Existence of Weak Solutions Up to Collision for Viscous Fluid‐Solid Systems with Slip

We study in this paper the movement of a rigid solid inside an incompressible Navier‐Stokes flow within a bounded domain. We consider the case where slip is allowed at the fluid/solid interface through a Navier condition. Taking into account slip at the interface is very natural within this model, as classical no‐slip conditions lead to unrealistic collisional behavior between the solid and the domain boundary. We prove for this model existence of weak solutions of Leray type, up to collision, in three dimensions. The key point is that, due to the slip condition, the velocity field is discontinuous across the fluid/solid interface. This prevents obtaining global H¹ bounds on the velocity, which makes many aspects of the theory of weak solutions for Dirichlet conditions inappropriate. © 2014 Wiley Periodicals, Inc.     

Constante de Bers en genre 2

We introduce a new tool, the contiguity graph, which enables us to determine the Bers’s constant in genus two.     

Regularity Issues in the Problem of Fluid Structure Interaction

We investigate the evolution of rigid bodies in a viscous incompressible fluid. The flow is governed by the 2D Navier–Stokes equations, set in a bounded domain with Dirichlet boundary conditions. The boundaries of the solids and the domain have Hölder regularity C ^1,α , 0 < α ≦ 1. First, we show the existence and uniqueness of strong solutions up to the collision. A key ingredient is a BMO bound on the velocity gradient, which substitutes to the standard H ² estimate for smoother domains. Then, we study the asymptotic behaviour of one C ^1,α body falling over a flat surface. We show that a collision is possible in finite time if and only if α < 1/2.     

Frequency-coded quantum key distribution

We report an intrinsically stable quantum key distribution scheme based on genuine frequency-coded quantum states. The qubits are efficiently processed without fiber interferometers by fully exploiting the nonlinear interaction occurring in electro-optic phase modulators. The system requires only integrated off-the-shelf devices and could be used with a true single-photon source. Preliminary experiments have been performed with weak laser pulses and have demonstrated the feasibility of this new setup.     

Electron Transfer in Peptides: On the Formation of Silver Nanoparticles

Some microorganisms perform anaerobic mineral respiration by reducing metal ions to metal nanoparticles, using peptide aggregates as medium for electron transfer (ET). Such a reaction type is investigated here with model peptides and silver as the metal. Surprisingly, Ag⁺ ions bound by peptides with histidine as the Ag⁺‐binding amino acid and tyrosine as photoinducible electron donor cannot be reduced to Ag nanoparticles (AgNPs) under ET conditions because the peptide prevents the aggregation of Ag atoms to form AgNPs. Only in the presence of chloride ions, which generate AgCl microcrystals in the peptide matrix, does the synthesis of AgNPs occur. The reaction starts with the formation of 100 nm Ag@AgCl/peptide nanocomposites which are cleaved into 15 nm AgNPs. This defined transformation from large nanoparticles into small ones is in contrast to the usually observed Ostwald ripening processes and can be followed in detail by studying time‐resolved UV/Vis spectra which exhibit an isosbestic point.     

(−)‐Englerin A is a Potent and Selective Activator of TRPC4 and TRPC5 Calcium Channels

Current therapies for common types of cancer such as renal cell cancer are often ineffective and unspecific, and novel pharmacological targets and approaches are in high demand. Here we show the unexpected possibility for the rapid and selective killing of renal cancer cells through activation of calcium‐permeable nonselective transient receptor potential canonical (TRPC) calcium channels by the sesquiterpene (?)‐englerin A. This compound was found to be a highly efficient, fast‐acting, potent, selective, and direct stimulator of TRPC4 and TRPC5 channels. TRPC4/5 activation through a high‐affinity extracellular (?)‐englerin A binding site may open up novel opportunities for drug discovery aimed at renal cancer.