Synthesis of luminescent heterometallic bis-lanthanide complexes via selective, sequential metallation

A modular synthetic method for the differential incorporation of two lanthanide ions into a single molecular scaffold is reported; the mixed bimetallic Tb/Eu complex displays an interesting solvent polarity-dependent ratiometric luminescence.     

Bicomplex Quantum Mechanics: II. The Hilbert Space

Using the bicomplex numbers

Random sampling of bandlimited signals on graphs

We study the problem of sampling k-bandlimited signals on graphs. We propose two sampling strategies that consist in selecting a small subset of nodes at random. The first strategy is non-adaptive, i.e., independent of the graph structure, and its performance depends on a parameter called the graph coherence. On the contrary, the second strategy is adaptive but yields optimal results. Indeed, no more than $O(k\log ?(k))$ measurements are sufficient to ensure an accurate and stable recovery of all k-bandlimited signals. This second strategy is based on a careful choice of the sampling distribution, which can be estimated quickly. Then, we propose a computationally efficient decoder to reconstruct k-bandlimited signals from their samples. We prove that it yields accurate reconstructions and that it is also stable to noise. Finally, we conduct several experiments to test these techniques.     

Solid-phase synthesis of phenolic steroids: from optimization studies to a convenient procedure for combinatorial synthesis of biologically relevant estradiol derivatives

During the course of our studies on therapeutic agents for the treatment of breast cancer, we became interested in the solid-phase combinatorial synthesis of estradiol derivatives that contain a functionalized side chain at either position 16 beta or 7 alpha. Both types of compounds have already demonstrated inhibitory activity toward both biosynthesis and action of estradiol. As a first step, two versatile precursors bearing an azidoalkyl side chain at either position 16 beta or 7 alpha of estradiol were synthesized using standard solution-phase methods. Afterward, the effectiveness of five linkers to attach the phenolic function of these estradiol derivatives to a polystyrene resin was investigated; they were benzylic ether (Merrifield), 4-alkoxy-benzylic ethers (Wang, Sheppard), tetrahydropyranyl ether (Ellman), benzoic ester, and o-nitrobenzyl ether. To test the linker in a synthetic context, a short sequence of reactions, including reduction of the azide and acylation of the corresponding amine, was performed on the polymer-bound estradiol derivative. While all of the tested linkers proved effective in attaching the phenol functionality of the precursor, only the o-nitrobenzyl ether photolabile linker enabled the release of the final products in acceptable purities. Consequently, this linker was used to perform successfully the solid-phase synthesis of four different classes of estradiol derivatives in acceptable yields and excellent purities. This study was preliminary to the combinatorial synthesis of larger libraries of biologically relevant estradiol derivatives.     

Preconditioned iterative methods for coupled discretizations of fluid flow problems

Computational fluid dynamics, where simulations require largecomputation times, is one of the areas of application of highperformance computing. Schemes such as the SIMPLE (semi-implicitmethod for pressure-linked equations) algorithm are often usedto solve the discrete Navier-Stokes equations. Generally theseschemes take a short time per iteration but require a largenumber of iterations. For simple geometries (or coarser grids)the overall CPU time is small. However, for finer grids or morecomplex geometries the increase in the number of iterationsmay be a drawback and the decoupling of the differential equationsinvolved implies a slow convergence of rotationally dominatedproblems that can be very time consuming for realistic applications.So we analyze here another approach, DIRECTO, that solves theequations in a coupled way. With recent advances in hardwaretechnology and software design, it became possible to solvecoupled Navier-Stokes systems, which are more robust but implyincreasing computational requirements (both in terms of memoryand CPU time). Two approaches are described here (band blockLU factorization and preconditioned GMRES) for the linear solverrequired by the DIRECTO algorithm that solves the fluid flowequations as a coupled system. Comparisons of the effectivenessof incomplete factorization preconditioners applied to the GMRES(generalized minimum residual) method are shown. Some numericalresults are presented showing that it is possible to minimizeconsiderably the CPU time of the coupled approach so that itcan be faster than the decoupled one.     

Competition between antiferromagnetism and superconductivity in high-Tc cuprates

Using variational cluster perturbation theory we study the competition between d-wave superconductivity (dSC) and antiferromagnetism (AF) in the t-t(')-t(')-U Hubbard model. Large scale computer calculations reproduce the overall ground-state phase diagram of the high-temperature superconductors as well as the one-particle excitation spectra for both hole and electron doping. We identify clear signatures of the Mott gap as well as of AF and of dSC that should be observable in photoemission experiments.     

Fluctuations about hydrodynamic nonequilibrium steady states

Using an extension of the Langevin method, we calculate the fluctuations of a fluid about a stationary state held away from global thermal equilibrium by a temperature gradient or shear flow. In the former case, the Brillouin peaks in the light scattering spectrum acquire an asymmetry that is qualitatively similat to earlier results but different in detail.