We classify the manifolds which admit tops and we describe the associated metrics.     

Thianthrene-containing polyimides with monomer formation via nucleophilic aromatic substitution

Thianthrene-2,3,7,8-tetracarboxylic dianhydride was synthesized via nucleophilic aromatic substitution of N-phenyle-4,5-dichlorophthalimide with thiobenzamide, thioacetamide, and sodium sulfide. This monomer was then polymerized with aromatic diamines by the con-ventional low temperature technique in N,N-dimethylacetamide (DMAc) to yield soluble poly(amic acid)s. Polyimides were obtained by thermal cyclization of the poly(amic acid) films. Polymers obtained formed creasable thin films and had excellent thermal stability in air and nitrogen. The bent thianthrene structure limited crystallization and chain packing, as indicated by x-ray analysis. The amorphous thianthrene-containing polyimides were only soluble in H₂SO₄. © 1995 John Wiley & Sons, Inc.     

On the Convergence of a Non-incremental Homogenization Method for Nonlinear Elastic Composite Materials

In order to simulate the nonlinear behaviour of elastomer composite materials, we use a homogenization technique which induces nonlinear problems. This paper presents a non-incremental solving method which allows the reduction of computational costs. In this paper the equivalence between the proposed solving method and a Newton-type method is proved, which allows us to prove the convergence under realistic assumptions. Numerical results on a composite illustrate the performances of this method.