Two-step melting in two dimensions: first-order liquid-hexatic transition

Melting in two spatial dimensions, as realized in thin films or at interfaces, represents one of the most fascinating phase transitions in nature, but it remains poorly understood. Even for the fundamental hard-disk model, the melting mechanism has not been agreed upon after 50 years of studies. A recent Monte?Carlo algorithm allows us to thermalize systems large enough to access the thermodynamic regime. We show that melting in hard disks proceeds in two steps with a liquid phase, a hexatic phase, and a solid. The hexatic-solid transition is continuous while, surprisingly, the liquid-hexatic transition is of first order. This melting scenario solves one of the fundamental statistical-physics models, which is at the root of a large body of theoretical, computational, and experimental research.     

Phase characterization of the reflection on an extreme UV multilayer: comparison between attosecond metrology and standing wave measurements

We characterize the phase shift induced by reflection on a multilayer mirror in the extreme UV range (80-93?eV) using two techniques: one based on high order harmonic generation and attosecond metrology (reconstruction of attosecond beating by interference of two-photon transitions), and a second based on synchrotron radiation and measurements of standing waves (total electron yield). We find an excellent agreement between the results from the two measurements and a flat group delay shift (±40?as) over the main reflectivity peak of the mirror.     

Entropy-stable and entropy-dissipative approximations of a fourth-order quantum diffusion equation

Structure-preserving numerical schemes for a nonlinear parabolic fourth-order equation, modeling the electron transport in quantum semiconductors, with periodic boundary conditions are analyzed. First, a two-step backward differentiation formula (BDF) semi-discretization in time is investigated. The scheme preserves the nonnegativity of the solution, is entropy stable and dissipates a modified entropy functional. The existence of a weak semi-discrete solution and, in a particular case, its temporal second-order convergence to the continuous solution is proved. The proofs employ an algebraic relation which implies the G-stability of the two-step BDF. Second, an implicit Euler and $q$ -step BDF discrete variational derivative method are considered. This scheme, which exploits the variational structure of the equation, dissipates the discrete Fisher information (or energy). Numerical experiments show that the discrete (relative) entropies and Fisher information decay even exponentially fast to zero.     

Synthesis of thermosensitive guar‐based hydrogels with tunable physico‐chemical properties by click chemistry

Thermosensitive guar‐based hydrogels are obtained in water solutions by copper‐catalyzed 1,3‐dipolar cycloaddition between alkyne‐functionalized guars and α,ω‐diazido‐poly[(ethylene glycol)‐co‐(propylene glycol)]. Characterization by TGA, HR‐MAS ¹H NMR, and rheology have shown that hydrogels with tunable physico‐chemical properties, such as crosslinking density, viscoelasticity, swelling ratio, and so forth, could be obtained by varying the guar molar mass, the degree of alkyne functionality, the guar/crosslinker weight ratio, and the reaction temperature. Based on swelling measurements, it has been shown that the thermal sensitiveness of guar‐based hydrogels is fast, reversible, and intimately related to the weight fraction of the thermosensitive crosslinker in the network. Finally, the monitoring of doxorubicin hydrochloride release has demonstrated the potential of these hydrogels as temperature‐dependent drug release devices. The robust, efficient, and orthogonal approach described herein represents a general approach towards the development of well‐controlled guar‐based hydrogels using α,ω‐diazido crosslinkers. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 2733–2742, 2010     

Stress-based upper-bound method and convex optimization: case of the Gurson materialMéthode cinématique par les contraintes et optimisation convexe : cas du matériau de Gurson

A nonlinear interior point method associated with the kinematic theorem of limit analysis is proposed. Associating these two tools enables one to determine an upper bound of the limit loading of a Gurson material structure from the knowledge of the sole yield criterion. We present the main features of the interior point algorithm and an original method providing a rigorous kinematic bound from a stress formulation of the problem. This method is tested by solving in plane strain the problem of a Gurson infinite bar compressed between rough rigid plates. To cite this article: F. Pastor et al., C. R. Mecanique 334 (2006).