On the geometry of O’N

We classify the rank two BCDL ₂₀₀₃-geometries of O’Nan and show that the maximal rank of a BCDL ₂₀₀₃-geometry for O’Nan is 4. This bound is sharp since it is satisfied by the rank four geometry given by Buekenhout (Contemp Math 45:1–32, 1985).     

What is control of turbulence in crossed fields?

Convective instability in the cross-field system of thermonuclear reactors can be overridden by poloidal drifts. While in crossed fields, a long-time, large-scale turbulent regime, in which the eddies of some particular size are destined to persist longer than usual, would come into being. Perhaps, we may keep such vortexes using them as tools for maintaining the stability of still an illusory construct of plasma fusion.     

Solitary waves in Abelian Gauge Theories with strongly nonlinear potentials

We study the existence of radially symmetric solitary waves for a system of a nonlinear Klein–Gordon equation coupled with Maxwell's equation in presence of a positive mass. The nonlinear potential appearing in the system is assumed to be positive and with more than quadratical growth at infinity.     

Apparent viscosity of a mixture of a Newtonian fluid and interacting particles

We investigate the behavior of fluid–particle mixtures subject to shear stress, by mean of direct simulation. This approach is meant to give some hints to explain the influence of interacting red cells on the global behavior of the blood. We concentrate on the apparent viscosity, which we define as a macroscopic quantity which characterizes the resistance of a mixture against externally imposed shear motion. Our main purpose is to explain the non-monotonous variations of this apparent viscosity when a mixture of fluid and interacting particles is submitted to shear stress during a certain time interval. Our analysis of these variations is based on preliminary theoretical remarks, and some computations for some well-chosen static configurations. To cite this article: A. Lefebvre, B. Maury, C. R. Mecanique 333 (2005).     

Viscosity of concentrated protein solutions

The viscosity of solutions of four proteins (Bovine Serum Albumin, Ovalbumin, _s-1 Casein, Lysozyme), brought to the random coil conformation, has been measured over a large concentration range extending into the entanglement region. A master curve is obtained in the dilute and semi-dilute regions with the reduced variables and of Simha and Utracki.By using Graessley's expression for the polymer coil expansion at a given concentration in the semi-dilute region (c ^* c c ^**), a simple equation is established giving the relative viscosity _r as a function of concentrationc: forc ^* c c ^**, ln _r = 2a[]c ^*(c/c ^*)^1/2a – (2a - 1)[]c ^*; wherec ^* is the incipient overlap concentration, [] the intrinsic viscosity, anda the Mark-Houwink exponent for the polymer-solvent considered.This equation fits well the experimental results. The adjustment yields for the parametera values which are comprised between 0.6 and 0.7, as expected, for Bovine Serum Albumin and Ovalbumin, but very close to 0.5 for _s-1 Casein and Lysozyme. This can be explained by the fact that the molecular weights of the two latter proteins are lower than, or very close, the critical molecular weight; the critical molecular weight is estimated to be about 20000.     

PPV Polymerization through the Gilch Route: Diradical Character of Monomers

Despite various studies on the polymerization of poly(p‐phenylene vinylene) (PPV) through different precursor routes, detailed mechanistic knowledge on the individual reaction steps and intermediates is still incomplete. The present study aims to gain more insight into the radical polymerization of PPV through the Gilch route. The initial steps of the polymerization involve the formation of a p‐quinodimethane intermediate, which spontaneously self‐initiates through a dimerization process leading to the formation of diradical species; chain propagation ensues on both sides of the diradical or chain termination occurs by the formation of side products, such as [2.2]paracyclophanes. Furthermore, different p‐quinodimethane systems were assessed with respect to the size of their aromatic core as well as the presence of heteroatoms in/on the conjugated system. The nature of the aromatic core and the specific substituents alter the electronic structure of the p‐quinodimethane monomers, affecting the mechanism of polymerization. The diradical character of the monomers has been investigated with several advanced methodologies, such as spin‐projected UHF, CASSCF, CASPT2, and DMRG calculations. It was shown that larger aromatic cores led to a higher diradical character in the monomers, which in turn is proposed to cause rapid initiation.     

Fast density matrix-based partitioning of the energy over the atoms in a molecule consistent with the Hirshfeld-I partitioning of the electron density

For the Hirshfeld-I atom in the molecule (AIM) model, associated single-atom energies and interaction energies at the Hartree-Fock level are efficiently determined in one-electron Hilbert space. In contrast to most other approaches, the energy terms are fully consistent with the partitioning of the underlying one-electron density matrix (1DM). Starting from the Hirshfeld-I AIM model for the electron density, the molecular 1DM is partitioned with a previously introduced double-atom scheme (Vanfleteren et al., J Chem Phys 2010, 132, 164111). Single-atom density matrices are constructed from the atomic and bond contributions of the double-atom scheme. As the Hartree-Fock energy can be expressed solely in terms of the 1DM, the partitioning of the latter over the AIM naturally leads to a corresponding partitioning of the Hartree-Fock energy. When the size of the molecule or the molecular basis set does not grow too large, the method shows considerable computational advantages compared with other approaches that require cumbersome numerical integration of the molecular energy integrals weighted by atomic weight functions.     

Communication: stabilization of radical anions with weakly bound electron in condensed media: a case study of diacetonyl radical anion

The radical anion resulting from electron capture by diacetonyl molecule has been characterized by EPR and optical absorption spectroscopy in glassy ether matrices at 77 K. In non-polar alkane glasses this species was not observed under the same conditions, which confirms the crucial role of matrix interactions in stabilizing this species. Calculations at the MP2 level show the vertical detachment energy to increase gradually from roughly zero for a bare anion to ～1 eV for the complex involving six ether molecules.     

Barr’s embedding theorem for enriched categories

We generalize Barr’s embedding theorem for regular categories to the context of enriched categories.     

A semi-Markov process with an inverse Gaussian distribution as sojourn time

Let X_n denote the state of a device after n repairs. We assume that the time between two repairs is the time τ taken by a Wiener process {W(t), t ? 0}, starting from w₀ and with drift μ < 0, to reach c ∈ [0, w₀). After the nth repair, the process takes on either the value X_n?1 + 1 or X_n?1 + 2. The probability that X_n = X_n?1 + j, for j = 1, 2, depends on whether τ ? t₀ (a fixed constant) or τ > t₀. The device is considered to be worn out when X_n ? k, where k ∈ {1, 2, …}. This model is based on the ones proposed by Rishel (1991) [1] and Tseng and Peng (2007) [2]. We obtain an explicit expression for the mean lifetime of the device. Numerical methods are used to illustrate the analytical findings.