Symmetry Reduction in Symplectic and Poisson Geometry

We present a quick review of several reduction techniques for symplectic and Poisson manifolds using local and global symmetries compatible with these structures. Reduction based on the standard momentum map (symplectic or Marsden–Weinstein reduction) and on generalized distributions (the optimal momentum map and optimal reduction) is emphasized. Reduction of Poisson brackets is also discussed and it is shown how it defines induced Poisson structures on cosymplectic and coisotropic submanifolds.     

Bloch wave homogenization of a non-homogeneous Neumann problem

In this paper, we use the Bloch wave method to study the asymptotic behavior of the solution of the Laplace equation in a periodically perforated domain, under a non-homogeneous Neumann condition on the boundary of the holes, as the size of the holes goes to zero more rapidly than the domain period. This method allows to prove that, when the hole size exceeds a given threshold, the non-homogeneous boundary condition generates an additional term in the homogenized problem, commonly referred to as “the strange term” in the literature.     

DFT‐Aided Vibrational Circular Dichroism Spectroscopy Study of (−)‐S‐cotinine

The implementation of a strategy comprising the use of vibrational circular dichroism spectroscopy and DFT calculations allows determination of the solution‐state conformational distribution in (?)‐S‐cotinine, giving further proof of the extra conformer‐discriminating potential of this experimental technique, which may offer unique molecular fingerprints of subtly dissimilar molecular conformers of chiral samples. Natural bond orbital electronic structure calculations of the rotational barrier height between the two main conformers of the species indicate that hyperconjugative effects are the key force governing the conformational equilibrium. The negligible effect of the solvent’s polarity over both structure and conformational energy profile supports this result.     

Exo conformers of N‐(pyridin‐2‐yl)‐ and N‐(pyridin‐3‐yl)norbornene‐5,6‐dicarboximide crystals

Two isomeric pyridine‐substituted norbornenedicarboximide derivatives, namely N‐(pyridin‐2‐yl)‐exo‐norbornene‐5,6‐dicarboximide, (I), and N‐(pyridin‐3‐yl)‐exo‐norbornene‐5,6‐dicarboximide, (II), both C₁₄H₁₂N₂O₄, have been crystallized and their structures unequivocally determined by single‐crystal X‐ray diffraction. The molecules consist of norbornene moieties fused to a dicarboximide ring substituted at the N atom by either pyridin‐2‐yl or pyridin‐3‐yl in an anti configuration with respect to the double bond, thus affording exo isomers. In both compounds, the asymmetric unit consists of two independent molecules (Z′ = 2). In compound (I), the pyridine rings of the two independent molecules adopt different conformations, i.e. syn and anti, with respect to the methylene bridge. The intermolecular contacts of (I) are dominated by C—H...O interactions. In contrast, in compound (II), the pyridine rings of both molecules have an anti conformation and the two independent molecules are linked by carbonyl–carbonyl interactions, as well as by C—H...O and C—H...N contacts.     

Non-dominated sorting procedure for Pareto dominance ranking on multicore CPU and/or GPU

Evolutionary multi-objective optimization algorithms aim at finding an approximation of the Pareto set. For hard to solve problems with many conflicting objectives, the number of functions evaluations to represent the Pareto front can be large and time consuming. Parallel computing can reduce the wall-clock time of such algorithms. Previous studies tackled the parallelization of a particular evolutionary algorithm. In this research, we focus on improving one of the most time consuming procedures—the non-dominated sorting—, which is used in the state-of-the-art multi-objective genetic algorithms. Here, three parallel versions of the non-dominated sorting procedure are developed: (1) a multicore (based on Pthreads); (2) a Graphic Processing Unit (GPU) (based on CUDA interface); and (3) a hybrid (based on Pthreads and CUDA). The user can select the most suitable option to efficiently compute the non-dominated sorting procedure depending on the available hardware. Results show that the use of GPU computing provides a substantial improvement in terms of performance. The hybrid approach has the best performance when a good load balance is established among cores and GPU.     

pH-induced changes in the fabrication of multilayers of poly(acrylic acid) and chitosan: fabrication, properties, and tests as a drug storage and delivery system

Multilayers of poly(acrylic acid), PAA, and chitosan, CHI, have been built by the layer-by-layer (LbL) method from aqueous solutions at different pH values and analyzed by the dissipative quartz crystal microbalance (D-QCM) and ellipsometry. The results showed that under all of the assembly conditions considered the growth of the films is nonlinear. The thickness of the PAA layers increases as the pH of the assembling solutions decreases, whereas the adsorption of CHI is almost unaffected by the pH conditions. The comparison of the thickness obtained by D-QCM and by ellipsometry has allowed us to calculate the water content of the films, showing that the multilayers are highly hydrated, with an average water content higher than 20%. The analysis of D-QCM data has provided high-frequency values of the complex shear modulus that are in the megapascal range and shows a transition from mainly viscous to mainly elastic behavior for the added PAA layers, depending on the pH. The monomer surface density in each layer (obtained from the combination of ellipsometry and differential refractive index measurements) indicated that the monomer density depends on the assembly conditions. It was found that the adsorption kinetics is a bimodal process, with characteristic times that depend on the number and nature of the layers. Finally, the possibility of using of these multilayers as a drug storage and delivery system has been evaluated.     

Alkyl group effect on the conformational isomerism of trans-2-bromoalkoxycyclohexanes analyzed by nmr spectroscopy and theoretical calculations

Suitable (3)J(H,H) coupling constants and theoretical calculations were used to define the conformational preferences of trans-2-bromoalkoxycyclohexanes (alkoxy = OMe, OEt, O(i)Pr, and O(t)Bu) for the isolated molecule and as a function of the medium. The diaxial conformer was preponderant, or at least similarly populated to the diequatorial form, for the tert-butoxy derivative only, while the diequatorial conformer was prevalent for the remaining alkoxy derivatives (except for the OMe derivative in CCl(4) solution). The conformational behavior of these compounds was analyzed on the basis of classical steric effects and attractive electron delocalizations, by means of natural bond orbital analysis.     

Rheology of poly(methyl methacrylate) Langmuir monolayers: percolation transition to a soft glasslike system

An experimental study of the equilibrium properties and of the surface rheology of Langmuir monolayers of poly(methyl methacrylate) (PMMA) at the air/water interface has been carried out as a function of polymer concentration (Γ) and molecular weight (M(w)). Dilational and shear complex elasticity moduli covering a frequency range from 10(-3) to 0.2 Hz have been discussed. It was found that the air∕water interface behaves as a poor solvent for PMMA monolayers, thus suggesting that the polymer coils take collapsed soft-disks (pancakes) shape at the interface. The equilibrium and dynamic results suggest a fluid-to-soft-glass transition as the polymer concentration increases above a critical packing fraction at constant temperature. This two-dimensional transition is in agreement with results previously discussed for the dilational rheology of poly(4-hydroxystyrene) [F. Monroy, F. Ortega, R. G. Rubio, H. Ritacco, and D. Langevin, J. Chem. Phys. 95, 056103 (2005)]. Furthermore, the Γ-dependence of the relaxation dynamics of the monolayers suggests that the gel state may be considered as a fragile soft glass.