Critical behaviour and intermittency in Sinai''s billiard

We study numerically the transition that occurs in the dynamics of Sinai's billard when the circles come into contact. Singular behaviours are predicted by a local analysis of the region of phase space where the motion is nearly integrable. The link with intermittency is discussed. We use a renormalization transformation and deduce the scaling laws. We recover, transposed in the language of critical phenomena, certain predictions of the ergodic theory.     

Maslov form and J-volume of totally real immersions

On every totally real submanifold Mⁿ of ⁿ, one can define a Maslov class analogous to the one defined for the Lagrangian submanifolds of ⁿ. We define here a closed 1-form, expressed in terms of the extrinsic local geometric invariants of Mⁿ and the complex structure of ⁿ, whose cohomology class is the Maslov class of Mⁿ. This generalizes to the totally real case, the result of Morvan (1981). This 1-form can still be defined if the ambient space ⁿ is substituted by a Kahler manifold , but it is not closed in general. However, we can build a variational problem on the space of totally real immersions, whose critical points are totally real submanifolds whose form defined above vanishes identically. In the case where , we give a characterization and many examples of such submanifolds. Finally we study the second variation and prove a stability result for the critical submanifolds of a Kahler manifold with non-positive Ricci tensor. This extends the well-known results on Lagrangian submanifolds of      

Pierre Turq,an inspirational scientist in charge and at interfaces

Pierre Turq has made decisive contributions to the theory and to the multiscale simulation of charged systems, such as molten salts, electrolyte solutions and colloidal suspensions, in the bulk, at interfaces and under confinement. His research line focussed on dynamical properties and was characterised by constant efforts to connect his theoretical work to both experiments and practical applications. In this article, his colleagues and former students pay a tribute to his past and current research interests by illustrating some recent developments accomplished in his laboratory.     

Superintegrability in Two Dimensions and the Racah–Wilson Algebra

The analysis of the most general second-order superintegrable system in two dimensions: the generic 3-parameter model on the 2-sphere is cast in the framework of the Racah problem for the \({\mathfrak{su}(1,1)}\) algebra. The Hamiltonian of the 3-parameter system and the generators of its quadratic symmetry algebra are seen to correspond to the total and intermediate Casimir operators of the combination of three \({\mathfrak{su}(1,1)}\) algebras, respectively. The construction makes explicit the isomorphism between the Racah–Wilson algebra, which is the fundamental algebraic structure behind the Racah problem for \({\mathfrak{su}(1, 1)}\) , and the invariance algebra of the generic 3-parameter system. It also provides an explanation for the occurrence of the Racah polynomials as overlap coefficients in this context. The irreducible representations of the Racah–Wilson algebra are reviewed as well as their connection with the Askey scheme of classical orthogonal polynomials.     

Observation of a non-adiabatic geometric phase for elastic waves

We report the experimental observation of a geometric phase for elastic waves in a waveguide with helical shape. The setup reproduces the experiment by Tomita and Chiao [A. Tomita, R.Y. Chiao, Phys. Rev. Lett. 57 (1986) 937–940, 2471] that showed first evidence of a Berry phase, a geometric phase for adiabatic time evolution, in optics. Experimental evidence of a non-adiabatic geometric phase has been reported in quantum mechanics. We have performed an experiment to observe the polarization transport of classical elastic waves. In a waveguide, these waves are polarized and dispersive. Whereas the wavelength is of the same order of magnitude as the helix’s radius, no frequency dependent correction is necessary to account for the theoretical prediction. This shows that in this regime, the geometric phase results directly from geometry and not from a correction to an adiabatic phase.     

Nearest-neighbor configuration in (GaIn)(NAs) probed by x-ray absorption spectroscopy

Ga(1-x)In(x)N(y)As(1-y) is a promising material system for the fabrication of inexpensive "last-mile" optoelectronic components. However, details of its atomic arrangement and the relationship to observed optical properties is not fully known. Particularly, a blueshift of emission wavelength is observed after annealing. In this work, we use x-ray absorption fine structure to study the chemical environment around N atoms in the material before and after annealing. We find that as-grown molecular beam epitaxy material consists of a nearly random distribution of atoms, while postannealed material shows segregation of In toward N. Ab initio simulations show that this short-range ordering creates a more thermodynamically stable alloy and is responsible for blueshifting the emission.     

The raspberry model for protein-like particles: Ellipsoids and confinement in cylindrical pores

The study of protein mass transport via atomistic simulation requires time and length scales beyond the computational capabilities of modern computer systems. The raspberry model for colloidal particles in combination with the mesoscopic hydrodynamic method of lattice Boltzmann facilitates coarse-grained simulations that are on the order of microseconds and hundreds of nanometers for the study of diffusive transport of protein-like colloid particles. The raspberry model reproduces linearity in resistance to motion versus particle size and correct enhanced drag within cylindrical pores at off-center coordinates for spherical particles. Owing to the high aspect ratio of many proteins, ellipsoidal raspberry colloid particles were constructed and reproduced the geometric resistance factors of Perrin and of Happel and Brenner in the laboratory-frame and in the moving body-frame. Accurate body-frame rotations during diffusive motion have been captured for the first time using projections of displacements. The spatial discretization of the fluid leads to a renormalization of the hydrodynamic radius, however, the data describes a self-consistent hydrodynamic frame within this renormalized system.     

Reaction of quinine, 9-epiquinine and their acetates in superacid in the presence of hydrogen peroxide: an access to new fluorhydrins and/or ketones

In HF-SbF₅, in the presence of H₂O₂ (source of OH⁺ equivalent) quinine 1a yields 10-keto derivatives 4a and 5a and cyclic ether 3 as the major product. In the same conditions 1b, 2a, and 2b give the 10-keto and 10-fluoro-3-hydroxy analogs.