Polymer nanocomposites are mixtures of nanoparticles and polymer chains, where the filler particles are usually added to enhance mechanical properties, e.g. of car tire materials. Performance depends to a great extent on the structure of the filler, i.e. its dispersion state in the polymer matrix, which itself depends on mixing protocols, but also on the thermodynamics of the system. The latter can be tuned by performing either chemical surface modifications of the nanoparticles, or by playing with the mass and/or grafting properties of the polymer chains. In this talk, some straightforward ways to obtain information from small-angle scattering on the structure of nanocomposites will be presented [1]. In particular, we will review recent results on nanocomposites close to industrial applications, including what is probably one of the first quantitative analyses of such disordered structures by a combination of SAXS, TEM and numerical simulations [2]. This analysis will then be applied to the impact of small molecules on such structures [3]. Concerning chain structure, a quick outlook on why contrast-matching with SANS in nanocomposites often fails will be proposed [4]. REFERENCES1.A.-C. Genix and J. Oberdisse, Structure and dynamics of polymer nanocomposites studied by X-ray and neutron scattering techniques. Current Opinion in Colloid & Interface Science 2015, 20, 293-303 (2015).2. G. P. Baeza, A. C. Genix, C. Degrandcourt, L. Petitjean, J. Gummel, M. Couty and J. Oberdisse, Multiscale Filler Structure in Simplified Industrial Nanocomposite Silica/SBR Systems Studied by SAXS and TEM, Macromolecules, 46, 317-329 (2013).3. D. Musino, A.-C. Genix, C. Fayolle, A. Papon, L. Guy, N. Meissner, P. Weda, T. Bizien, T. Chaussée, J. Oberdisse, Synergistic effect of small molecules on large-scale structure of simplified industrial nanocomposites, submitted.4. A. Banc, A.-C. Genix, C. Dupas, M. Sztucki, R. Schweins, M.-S. Appavou, J. Oberdisse, Origin of small-angle scattering from contrast-matched nanoparticles: A study of chain and filler structure in polymer nanocomposites, Macromolecules, 48, 6596−6605 (2015).

I'll discuss the modular properties of D3-brane instantons appearing in Calabi-Yau string compactifications. I'll show that the D3-instanton contribution to a certain geometric potential on the hypermultiplet moduli space can be related to the elliptic genus of (0,4) SCFT. The modular properties of the potential imply that the elliptic genus associated with non-primitive divisors of Calabi-Yau is only mock modular. I'll show how to construct its modular completion and to make manifest the modular invariance of the twistorial construction of D-instanton corrected hypermultiplet moduli space.

Diluted Magnetic Semiconductors (DMS) form a new class of magnetic materials, which fill the gap between ferromagnets and semiconductors. In the early literature these DMS were often named semimagnetic semiconductors, because they are midway between non magnetic and magnetic materials.DMS are semiconductor compounds (A1−xMxB) in which a fraction x of thecations is substituted by magnetic impurities , thereby introducing magnetic properties into the host semiconductor AB. This makes a great difference with semiconducting ferromagnets, i.e., ferromagnetic materials exhibitingsemiconductor-like transport properties, which have been known for some time (see a review in [2]). A DMS is expected to retain most of its classical semiconducting properties, and to offer the opportunity of a full integration into heterostructures, including heterostructures with the host material. The greatchallenge and ultimate goal of the research in this field is to obtain DMS ferromagnetic at room temperature, which can be integrated in semiconductor heterostructures for electronic or optoelectron c applications. This is one of the key issue for the advent of spintronics devices. Among the principal DMS families, II-VI and, to a less extent, III-V based DMS, with Mn as the magnetic impurity, are best understood. For this reason the present chapter will be mainly based on these compounds to introduce the well established basic physics of DMS. More details can be found in reviewpapers such as [3–5]. Some issues related to work in progress, generally on novel materials, will be also discussed but only briefly.

We will discuss recent results on the theoretical and experimental investigations on solitons in a superfluid Fermi gas along the BCS-BEC crossover. On the theory side, by solving the Bogoliubov de Gennes equations and looking for real and odd solutions for the order parameter, it has been shown that a dark soliton at unitarity posses a large density contrast and fermionic bound states. The superfluid gap is found to be significantly quenched by the presence of the soliton due to the occurrence of Andreev fermionic bound states localized near the nodal plane of the order parameter. By solving the time dependent Bogoliubov de Gennes equations, also the decay and collisions of dark solitons has been investigated. Recently, a cascade of Solitonic Excitations in a Superfluid Fermi gas has been experimentally observed.