Structural Optimization of Thin Elastic Plates: The Three Dimensional Approach

The natural way to find the most compliant design of an elastic plate is to consider the three-dimensional elastic structures which minimize the work of the loading term, and pass to the limit when the thickness of the design region tends to zero. In this paper, we study the asymptotics of such a compliance problem, imposing that the volume fraction remains fixed. No additional topological constraint is assumed on the admissible configurations. We determine the limit problem in different equivalent formulations, and we provide a system of necessary and sufficient optimality conditions. These results were announced in Bouchitté et al. (C. R. Acad. Sci. Paris, Ser. I. 345:713–718, 2007). Furthermore, we investigate the vanishing volume fraction limit, which turns out to be consistent with the results in Bouchitté and Fragalà (Arch. Rat. Mech. Anal. 184:257–284, 2007; SIAM J. Control Optim. 46:1664–1682, 2007). Finally, some explicit computation of optimal plates are given.     

3-Indolylacyl radical cyclizations upon pyridines and tetrahydropyridines: access to ergoline-related indole [cd]-fused isoquinolines

Cyclizations of selenoester-derived 3-indolylacyl radicals, involving the homolytic acylation of pyridines or the addition to double bonds included in tetrahydropyridine rings, have been used to synthesize indole [cd]-fused isoquinolines related to the natural ergoline system.     

Imidazole derivatives as absorption probes for pluronics core-shell aggregates micropolarity investigation

Using the absorption probes 1-H-imidazol-1-yloxy-4,5-dihydro-4,4,5,5-tetramethyl-2-ethyl-3-oxide, 1-H-imidazol-1-yloxy-4,5-dihydro-4,4,5,5-tetramethyl-2-nitrophenyl-3-oxide, and 1-H-imidazol-1-yloxy-4,5-dihydro-4,4,5,5-tetramethyl-2-undecyl-3-oxide, the micropolarity of micellar aggregates formed in aqueous solutions of poly(ethylene oxide)–poly(propylene oxide)–poly(ethylene oxide) triblock copolymers, Pluronics L62, L64, and F127, as well as in reverse micellar systems of F127/butanol/water, has been investigated These absorption probes have different hydrophilic/hydrophobic features and solvatochromic properties. Their specific absorption parameters, sensitive to changes in micropolarity, were calibrated using the reference curves carried out in homogeneous tetraethyleneglycol/water mixtures. The probes were able to detect changes in the micelle micropolarity induced by hydration. Thus, with the help of calibration solutions, the effective local hydration of the polymeric chain sensed by the molecular probe solubilized in the guest aggregate was quantified and hypothetical relative locations of the probes in micelles have been proposed. The probes evidence differences in the micropolarity function of the structure (nature) and concentration of the Pluronic block copolymers.     

Reshaping elastic nanotubes via self-assembly of surface-adhesive nanoparticles

Elastic sheets with macroscopic dimensions are easy to deform by bending and stretching. Yet shaping nanometric sheets by mechanical manipulation is hard. Here we show that nanoparticle self-assembly could be used to this end. We demonstrate that spherical nanoparticles adhering to the outer surface of an elastic nanotube can self-assemble into linear structures: rings or helices on stretchable nanotubes, and axial strings on nanotubes with high rigidity to stretching. These self-assembled structures are inextricably linked to a variety of deformed nanotube profiles, which can be controlled by tuning the concentration of nanoparticles, the nanoparticle-nanotube diameter ratio and the elastic properties of the nanotube. Our results open the possibility of designing nanoparticle-laden tubular nanostructures with tailored shapes, for potential applications in materials science and nanomedicine.     

Measurements of gas desorption from polyethylene-UHMWPE irradiated by 5 MeV electrons

Gas desorption in vacuum from electron irradiated ultra high molecular weight polyethylene (PE) is measured with a high sensible mass quadrupole spectrometer. Measurements are performed in thick PE irradiated with 5 MeV electron beams at doses of the order of tens of kGy. The irradiation modifies the PE molecules producing dehydrogenation, emission of different C _x –H _y groups, C-enrichment and carbon cross-linking processes. Results indicate that the radiation damage depends on the dose and that a significant change of chemical and physical polymer properties is reached for a critical dose of 18 kGy.     

Decoherence for Quantum Markov Semi-Groups on Matrix Algebras

In this work we describe a necessary and sufficient condition for decoherence of quantum Markov evolutions acting on matrix spaces (according to the definition introduced by Blanchard and Olkiewicz). This condition is related to the spectral analysis of the generator ${\mathcal{L}}$ of the semigroup and is easily stated: the evolution displays decoherence if and only if the maximal algebra ${\mathcal{N}(\mathcal{T})}$ on which the semigroup is *-automorphic contains all the eigenvalues of ${\mathcal{L}}$ associated with eigenvectors with null real part. Moreover, this condition is surely verified when the semigroup admits a faithful invariant state.     

Super-Hydrodynamic Limit in Interacting Particle Systems

This paper is a follow-up of the work initiated in (Arab J Math, 2014), where we investigated the hydrodynamic limit of symmetric independent random walkers with birth at the origin and death at the rightmost occupied site. Here we obtain two further results: first we characterize the stationary states on the hydrodynamic time scale as a family of linear macroscopic profiles parameterized by their mass. Then we prove that beyond hydrodynamics there exists a longer time scale where the evolution becomes random. On such a super-hydrodynamic scale the particle system is at each time close to the stationary state with same mass and the mass fluctuates performing a Brownian motion reflected at the origin.     

The subalgebra lattice of a finite algebra

The aim of this paper is to characterize pairs (L, A), where L is a finite lattice and A a finite algebra, such that the subalgebra lattice of A is isomorphic to L. Next, necessary and sufficient conditions are found for pairs of finite algebras (of possibly distinct types) to have isomorphic subalgebra lattices. Both of these characterizations are particularly simple in the case of distributive subalgebra lattices. We do not restrict our attention to total algebras only, but we consider the more general case of partial algebras. Moreover, we use connections between algebras and hypergraphs to solve these problems.