A dissipation‐free numerical method to solve one‐dimensional hyperbolic flow equations

In this paper, a numerical method to capture the shock wave propagation in 1‐dimensional fluid flow problems with 0 numerical dissipation is presented. Instead of using a traditional discrete grid, the new numerical method is built on a range‐discrete grid, which is obtained by a direct subdivision of values around the shock area. The range discrete grid consists of 2 types: continuous points and shock points. Numerical solution is achieved by tracking characteristics and shocks for the movements of continuous and shock points, respectively. Shocks can be generated or eliminated when triggering entropy conditions in a marking step. The method is conservative and total variation diminishing. We apply this new method to several examples, including solving Burgers equation for aerodynamics, Buckley‐Leverett equation for fractional flow in porous media, and the classical traffic flow. The solutions were verified against analytical solutions under simple conditions. Comparisons with several other traditional methods showed that the new method achieves a higher accuracy in capturing the shock while using much less grid number. The new method can serve as a fast tool to assess the shock wave propagation in various flow problems with good accuracy.     

Multifractal Analysis of Inhomogeneous Bernoulli Products

We are interested to the multifractal analysis of inhomogeneous Bernoulli products which are also known as coin tossing measures. We give conditions ensuring the validity of the multifractal formalism for such measures. On another hand, we show that these measures can have a dense set of phase transitions.     

Rate constants for the reaction OH + CO as functions of temperature and water concentration

Rate constants for the reaction OH + CO have been measured as functions of temperature (340–1220 K) and water concentration in the presence of 1 atm of argon. Results at zero water concentration yield the expression, log k_? (cm³ molecule^?1 S^?1) = ?12.96 + 4.7 × 10^?4 T, for the reaction rate constant as a function of temperature. These results are in very good agreement with previous direct measurements and in reasonable agreement with flame and shock tube measurements. Explanations are offered for the involvement of the water molecule in the present experiments and earlier measurements from this laboratory throughout the entire temperature range. Results are consistent with previous results showing little, if any, pressure effect of Ar on the reaction up to 1 atm of Ar.     

Synthetic metals based on tetramethyltetraselenafulvalene(TMTSF): Varied anisotropy in the low temperature (125K) structures of (TMTSF)2X,X=C104-, PF6-, and AsF6-.

The low temperature (125K) X-ray crystal structures of (TMTSF)₂X, X=C10₄^-, PF₆^-, and AsF₆^- reveal decreases in the intermolecular interand intrastack Se-Se contact distances upon cooling (298K to 125K) which are highly anisotropic and different from one salt to another. The changes in the interstack distances, which are normal to the stacking direction, are approximately twice those involving intrastack Se-Se interactions. These observations establish that the anisotropic structural changes which accompany decreased temperature are common to numerous (TMTSF)₂X radical cation conducting salts.     

Study of active naphtodianthrone St John's Wort compounds by electrospray ionization Fourier transform ion cyclotron resonance and multi‐stage mass spectrometry in sustained off‐resonance irradiation collision‐induced dissociation and infrared multiphoton dissociation modes

Five well‐known active naphtodianthrone constituents of Hypericum perforatum (St John's Wort) extracts have been investigated by electrospray ionization Fourier transform ion cyclotron resonance mass spectrometry (ESI‐FTICRMS) and ESI‐FTICRMSⁿ. The studied compounds were hypericin, pseudohypericin, protohypericin, protopseudohypericin (biosynthetic precursors of the two former compounds, respectively) and isopseudohypericin (alkaline degradation product of pseudohypericin). Dissociation mass spectrometry measurements performed on the [M–H]^? ion presented a variable efficiency as a function of the used activation mode. Sustained off‐resonance irradiation collision‐induced dissociation (SORI–CID) only led to a restricted number of fragment ions. In contrast, IRMPD ensured the detection of numerous product ions. Ions detected in ESI‐FTICRMS and ESI‐FTICRMSⁿ experiments were measured with a very high mass accuracy (typically mass error is lower than 0.5 mDa at m/z close to 500) that allowed unambiguous formulae to be assigned to each signal observed in a mass spectrum. In spite of similar structures, specific fragmentation patterns were observed for the different compounds investigated. This study may be useful in the future to characterize in natural extracts these compounds (or derivatives of these compounds) by liquid chromatography/tandem mass spectrometry (LC/MS/MS) experiments by considering the MS/MS transitions highlighted in this paper. Copyright © 2009 John Wiley & Sons, Ltd.