On Some Types of Rigid Sets in Banach Spaces

One of the properties characterizing Euclidean spaces says - roughly speaking- that their unit sphere has nice invariant properties. More precisely, a finite dimensional normed space has an Euclidean norm if and only if the group of isometries acts transitively on its unit sphere (the norm is “transitive”); such property of the sphere is also called “rigidity”. More recently, another notion of “rigidity” for compact sets, connected with “isometric sequences”, received some attention. Infinite rigid sets are diametral; moreover, under suitable assumptions on the space, they are also contained in the boundary of a sphere. These notions are connected with many problems, in different areas. Here we discuss and compare these two notions of rigid set, trying to indicate new relations among them and with some other properties of sets. Several examples complete the paper.     

Spectral stability results for higher-order operators under perturbations of the domain

We analyze the spectral behavior of higher-order elliptic operators when the domain is perturbed. We provide general spectral stability results for Dirichlet and Neumann boundary conditions. Moreover, we study the bi-harmonic operator with the so-called intermediate boundary conditions. We give special attention to this last case and analyze its behavior when the boundary of the domain has some oscillatory behavior. We will show that there is a critical oscillatory behavior and that the limit problem depends on whether we are above, below or just sitting on this critical value.     

The Fundamentals of Real‐Time Surface Plasmon Resonance/Electrogenerated Chemiluminescence

We report the integration of surface plasmon resonance (SPR), cyclic voltammetry and electrochemiluminescence (ECL) responses to survey the interfacial adsorption and energy transfer processes involved in ECL on a plasmonic substrate. It was observed that a Tween 80/tripropylamine nonionic layer formed on the gold electrode of the SPR sensor, while enhancing the ECL emission process, affects the electron transfer process to the luminophore, Ru(bpy)₃²⁺, which in turn has an impact on the plasmon resonance. Concomitantly, the surface plasmon modulated the ECL intensity, which decreased by about 40 %, due to an interaction between the excited state of Ru(bpy)₃²⁺ and the plasmon. This occurred only when the plasmon was excited, demonstrating that the optically excited surface plasmon leads to lower plasmon‐mediated luminescence and that the plasmon interacts with the excited state of Ru(bpy)₃²⁺ within a very thin layer.     

Van der Waals interactions in DFT made easy by Wannier functions

Ubiquitous van der Waals interactions between atoms and molecules are important for many molecular and solid structures. These systems are often studied from first principles using the density functional theory (DFT). However, the commonly used DFT functionals fail to capture the essence of van der Waals effects. Most attempts to correct for this problem have a basic semiempirical character, although computationally more expensive first principles schemes have been recently developed. We here describe a novel approach, based on the use of the maximally localized Wannier functions, that appears to be promising, being simple, efficient, accurate, and transferable (charge polarization effects are naturally included). The results of test applications to small molecules and bulk graphite are presented.     

Excimer laser crystallization of microcrystalline silicon for TFTs on flexible substrate

Microcrystalline silicon (μc-Si) films have been deposited on PDMS as well as on PEN substrate. Excimer laser annealing was used to improve the crystalline structure and so to obtain high mobility TFTs. The effect of the laser annealing on the crystalline structure of silicon films is studied using different characterization techniques and discussed. Mobility values of 60 cm²/V s with PDMS and 46 cm²/V s with PEN are obtained.     

The vibrational spectra of the cyanide ligand revisited: the ν(CN) infrared and Raman spectroscopy of Prussian blue and its analogues

A careful analysis of the Raman spectra of the M′_x[M(CN)₆]_y Prussian blue species has enabled a general model for the interpretation of the ν(CN) vibrational spectra. The spectral patterns are derived from those of the metal ions with local O_h symmetry. Two limiting models are discussed. A ‘localized mode’ model, involving matrix‐isolated species, is in much better accord with the observations than a ‘factor group’ model. The use of the infrared feature as fingerprint of specific M CN M′ units arises from the axis‐specific nature of individual T_1u modes. The interpretation of the A_1g and E_g Raman features is done in terms of localized vibrations, with involvement of additional energy terms from the lattice motions. Copyright © 2011 John Wiley & Sons, Ltd.     

Effect of wall slip on the viscoelastic particle ordering in a microfluidic channel

The formation of a line of equally spaced particles at the centerline of a microchannel, referred as “particle ordering,” is desired in several microfluidic applications. Recent experiments and simulations highlighted the capability of viscoelastic fluids to form a row of particles characterized by a preferential spacing. When dealing with non-Newtonian fluids in microfluidics, the adherence condition of the liquid at the channel wall may be violated and the liquid can slip over the surface, possibly affecting the ordering efficiency. In this work, we investigate the effect of wall slip on the ordering of particles suspended in a viscoelastic liquid by numerical simulations. The dynamics of a triplet of particles in an infinite cylindrical channel is first addressed by solving the fluid and particle governing equations. The relative velocities computed for the three-particle system are used to predict the dynamics of a train of particles flowing in a long microchannel. The distributions of the interparticle spacing evaluated at different slip coefficients, linear particle concentrations, and distances from the channel inlet show that wall slip slows down the self-assembly mechanism. For strong slipping surfaces, no significant change of the initial microstructure is observed at low particle concentrations, whereas strings of particles in contact form at higher concentrations. The detrimental effect of wall slip on viscoelastic ordering suggests care when designing microdevices, especially in case of hydrophobic surfaces that may enhance the slipping phenomenon.     

History of accelerator neutrino beams

Neutrino beams obtained from proton accelerators were first operated in 1962. Since then, neutrino beams have been intensively used in particle physics and evolved in many different ways. We describe the characteristics of various neutrino beams, relating them to the historical development of the physics studies and discoveries. We also discuss some of the ideas still under consideration for future neutrino beams.

     

Friedel–Crafts Reaction of Benzyl Fluorides: Selective Activation of C?F Bonds as Enabled by Hydrogen Bonding

A Friedel–Crafts benzylation of arenes with benzyl fluorides has been developed. The reaction produces 1,1‐diaryl alkanes in good yield under mild conditions without the need for a transition metal or a strong Lewis acid. A mechanism involving activation of the C F bond through hydrogen bonding is proposed. This mode of activation enables the selective reaction of benzylic C F bonds in the presence of other benzylic leaving groups.