pH-sensitive nanostructured architectures based on synthetic and/or natural weak polyelectrolytes

This study aims to evidence the influence of polyelectrolytes structure and the number of double layers on the properties of some new nanostructured architectures formed by layer-by-layer self-assembly of complementary weak polyelectrolytes on planar surfaces. For this purpose, we used chitosan and poly(allylamine hydrochloride) as polycations, and poly(acrylic acid) and poly(2-acrylamido-2-methylpropanesulfonic acid–co-acrylic acid) as polyanions. To get a direct image on the polyelectrolyte multilayers formation and properties, gravimetry, infrared spectroscopy, and atomic force microscopy have been used. The capacity of the polyions to overcompensate the complementary polyions charges, and thus to influence the swelling degree in water of thin films, was strongly influenced by the chain structure and flexibility. A special attention was paid to the responsiveness of the new composite materials to the pH of the swelling environment.     

Polyhydrosilanes I. Synthesis

Abstract

Using the well known Wurtz coupling technique, polyhydrosilanes copolymers with diphenyl - and methyl(phenyl) - sequences, were synthesised. This work describes the possibility to maintain stable Si-H group and to obtain in good yields, soluble, high molecular, functional polysilanes. IR, ¹-NMR, ¹³C, UV spectral data, quantitative elemental Si and H (from Si-H) analyses and indirect molecular weight investigation sustain the molecular structure of the copolysilanes.     

Eigenvalue problems for anisotropic discrete boundary value problems

In this paper, we prove the existence of a continuous spectrum for a family of discrete boundary value problems. The main existence results are obtained by using critical point theory. The equations studied in the paper represent a discrete variant of some recent anisotropic variable exponent problems, which deserve as models in different fields of mathematical physics.     

A complementarity-based rolling friction model for rigid contacts

In this work (also, preprint ANL/MCS-P3020-0812, Argonne National Laboratory) we introduce a complementarity-based rolling friction model to characterize dissipative phenomena at the interface between moving parts. Since the formulation is based on differential inclusions, the model fits well in the context of nonsmooth dynamics, and it does not require short integration timesteps. The method encompasses a rolling resistance limit for static cases, similar to what happens for sliding friction; this is a simple yet efficient approach to problems involving transitions from rolling to resting, and vice-versa. We propose a convex relaxation of the formulation in order to achieve algorithmic robustness and stability; moreover, we show the side effects of the convexification. A natural application of the model is the dynamics of granular materials, because of the high computational efficiency and the need for only a small set of parameters. In particular, when used as a micromechanical model for rolling resistance between granular particles, the model can provide an alternative way to capture the effect of irregular shapes. Other applications can be related to real-time simulations of rolling parts in bearing and guideways, as shown in examples.     

On the number of solutions to systems of Pell equations

We prove that, for positive integers a, b, c and d with c≠d, a>1, b>1, the number of simultaneous solutions in positive integers to ax²−cz²=1, by²−dz²=1 is at most two. This result is the best possible one. We prove a similar result for the system of equations x²−ay²=1, z²−bx²=1.     

Singular open book structures from real mappings

We define open book structures with singular bindings. Starting with an extension of Milnor’s results on local fibrations for germs with nonisolated singularity, we find classes of genuine real analytic mappings which yield such open book structures.