Convergence of a level‐set algorithm in scalar conservation laws

This article is concerned with the convergence of the level‐set algorithm introduced by Aslam (J Comput Phys 167 (2001), 413–438) for tracking the discontinuities in scalar conservation laws in the case of linear or strictly convex flux function. The numerical method is deduced by the level‐set representation of the entropy solution: the zero of a level‐set function is used as an indicator of the discontinuity curves and two auxiliary states, which are assumed continuous through the discontinuities, are introduced. We rewrite the numerical level‐set algorithm as a procedure consisting of three big steps: (a) initialization, (b) evolution, and (c) reconstruction. In (a), we choose an entropy admissible level‐set representation of the initial condition. In (b), for each iteration step, we solve an uncoupled system of three equations and select the entropy admissible level‐set representation of the solution profile at the end of the time iteration. In (c), we reconstruct the entropy solution using the level‐set representation. We prove the convergence of the numerical solution to the entropy solution in for every , using ‐weak bounded variation (BV) estimates and a cell entropy inequality. In addition, some numerical examples focused on the elementary wave interaction are presented. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1310–1343, 2015     

Ion pairs of crystal violet in sodium bis(2-ethylhexyl)sulfosuccinate reverse micelles

The interfacial localization and the ion pair formation of the positively charged dye crystal violet (CV) in sodium bis(2-ethylhexyl)sulfosuccinate reverse micelles (AOT RMs) were studied by several structural and spectroscopic techniques and by quantum chemical calculations. The size and shape of the AOT RMs in the presence of CV were investigated by small-angle X-ray scattering, showing that CV does not significantly change the RM structure. CV localization as a function of the water to surfactant molar ratio (w(0)) was characterized by H(1) and (13)C NMR, indicating the close proximity of CV to the sulfosuccinate group of AOT at small and large w(0) values. These results were confirmed by calculation of magnetic shielding constants using the gauge-independent atomic orbital method with the HF/6-31G(d) basis set. Two different types of ion pairs between AOT and CV, i.e., contact ion pair (CIPs) and solvent-separated ion pair (SSIPs), were characterized by UV-vis spectroscopy and quantum chemical calculations using the semiempirical ZINDO-CI method. In nonpolar isotropic solvents CIPs are formed with an association constant (K(ASSOC)) of 2 x 10(4) mol(-1) L in isooctane and 750 mol(-1) L in chloroform. In AOT RMs at low w(0), CV-AOT CIPs are also formed. By increasing w(0), there is a sharp decrease in the CIP association free energy, and SSIPs are formed. (CV(+))(H(2)O)(AOT(-)) SSIPs are stable in the AOT RM up to the largest w(0) tested (w(0) = 33).     

(1)H and (13)C NMR spectral data for a tricyclic derivative of a Diels-Alder adduct

A complete NMR analysis with full assignment for (1)H and (13)C NMR spectral data for 5-(acetyloxy)-3-hydroxy-9,10-dimethoxy-6-oxo-11-oxatricyclo[6.2.1.0(2,7)]undec-2-yl acetate is described. This compound was prepared by rapid hydrogenation of the unstable Diels-Alder adduct obtained from the reaction between 3,4-dimethoxyfuran and 2,5-diacetoxy-1,4-benzoquinone. Full homonuclear hydrogen coupling constants measurements and molecular mechanics calculations were performed for the determination of the relative stereochemistry.     

Evidence of site-specific fragmentation on thioacetic acid, CH3C(O)SH, irradiated with synchrotron radiation around the S 2p and O 1s regions

Site-specific fragmentations following S 2p and O 1s photoexcitation of thioacetic acid, CH3C(O)SH, have been studied by means of synchrotron radiation. Total ion yield (TIY) spectra were measured and multicoincidence techniques, which include photoelectron-photoion coincidence (PEPICO) and photoelectron-photoion-photoion coincidence (PEPIPICO) time-of-flight mass spectrometry, were applied. The equivalent-core approximation was employed in order to estimate ionization transition values, and the observed peaks were tentatively assigned. A site-specific fragmentation is moderately observed by comparing the mass spectra collected at resonant energies around the inner and shallow inner shell S 2p and O 1s ionization edges. Beside H+ ion, the most abundant ions observed at the S 2p edge excitation were CH3CO+, SH+, S+, and CH3+. At the O 1s region the large CH3CO+ fragment was depressed, and small CHx+ (x = 0, 1, 2, 3), S+, and SH+ fragments were dominant. The dissociation dynamic for the main ion-pair production has been discussed. Two- and three-body dissociation channels have been observed in the PEPIPICO spectra, and the dissociation mechanisms were proposed.     

Proton-induced luminescence of mono- and dinuclear rhenium(I) tricarbonyl complexes containing 4-pyridinealdazine

New mono- and dinuclear rhenium(I) tricarbonyls, of formulas [Re(bpy)(CO)3(PCA)]+ (1), [(bpy)(CO)3Re(I)(PCA)Re(I)(CO)3(bpy)]2+ (2), and [(bpy)(CO)3Re(I)(PCA)Ru(II)(NH3)5]3+ (3) (bpy = 2,2'-bipyridine, PCA = 4-pyridinecarboxaldehydeazine), have been synthesized as PF6- salts and characterized by spectroscopic, electrochemical, and photophysical techniques. These species do not emit at room temperature in CH(3)CN; however, in aqueous solutions, a decrease in pH induces luminescence in all of them, due to protonation of one of the N atoms of the -C=N-N=C- chain of PCA, as indicated by the pKa values of the ground states, obtained by absorption measurements, which are ca. 3 orders of magnitude lower than the pKa value of the pyridine N of PCA in complex 1. On the other hand, the values of pKa* of the excited states, obtained by emission measurements, of complexes 1 and 2 are similar (pKa* = 2.7 +/- 0.1 at I = 0.1 M) and higher than those of the corresponding ground states. At low values of pH, chemical decomposition takes place rapidly in complex 3, but not in 1 and 2, supporting the possible use of these latter species as luminescent sensors of pH. The heterodinuclear complex, of formula [(bpy)(CO)3Re(I)(PCA)Ru(III)(NH3)5]4+, was obtained by bromine oxidation of the [Re(I), Ru(II)] precursor in CH3CN solution; from spectral and electrochemical measurements, the recombination charge-transfer reaction [Re(II), Ru(II) ] --> [Re(I), Ru(III)], which occurs after photoexcitation, is predicted to lie in the Marcus inverted region.     

Gauge-invariant metric fluctuations from NKK theory of gravity: de Sitter expansion

In this Letter we study gauge-invariant metric fluctuations from a noncompact Kaluza–Klein (NKK) theory of gravity in de Sitter expansion. We recover the well-known result δρ/ρ?2Φ$\delta \rho /\rho ?2\Phi$, obtained from the standard 4D semiclassical approach to inflation. The spectrum for these fluctuations should be dependent of the fifth (spatial-like) coordinate.     

Detection and identification of IHN and ISA viruses by isothermal DNA amplification in microcapillary tubes

Unique base sequences derived from RNA of both infectious hematopoietic necrosis virus (IHNV) and infectious salmon anemia virus (ISAV) were detected and identified using a combination of surface-associated molecular padlock DNA probes (MPPs) and rolling circle amplification (RCA) in microcapillary tubes. DNA oligonucleotides with base sequences identical to RNA obtained from IHNV or ISAV were recognized by MPPs. Circularized MPPs were then captured on the inner surfaces of glass microcapillary tubes by immobilized DNA oligonucleotide primers. Extension of the immobilized primers by isothermal RCA produced DNA concatamers, which were labeled with fluorescent SYBR Green II nucleic acid stain, and measured by microfluorimetry. Molecular padlock probes, combined with this method of surface-associated isothermal RCA, exhibited high selectivity without the need for thermal cycling. This method is applicable to the design of low-power field sensors capable of multiplex detection of viral, bacterial, and protozoan pathogens within localized regions of microcapillary tubes.      

Navier–Stokes Equations on Weighted Graphs

Navier–Stokes equations arise in the study of incompressible fluid mechanics, star movement inside a galaxy, dynamics of airplane wings, etc. In the case of Newtonian incompressible fluids, we propose an adaptation of such equations to finite connected weighted graphs such that it produces an ordinary differential equation with solutions contained in a linear subspace, this subspace corresponding to the Newtonian conservation law. We discuss the particular case when the graph is the complete graph K _m , with constant weight, and provide a necessary and sufficient condition for it to have solutions.