Periodic Duffing delay equations with state dependent impulses

Conditions are obtained for the Duffing equation with delay and state dependent impulses to admit a periodic solution.     

Metallic glasses: Mössbauer contribution, physical properties and applications

We report first on the essential contributions of Mössbauer spectrometry to investigate iron-based metallic glasses. In addition to the analysis of the distributions of hyperfine data in terms of Fe coordination and neighbours, Mössbauer spectrometry is able to estimate the magnetic anisotropy from the magnetic texture, which can be correlated to the solidification process. After an overview of the different physical properties of the amorphous metallic alloys we also present their most advanced applications.     

A Frequency Selection Criterion in Spatially Developing Flows

The possible existence of global modes or self-excited linear resonances in spatially developing systems is explored within the framework of the WKBJ approximation. It is shown that the existence and properties of the dominant global mode may be deduced from the variations of the local absolute frequency ω₀ with distance X. The main results are summarized in two theorems: (1) A system with no region of absolute instability does not sustain temporally growing global modes with an O(1) growth rate. (2) If the singularity X, closest to the real X-axis of the complex function ω₀(X) is a saddle point, the most unstable global mode has, to leading order in the WKBJ approximation, a complex frequency ω₀(X_s). Thus, it will be temporally growing only if ω₀(X_s) is positive.     

Existence of Equilibria in Economies with Externalities and Nonconvexities

We consider a general equilibrium model of an economy in which the production possibilities, the consumption sets and the preferences of the consumers are represented by set-valued mappings which depend on the environment to take into account the possibility of external effect. In order to encompass all kinds of nonconvexities, we do not put any convexity assumption either on the graph of the set-valued mapping which describes the technological possibilities or on the production set for a given environment. The firms are instructed to set their prices according to general pricing rules which may depend on the production plans of other producers and on consumption plans.We report an existence result of general equilibria. As in the model without external effects, the key hypotheses are bounded loss and survival assumptions. Nevertheless, we also assume that the set-valued mappings which describe the fundamentals of the economy are lower semi-continuous and have a closed graph.Our framework is sufficiently large to generalize previous works on the existence of competitive equilibria with externalities when the firms have convex production sets and on the existence of equilibria with general pricing rule without externality.     

From dispersed nanodiscs to thin films of layered organic material via reversible swelling

We show that nanodiscs stabilized with polymers order and pile up on a surface upon drying. The resulting surface films with an average thickness of one micron are made of collapsed cohesive layers with smectic long-range order. This occurs with and without plastifying stabilizing polymer and produces crevasses. The stacked discs undergo a two-to-three-dimensional crystallization while bottom layers close to the surface fuse and produce infinite bilayers. Small angle X-ray scattering experiments demonstrate that excess polymer is segregated from the crystalline stack. Water adsorption isotherms show that reversible swelling of the excess polymer does not destroy the compact stack of partially fused nanodiscs collapsed parallel to the surface. In the absence of chemical binding, the stacks of layered nanodiscs can be removed by simple washing with pure water. AFM, TEM and SEM experiments demonstrate that presence of crevasses is quenched by the presence of a plastifying polymer.