On the optimal shape of magnetic swimmers

Magnetic actuation of elasto-magnetic devices has long been proposed as a simple way to propel fluid and achieve locomotion in environments dominated by viscous forces. Under the action of an oscillating magnetic field, a permanent magnet, when attached to an elastic tail, is able to generate bending waves and sufficient thrust for propulsion. We study the hydrodynamical effects of the magnetic head geometry using a geometrically exact formulation for the elastic tail elastohydrodynamics.We show that the spherical head geometry fails to take full advantage of the propulsive potential from the flexible tail. Nevertheless, while elongated prolate spheroids demonstrate a superior swimming performance, this is still regulated by the nature of the imposed magnetic field. Interestingly, the highest swimming speed is observed when the magnitude of the magnetic field is weak due to delays between the orientation of the magnetic moment and the oscillating magnetic field. This allows the stored elastic energy from the deformed tail to relax during the phase lag between the imposed magnetic field and the swimmer’s magnetic moment, favouring in this way the net propulsion. In particular, this result suggests the existence of optimal magnetic actuations that are non-smooth, and even discontinuous in time, in order to fully explore the propulsive potential associated with the relaxation dynamics of periodically deformed elastic filaments.     

Synthesis of linear and hyperbranched sugar‐grafted polysiloxanes using N‐hydroxysuccinimide‐activated esters

A straightforward method for the preparation of polysiloxanes grafted with carbohydrate side groups is described. Two kinds of backbones have been functionalized, namely one‐dimensional, linear polysiloxanes, and hyperbranched poly(siloxysilane)s based on cyclotetrasiloxanes. The method enables us to keep a good integrity of the polysiloxane backbone. The introduction of intermediate activated esters as side groups on the polysiloxane backbone ensures a complete homogeneity of the reaction medium during sugar grafting in dimethyl sulfoxide, and consequently an easy grafting with the unprotected amino sugar. Solubility of the resulting polysiloxanes has been tested in various solvents. The sugar‐grafted polysiloxanes are good candidates for applications such as silicone formulations, hydrophilic silicone elastomers, interactions with metallic nanoparticles, and suspension stabilization, or as starting point for the design of more complex polysiloxanes for molecular recognition. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 3607–3618     

Characterization of polyether‐poly(methyl methacrylate)‐lithium perchlorate blend electrolytes

Solid polymer electrolyte (SPE) systems based on interpenetrating blends of poly(ethylene oxide‐co‐propylene oxide) and poly(methyl methacrylate) host matrices, with lithium perchlorate as guest salt, were prepared. These electrolytes were presented as free‐standing films, and their thermal and electrochemical properties were characterized by conductivity and electrochemical stability measurements. The properties of the interpenetrating blends of poly(ethylene oxide‐co‐propylene oxide) and poly(methyl methacrylate) host matrices as the electrolyte component of a solid‐state electrochromic device are reported and the results obtained suggest that this electrolyte provides an encouraging performance in this application. The most conducting electrolyte composition of this SPE system is the formulation designated as SPE2‐0PC (5.01 × 10^?4 S cm^?1 at about 57°C). The lowest decomposition temperature was registered with the SPE6‐15PC composition (233°C). The average transmittance in the visible region of the spectrum was above 41% for all the samples analyzed. After coloration the device assembled with 71 wt% PC presented an average transmittance of 15.71% and an optical density at 550 nm of 0.61. Copyright © 2010 John Wiley & Sons, Ltd.     

Fonctions rationnelles et problème de Gleason associés à l'opérateur de Dirac

We define developments in terms of homogeneous polynomials for regular functions (that is, in the kernel of the Dirac operator) and obtain new developments for hyperholomorphic functions (that is, in the kernel of the Cauchy–Fueter operator). Rational functions associated to the Dirac operator are also studied. To cite this article: D. Alpay et al., C. R. Acad. Sci. Paris, Ser. I 343 (2006).     

Internal waves generated by a moving sphere and its wake in a stratified fluid

The internal gravity waves and the turbulent wake of a sphere moving through stratified fluid were studied by the fluorescent dye technique. The Reynolds number Re=U·2a/v was kept nearly constant at about 3 · 10³ and the Froude number F;U/a N ranged from 0.5 to 12.5. It is observed that waves generated by the body are dominant only when F<4 and are replaced by waves generated by the large scale coherent structures of the wake when F>4.     

Highly Stereoselective Synthesis of Natural‐Product‐Like Hybrids by an Organocatalytic/Multicomponent Reaction Sequence

In an endeavor to provide an efficient route to natural product hybrids, described herein is an efficient, highly stereoselective, one‐pot process comprising an organocatalytic conjugate addition of 1,3‐dicarbonyls to α,β‐unsaturated aldehydes followed by an intramolecular isocyanide‐based multicomponent reaction. This approach enables the rapid assembly of complex natural product hybrids including up to four different molecular fragments, such as hydroquinolinone, chromene, piperidine, peptide, lipid, and glycoside moieties. The strategy combines the stereocontrol of organocatalysis with the diversity‐generating character of multicomponent reactions, thus leading to structurally unique peptidomimetics integrating heterocyclic, lipidic, and sugar moieties.