Controlling electrostatic co-assembly using ion-containing copolymers: from surfactants to nanoparticles

In this review, we address the issue of the electrostatic complexation between charged-neutral diblock copolymers and oppositely charged nanocolloids. We show that nanocolloids such as surfactant micelles and iron oxide magnetic nanoparticles share similar properties when mixed with charged-neutral diblocks. Above a critical charge ratio, core-shell hierarchical structures form spontaneously under direct mixing conditions. The core-shell structures are identified by a combination of small-angle scattering techniques and transmission electron microscopy. The formation of multi-level objects is driven by the electrostatic attraction between opposite charges and by the release of the condensed counterions. Alternative mixing processes inspired from molecular biology are also described. The protocols applied here consist in screening the electrostatic interactions of the mixed dispersions, and then removing the salt progressively as an example by dialysis. With these techniques, the oppositely charged species are intimately mixed before they can interact, and their association is monitored by the desalting kinetics. As a result, sphere- and wire-like aggregates with remarkable superparamagnetic and stability properties are obtained. These findings are discussed in the light of a new paradigm which deals with the possibility to use inorganic nanoparticles as building blocks for the design and fabrication of supracolloidal assemblies with enhanced functionalities.     

Ginzburg–Landau Vortices Driven by the Landau–Lifshitz–Gilbert Equation

A simplified model for the energy of the magnetization of a thin ferromagnetic film gives rise to a version of the theory of Ginzburg–Landau vortices for sphere-valued maps. In particular, we have the development of vortices as a certain parameter tends to 0. The dynamics of the magnetization are ruled by the Landau–Lifshitz–Gilbert equation, which combines characteristic properties of a nonlinear Schrödinger equation and a gradient flow. This paper studies the motion of the vortex centers under this evolution equation.     

A survey of Sylvester's problem and its generalizations

Summary LetP be a finite set of three or more noncollinear points in the plane. A line which contains two or more points ofP is called aconnecting line (determined byP), and we call a connecting lineordinary if it contains precisely two points ofP. Almost a century ago, Sylvester posed the disarmingly simple question:Must every set P determine at least one ordinary line? No solution was offered at that time and the problem seemed to have been forgotten. Forty years later it was independently rediscovered by Erdös, and solved by Gallai. In 1943 Erdös proposed the problem in the American Mathematical Monthly, still unaware that it had been asked fifty years earlier, and the following year Gallai's solution appeared in print. Since then there has appeared a substantial literature on the problem and its generalizations.In this survey we review, in the first two sections, Sylvester's problem and its generalization to higher dimension. Then we gather results about the connecting lines, that is, the lines containing two or more of the points. Following this we look at the generalization to finite collections of sets of points. Finally, the points will be colored and the search will be for monochromatic connecting lines.     

Maximizing the value of an Earth observation satellite orbit

Earth observation satellites are platforms equipped with optical instruments that orbit the planet. During the course of an orbit, they take photographs of some regions of the Earth at the request of customers. Each photograph generates a profit but, due to the presence of several constraints, not all requests can be satisfied. The problem is to select a subset of requests of maximal profit for a given orbit. The problem is solved by means of a tabu search heuristic and computational results are reported. This work was initiated as part of a challenge organized by the French Operational Research Society. The algorithm won the second prize in the final round of the competition.     

Polarization-selective grating mirrors used in the generation of radial polarization

Two novel methods to control the polarization of laser radiation are presented. The discrimination between different polarization distributions isperformed with a corrugation grating in the top high-index layer of a multilayer mirror, which couples the undesired polarization into a lossy waveguidemode of the multilayer. The generation of radially polarized radiation in a laser resonator is presented as a practical verification of the principle.This revised version was published online in May 2005. The Article Category was removed.This revised version was published online in August 2005 with a corrected cover date.     

Dynamical systems — Past and present

Plenary lecture at the International Congress of Mathematicians (Berlin 1998, August 18–27). Reprinted from Doc. Math. J., DMV, Extra Volume ICM I, 1998, pp. 381–402. ©J.Moser, 1998.