On the relaxation of nonconvex superficial integral functionals

We present a new approach to the variational relaxation of functionals of the type:

where is a continuous function with growth conditions of order p≥1 but not necessarily convex. We essentially study the case when μ is the k-dimensional Hausdorff measure restricted to a suitable piece of a k-dimensional smooth submanifold of .     

Diastereoselective synthesis of enantiopure acyclic beta,beta'-disubstituted vinylsulfoxides

Thermal elimination of sulfenic acid from enantiopure beta,beta'-disubstituted bis-sulfoxides allows the stereoselective synthesis of enantiopure acyclic beta,beta'-disubstituted vinylsulfoxides. This mild and stereospecific synthesis provides either ( E) or ( Z) vinylsulfoxides in high yields and is compatible with acid or base sensitive functional groups.     

Desymmetrization of a meso-allylic acetal by enantioselective conjugate elimination

An unprecedented enantioselective deprotonation/conjugate elimination sequence, which transforms an allylic meso-dioxepane into a chiral diene, is described. The best desymmetrization conditions (ee up to 70%) involve s-BuLi and sparteine at -78 degrees C in THF.     

Highly efficient nonlinear filter for femtosecond pulse contrast enhancement and pulse shortening

We propose a highly efficient scheme for temporal filters devoted to femtosecond pulse contrast enhancement. The filter is based on cross-polarized wave generation with a spatially suger-Gaussian-shaped beam. In a single nonlinear crystal scheme the energy conversion to the cross-polarized pulse can reach 28%. We demonstrate that the process enables a significant spectral broadening. For an efficiency of 23% the pulse shortening is estimated to 2.2, leading to an intensity transmission of the nonlinear filter of 50%.     

Extending applicability of bimetric theory: chameleon bigravity

This article extends bimetric formulations of massive gravity to make the mass of the graviton to depend on its environment. This minimal extension offers a novel way to reconcile massive gravity with local tests of general relativity without invoking the Vainshtein mechanism. On cosmological scales, it is argued that the model is stable and that it circumvents the Higuchi bound, hence relaxing the constraints on the parameter space. Moreover, with this extension the strong coupling scale is also environmentally dependent in such a way that it is kept sufficiently higher than the expansion rate all the way up to the very early universe, while the present graviton mass is low enough to be phenomenologically interesting. In this sense the extended bigravity theory serves as a partial UV completion of the standard bigravity theory. This extension is very generic and robust and a simple specific example is described.     

Rapidly and Slowly Oscillating Periodic Solutions of a Delayed Van der Pol Oscillator

In this paper, we introduce a method to prove existence of several rapidly and slowly oscillating periodic solutions of a delayed Van der Pol oscillator. The proof is a combination of pen and paper analytic estimates, the contraction mapping theorem and a computer program using interval arithmetic. Using this approach we extend some existence results obtained by Nussbaum (Ann Mat Pura Appl 4(101):263–306, 1974).     

Shallow, deep and very deep cuts in the analytic center cutting plane method

In this paper we show that the cut does not need to go through the query point: it can be deep or shallow. The primal framework leads to a simple analysis of the potential variation, which shows that the inequality needed for convergence of the algorithm is in fact attained at the first iterate of the feasibility step. Received July 3, 1996 / Revised version received July 11, 1997 Published online August 18, 1998     

Radical Complexity

This is an informal and sketchy review of five topical, somewhat unrelated subjects in quantitative finance and econophysics: (i) models of price changes; (ii) linear correlations and random matrix theory; (iii) non-linear dependence copulas; (iv) high-frequency trading and market stability; and finally—but perhaps most importantly—(v) “radical complexity” that prompts a scenario-based approach to macroeconomics heavily relying on Agent-Based Models. Some open questions and future research directions are outlined.     

Triblock copolymers in a selective solvent: Dilute and semi-dilute solutions

Triblock copolymers polystyrene-polyisoprene-polystyrene were studied in dilute and semi-dilute solutions in a selective solvent, i.e. a non-solvent for polystyrene and a good solvent for polyisoprene. The mass of the copolymer is equal to 1.6×10⁵g/mol and it contains 70% of polyisoprene. At a concentration C equal to 1.6×10⁻³ g/cm³ triblock aggregation occurs. Experiments performed on dilute solutions¹ plead in favor of loose and polydisperse aggregates rather than spherical micelles: 1) the form factor of the aggregates shows a smooth decrease at qR<1; 2) internal modes are observed by quasi-elastic light scattering; 3) specific viscosity measurements show that the internal concentration of unimers and aggregates are identical; 4) the unimer concentration and the aggregation number depend on the copolymer concentration. In semi-dilute solutions² (C>3×10⁻² g/cm³), dynamical properties are strongly affected by the temperature. Viscosity and longest relaxation time increase by a factor 10⁵ as the temperature decreases from 50°C to 5°C, whereas the plateau modulus G remains independent of the temperature and proportional to the concentration. Small angle neutron scattering experiments reveal a cubic structure having a unit cell dimension d independent of the temperature and varying as C^−1/3 leading to G∼1/d³. Quasi-elastic light scattering experiments performed on this system show a wide relaxation function extending over 7 decades of time. These results argue for a lattice made of polystyrene nodes linked together by the polyisoprene middle blocks, the dynamics being governed by the glass transition of the nodes.     

Fluctuating Hydrodynamics and Debye-Hückel-Onsager Theory for Electrolytes

We apply fluctuating hydrodynamics to strong electrolyte mixtures to compute the concentration corrections for chemical potential, diffusivity, and conductivity. We show these corrections to be in agreement with the limiting laws of Debye, Hückel, and Onsager. We compute explicit corrections for a symmetric ternary mixture and find that the co-ion Maxwell-Stefan diffusion coefficients can be negative, in agreement with experimental findings.