Variable metric bundle methods: From conceptual to implementable forms

To minimize a convex function, we combine Moreau-Yosida regularizations, quasi-Newton matrices and bundling mechanisms. First we develop conceptual forms using “reversal” quasi-Newton formulae and we state their global and local convergence. Then, to produce implementable versions, we incorporate a bundle strategy together with a “curve-search”. No convergence results are given for the implementable versions; however some numerical illustrations show their good behaviour even for large-scale problems.     

High-power laser with Nd:YAG single-crystal fiber grown by the micro-pulling-down technique

We present optical characterization and laser results achieved with single-crystal fibers directly grown by the micro-pulling-down technique. We investigate the spectroscopic and optical quality of the fiber, and we present the first laser results. We achieved a cw laser power of 10 W at 1064 nm for an incident pump power of 60 W at 808 nm and 360 kW peak power for 12 ns pulses at 1 kHz in the Q-switched regime. It is, to the best of our knowledge, the highest laser power ever achieved with directly grown single-crystal fibers.     

Covalent Grafting of BPin functions on Carbon Nanotubes and Chan–Lam–Evans Post-Functionalization

The chemical functionalization of carbon nanotubes is often a prerequisite prior to their use in various applications. The covalent grafting of 4,4,5,5-tetramethyl-1,3,2-dioxaborolane (BPin) functional groups directly on the surface of multi- and single-walled carbon nanotubes, activated by nucleophilic addition of nBuLi, was carried out. Thermogravimetric analysis (TGA) coupled with mass spectrometry, Raman spectroscopy, X-ray photoelectron spectroscopy (XPS) and time-of-flight secondary ions mass spectrometry (ToF-SIMS) confirmed the efficiency of this methodology and proved the integrity and covalent grafting of the BPin functional groups. These groups were further reacted with various nucleophiles in the presence of a copper(II) source in the conditions of the aerobic Chan–Lam–Evans coupling. The resulting materials were characterized by TGA, XPS and ToF-SIMS. This route is efficient, reliable and among the scarce reactions that enable the direct grafting of heteroatoms at carbonaceous material surfaces.     

Thermoset modified with polyethersulfone: Characterization and control of the morphology

Thermoset (TS) epoxy resins can be toughened with a thermoplastic (TP) for high-performance applications. The final structure morphology has to be controlled to achieve high mechanical properties and high impact resistance. Four polyethersulfone-modified epoxy resins are considered. They consist of different epoxy monomer structure (TGAP, triglycidyl-p-aminophenol and TGDDM, tetraglycidyl diaminodiphenylmethane) and a fixed amount of thermoplastic, and they are cured with two different amounts of curing agent. A reaction-induced phase separation occurs for all formulations generating morphologies, different in shapes and scales. The aim is to control the final morphology and in particular its dominant length scale. This morphology depends on the phase separation process, from the initiation to its final stage. The initiation relies on the relative miscibility of the components and on the stoichiometry between epoxy and curing agent. The kinetics depends on the viscosity of the systems. The different morphologies are characterized by electron microscopy or neutron scattering. Dynamic mechanical analysis allows confirming the presence of a phase separation even when it is not observable by electron microscopy. Vermicular morphologies with few hundreds nanometer width are obtained for the systems containing the TGAP as epoxy monomer. Systems formulated with TGDDM presents morphologies on much smaller scale of order a few tens of nanometers. We interpret the different sizes of the morphologies as a consequence of a larger viscosity for the TGDDM systems as compared to the TGAP ones rather than by a latter initiation of phase separation.     

Comment on the analysis of angle-dependent X-ray magnetic circular dichroism in systems with reduced dimensionality

The magnetic dipole term T appearing in the X-ray magnetic circular dichroism (XMCD) spin sum rule can be eliminated from the analysis within the spin sum rule by angle-dependent XMCD spectroscopy if the effects of spin–orbit coupling are small so that T_x+T_y+T_z≈0. It is shown by the ab initio electron theory for the extreme case of a low-dimensional system, i.e., for a free-standing monatomic Co wire that this relation is strongly violated, indicating that the determination of T by the angle-dependent XMCD is possibly not very reliable for low-dimensional magnetic systems.     

Random and Deterministic Triangle Generation of Three-Dimensional Classical Groups II

Let p ₁, p ₂, p ₃ be primes. This is the second article in a series of three on the (p ₁, p ₂, p ₃)-generation of the finite projective special unitary and linear groups PSU₃(p ⁿ ), PSL₃(p ⁿ ), where we say a noncyclic group is (p ₁, p ₂, p ₃)-generated if it is a homomorphic image of the triangle group T _{p 1, p 2, p 3} . This paper is concerned with the case where p ₁ = 2 and p ₂ = p ₃. We determine for any prime p ₂ the prime powers p ⁿ such that PSU₃(p ⁿ ) (respectively, PSL₃(p ⁿ )) is a quotient of T = T _{2, p 2, p 2} . We also derive the limit of the probability that a randomly chosen homomorphism in Hom(T, PSU₃(p ⁿ )) (respectively, Hom(T, PSL₃(p ⁿ ))) is surjective as p ⁿ tends to infinity.     

{C \ell{^\ast_3}} Invariance of the Dirac Equation and Electromagnetism

In order to obtain a form invariance of the Dirac wave, the relativistic quantum theory uses ${{\rm SL}(2, \mathbb{C})}$ , a subset of the Clifford algebra C? ₃ of the 3-dimensional physical space. In Dirac theory and electromagnetism, we study a replacement of this invariance group by the full group ${C \ell{^\ast_3}}$ consisting of all invertible elements in C? ₃. We extend this invariance to systems of identical particles. We explain how geometry linked to the Dirac wave implies existence of a second space-time variety, and we review its consequences to particle physics.