Long time behaviour of the solution to non-linear Kraichnan equations

We consider the solution of a nonlinear Kraichnan equation with a covariance kernel k and boundary condition H(t, t)=1. We study the long time behaviour of H as the time parameters t, s go to infinity, according to the asymptotic behaviour of k. This question appears in various subjects since it is related with the analysis of the asymptotic behaviour of the trace of non-commutative processes satisfying a linear differential equation, but also naturally shows up in the study of the so-called response function and aging properties of the dynamics of some disordered spin systems.     

Caractérisation du module d'une fonction additive à l'aide d'une équation fonctionnelle

Sans résumé     

‘All‐supramolecular’ Nanocapsules from Low‐Molecular Weight Ureas Through Interfacial Addition Reaction in Miniemulsion

This contribution presents a new strategy for preparing nanocapsules with a shell made of a supramolecular polymer which repeating units are held together by reversible interactions rather than covalent bonds. These nanocapsules were prepared in classical miniemulsion through interfacial addition reaction of a diisocyanate (IPDI) and a monoamine (iBA), forming low‐molecular weight bis‐ureas moieties which are strong self‐complementary interacting molecules through hydrogen‐bonding. The nanocapsules present a diameter around 100 nm, and MALDI‐TOF MS and ¹H NMR analyses confirm the expected molecular characteristics for the shell. This strategy opens the scope of a new type of nanomaterials exhibiting stimuli‐responsiveness due to the reversible interaction linking the repeating units.

     

Symplectic automorphisms on Kummer surfaces

Nikulin proved that the isometries induced on the second cohomology group of a K3 surface X by a finite abelian group G of symplectic automorphisms are essentially unique. Moreover he computed the discriminant of the sublattice of H²(X,\mathbbZ){H^2(X,\mathbb{Z})} which is fixed by the isometries induced by G. However for certain groups these discriminants are not the same as those found for explicit examples. Here we describe Kummer surfaces for which this phenomena happens and we explain the difference.     

Reversible activation of diblock copolymer monolayers at the interface by pH modulation, 2: Membrane interactions at the solid/liquid interface

A monolayer of the pH-responsive poly[2-(dimethylamino)ethyl methacrylate-block-methyl methacrylate] diblock copolymer [PDMAEMA-PMMA] was transferred from the air/water interface to a silicon substrate for evaluation as a tunable interlayer between biological material and solid substrates. Specular neutron reflectivity experiments revealed that the weak polyelectrolyte PDMAEMA chains at the solid/liquid interface can be reversibly activated by pH modulation. The thickness, scattering length density, and surface roughness of the polymer film can be systematically controlled by pH titration. As a simple model of plasma membranes, a lipid bilayer was deposited onto the polymer film. The membrane-substrate interaction was characterized by neutron reflectivity experiments, demonstrating that the membrane-substrate distance could be reversibly regulated by pH titration. These results confirm the potential of stimuli-responsive polymers for precise control of cell-surface interactions.