π‐Extended Indenofluorenes

A series of π‐extended aromatic indenofluorene (IF) analogues with naphthalene and anthracene cores have been synthesized through acid‐catalyzed intramolecular cyclization. The regioselectivity of the reaction is controlled by a combination of steric and electronic factors and in some cases several possible regioisomers have resulted from the same precursor. The effects of ring connectivity on the optoelectronic properties were investigated by DFT calculations, absorption/emission spectroscopy, cyclic voltammetry, and spectroelectrochemical studies. All regioisomers exhibited a redshift of their absorption/emission bands relative to the parent IF analogues, but the magnitude of this shift and other optoelectronic properties (luminescence quantum yield, etc.) depends on the ring connectivity in a less obvious manner.     

Anisotropic curvature-driven flow of convex sets

We study in this paper the mean curvature evolution, and in particular the anisotropic mean curvature evolution, of convex sets in R^N${\mathbb{R}}^N$ (without driving forces). If the anisotropy is smooth, we show that the evolution remains convex. If the anisotropy is crystalline, we build a convex evolution which satisfies an equation which is a weak form of the crystalline curvature motion equation.     

A Remark on the Smoothness of Bounded Regions Filled with a Steady Compressible and Isentropic Fluid

For convenient adiabatic constants, existence of weak solutions to the steady compressible Navier-Stokes equations in isentropic regime in smooth bounded domains is well known. Here we present a way how to prove the same result when the bounded domains considered are Lipschitz.     

High-harmonic generation from plasma mirrors at kilohertz repetition rate

We report the first demonstration of high-harmonic generation from plasma mirrors at a 1 kHz repetition rate. Harmonics up to nineteenth order are generated at peak intensities close to 101? W/cm2 by focusing 1 mJ, 25 fs laser pulses down to 1.7 μm FWHM spot size without any prior wavefront correction onto a moving target. We minimize target surface motion with respect to the laser focus using online interferometry to ensure reproducible interaction conditions for every shot and record data at 1 kHz with unprecedented statistics. This allows us to unambiguously identify coherent wake emission as the main generation mechanism.     

Geometric quantization of the BRST charge

In the first half of this paper (Sects. 1–4) we generalise the standard geometric quantization procedure to symplectic supermanifolds. In the second half (Sects. 5, 6) we apply this to two examples that exhibit classical BRST symmetry, i.e., we quantize the BRST charge and the ghost number. More precisely, in the first example we consider the reduced symplectic manifold obtained by symplectic reduction from a free group action with Ad^*-equivariant moment map; in the second example we consider a foliated configuration space, whose cotangent bundle admits the construction of a BRST charge associated to this foliation. We show that the classical BRST symmetry can be described in terms of a hamiltonian supergroup action on the extended phase space, and that geometric quantization gives us a super-unitary representation of this supergroup. Finally we point out how these results are related to reduction at the quantum level, as compared with the reduction at the classical level.Research supported by the Dutch Organization for Scientific Research (NWO)     

Existence of Weak Solutions for the Unsteady Interaction of a Viscous Fluid with an Elastic Plate

The purpose of this work is to study the existence of solutions for an unsteady fluid-structure interaction problem. We consider a three-dimensional viscous incompressible fluid governed by the Navier–Stokes equations, interacting with a flexible elastic plate located on one part of the fluid boundary. The fluid domain evolves according to the structure’s displacement, itself resulting from the fluid force. We prove the existence of at least one weak solution as long as the structure does not touch the fixed part of the fluid boundary. The same result holds also for a two-dimensional fluid interacting with a one-dimensional membrane.     

Steady Motions of Viscoelastic Fluids in Three‐Dimensional Exterior Domains. Existence, Uniqueness and Asymptotic Behaviour

. We study systems of nonlinear partial differential equations governing the steady motion of certain viscoelastic non‐Newtonian fluids around a rigid body ${\cal B}\subset\real^{3}$ . Considering the equations in a suitably decomposed form, we obtain, for small and sufficiently regular data, existence of a unique solution using a fixed‐point argument in an appropriate functional setting. This setting contains also the asymptotic decay of the solution. Our model equations include the second‐grade and the Maxwell fluid.     

Freezing and thawing porous media: experimental study with a dielectric capacitive method

A capacitive sensor-based apparatus has been used to study the ice/water phase change in consolidated porous media subjected to freezing and thawing. This technique relies on the dielectric properties of water, ice, air, and the mineral substrate in the radio-frequency range. It gives directly the freezing and thawing temperature depressions and indirectly provides an estimation of pore size distribution through the Gibbs–Thomson relation. It also holds good promise for evaluating the amount of liquid water in frozen porous media by combining drying and freezing tests. To cite this article: T. Fen-Chong, A. Fabbri, C. R. Mecanique 333 (2005).     

Piecewise rigidity

In this paper we provide a Liouville type theorem in the framework of fracture mechanics, and more precisely in the theory of SBV deformations for cracked bodies. We prove the following rigidity result: if u∈SBV(Ω,RN) is a deformation of Ω whose associated crack Ju has finite energy in the sense of Griffith's theory (i.e., HN−1(Ju)<∞), and whose approximate gradient ∇u is almost everywhere a rotation, then u is a collection of an at most countable family of rigid motions. In other words, the cracked body does not store elastic energy if and only if all its connected components are deformed through rigid motions. In particular, global rigidity can fail only if the crack disconnects the body.