Structural Stability of Discontinuous Galerkin Schemes

The goal of this work is to determine classes of traveling solitary wave solutions for a differential approximation of a discontinuous Galerkin finite difference scheme by means of an hyperbolic ansatz. It is shown that spurious solitary waves can occur in finite-difference solutions of nonlinear wave equation. The occurence of such a spurious solitary wave, which exhibits a very long life time, results in a non-vanishing numerical error for arbitrary time in unbounded numerical domain. Such a behavior is referred here to have a structural instability of the scheme, since the space of solutions spanned by the numerical scheme encompasses types of solutions (solitary waves in the present case) that are not solutions of the original continuous equations. This paper extends our previous work about classical schemes to discontinuous Galerkin schemes (David and Sagaut in Chaos Solitons Fractals 41(4):2193?C2199, 2009; Chaos Solitons Fractals 41(2):655?C660, 2009).     

The ubiquity of generalized cluster categories

Associated with a finite-dimensional algebra of global dimension at most 2, a generalized cluster category was introduced in Amiot (2009) [1]. It was shown to be triangulated, and 2-Calabi–Yau when it is Hom-finite. By definition, the cluster categories of Buan et al. (2006) [4] are a special case. In this paper we show that a large class of 2-Calabi–Yau triangulated categories, including those associated with elements in Coxeter groups from Buan et al. (2009) [7], are triangle equivalent to generalized cluster categories. This was already shown for some special elements in Amiot (2009) [1].     

Solution conformational preferences of glutaric, 3‐hydroxyglutaric, 3‐methylglutaric acid,and their mono‐ and dianions

Conformational preferences of glutaric, 3‐hydroxyglutaric and 3‐methylglutaric acid, and their mono‐ and dianions have been investigated with the aid of NMR spectroscopy. In contrast to succinic acid, glutaric acid displays essentially statistical conformational equilibria in polar and non‐polar solutions of high and low hydrogen‐bonding ability with no clear evidence for intramolecular hydrogen‐bonding interactions. The acid ionization constant ratios, K ₁/K₂, in D₂O and DMSO of glutaric, 3‐hydroxyglutaric, and 3‐methylglutaric acids also indicate that intramolecular interactions are much less important than, or indeed insignificant, for shorter‐chain acids. FTIR studies on 3‐methylglutaric acid indicate some preference for either association with solvent or dimerization, depending on the solvent, rather than intramolecular hydrogen bonding. Copyright © 2008 John Wiley & Sons, Ltd.     

2-μm high-power multiple-frequency single-mode Q-switched Ho:YLF laser for DIAL application

We report on the development and the demonstration of a two-wavelength single-frequency laser oscillator based on Ho:YLF crystal. This laser is especially suitable for application as a transmitter in differential absorption lidar (DIAL)/integrated path differential absorption (IPDA) measurements of atmospheric carbon dioxide (CO₂) using the R30 CO₂ absorption line at 2,050.967 nm. The oscillator consists in a fiber-coupled and free-space solid-state hybrid system and can be used in high-energy middle-rate or moderate-energy high-rate configurations. The latter produced On and Off sequentially single-frequency laser pulses with 13 mJ of energy at a repetition rate of 2 kHz and pulse duration of 42 ns. The pulse energy and frequency stabilities are specially documented in free-running, single-frequency and two-frequency seeding single-mode operations. Standard deviation is 7.7 % for pulse energy and 2 MHz for frequency stability for the two-wavelength seeding operation. Allan variance plot shows that frequency fluctuations are reduced below 70 kHz for 10 s of averaging which is suitable for accurate CO₂ DIAL or IPDA measurements.     

Use of isothermal microcalorimetry data for the determination of integral molar entropies of adsorption at the gas—solid interface by a quasi-equilibrium procedure

The aim of this paper is to describe the present position in the experimental determination of entropies of adsorption. After pointing out the limitations of the “isosteric” approach and after stressing the fact that the most interesting entropy to know is the integral molar entropy of adsorption, the authors show how the use of isothermal adsorption microcalorimetry, with a special quasi-reversible procedure, allows this entropy to be determined satisfactorily from the thermodynamic point of view.     

Insertion of dipolar molecules in channels of a centrosymmetric organic zeolite: molecular modeling and experimental investigations on diffusion and polarity formation

The mechanism of insertion of p-nitroaniline (PNA) and its diffusion behavior in channels of the hexagonal host structure of tris(o-phenylenedioxy)cyclotriphosphazene (TPP) was investigated by means of molecular modeling tools. Strong preferential sites in the bulk were found to be due to pi-pi and NH-pi interactions between PNA and channel walls of TPP. MD simulations showed that diffusion can be characterized by jumps from one site to the next, occurring mainly because of the dynamic flexibility of the host structure. Calculations of host-guest interactions between the TPP surface and PNA approaching the entrance of channels with its terminal H2N-first or O2N-first revealed that the H2N-first insertion is clearly preferred. Preferential insertion of PNA is found to be the reason for polar effects, observed experimentally. Because of a distinct guest-host recognition at the surface, guest-guest interactions were found to have a minor influence on polarity.     

Diffusion of asymmetric swimmers

Particles moving along curved trajectories will diffuse if the curvature fluctuates sufficiently in either magnitude or orientation. We consider particles moving at a constant speed with either a fixed or a Gaussian distributed magnitude of curvature. At small speeds the diffusivity is independent of the speed. At larger particle speeds, the diffusivity depends on the speed through a novel exponent. We apply our results to intracellular transport of vesicles. In sharp contrast to thermal diffusion, the effective diffusivity increases with vesicle size and so may provide an effective means of intracellular transport.     

Macrocyclic diiminodipyrromethane complexes: structural analogues of Pac-Man porphyrins

The complexation of palladium(II) by a unique family of [2+2] diiminodipyrromethane macrocycles yields compounds that adopt structures reminiscent of Pac-Man porphyrins.