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461.
    
New a posteriori error indicators based on edgewise slope‐limiting are presented. The L2‐norm is employed to measure the error of the solution gradient in both global and element sense. A second‐order Newton–Cotes formula is utilized in order to decompose the local gradient error from a ??1 finite element solution into a sum of edge contributions. The slope values at edge midpoints are interpolated from the two adjacent vertices. Traditional techniques to recover (superconvergent) nodal gradient values from consistent finite element slopes are reviewed. The deficiencies of standard smoothing procedures—L2‐projection and the Zienkiewicz–Zhu patch recovery—as applied to nonsmooth solutions are illustrated for simple academic configurations. The recovered gradient values are corrected by applying a slope limiter edge‐by‐edge so as to satisfy geometric constraints. The direct computation of slopes at edge midpoints by means of limited averaging of adjacent gradient values is proposed as an inexpensive alternative. Numerical tests for various solution profiles in one and two space dimensions are presented to demonstrate the potential of this postprocessing procedure as an error indicator. Finally, it is used to perform adaptive mesh refinement for compressible inviscid flow simulations. Copyright © 2006 John Wiley & Sons, Ltd.  相似文献   
462.
The values of the penetration depths and their temperature dependences were measured for differentc-axis orientations of a textured 2.2.1.2. sample. The remanent magnetic flux was studied. The giant mobility of the trapped vortex structure was found above 40 K.  相似文献   
463.
This study is concerned with proton-transfer photoreactions in hydrogen-bonded complexes and the formation of ionized forms of naphthols in the ground state, in the presence of crown ethers. It has been found that a loss in electronic excitation energy may occur during the proton transfer in the hydrogen bond. The efficiencies of the observed radiationless deactivation processes aie controlled by the nature of the excited proton donor.  相似文献   
464.
The study of the temporal and spectral behavior of relaxation oscillations in quasi-three-level systems allows the direct measurement of the absolute value and spectral profile of laser-transition absorption and emission cross sections, simultaneously and independently, not requiring the usual assumption of Boltzman distributions for the intermanifold sublevels.On leave from the General Physics Institute, Russian Academy of Sciences, Moscow, Russia  相似文献   
465.
The parameters of the muonium quadrupole interaction in α-quartz as well as the orientation of the EFG tensor principal axes are determined. It is shown that there is no temperature dependence of these characteristics in the temperature region 75–120 K. The assumption of the reversal of the sign of the q?uadrupole constant with temperature increase from 120 K to room temperature is confirmed. It is shown that the change of the quadrupole interaction strength and symmetry is caused by the diffusion of muonium.  相似文献   
466.
467.
Flash photolysis technique has been used to obtain the rate and thermodynamic parameters of the reversible dimerization reactions of a range of ten phenoxy radicals (I–X) in a toluene–dibutylphthalate mixture (0.6 cP ≤η≤18.4 cP): The main reason for the difference in the k1 values are the different steric hindrances in radicals. It has been found that the values of k1 for 2,6-diphenyl-4-methoxy- (I), 2-phenyl-(III), and 2-methoxyphenoxy (IV) radicals are 3–5 times smaller than the respective diffusion constants calculated according to the Debye formula with regard to the spin-statistical factor: The resultant ΔH1values for these radicals in toluene and dibutylphthalate are close to the activation energies of the viscous flow of the solvents B. Linear relationships with a slope equal to unity are observed between log k1 and log(T/η). The recombination of radicals I, III, and IV is limited by translational diffusion. The k1 values for 2,6-diphenyl- (VII), 2,6-di-tert-butyl- (IX), and 2,6-di-tert-butyl-4-methylphenoxy (X) radicals are 10–60 times smaller than kdiff and Δ H B. In the case of radical X in toluene ΔH1 0. The recombination of these three radicals includes an intermediate step of complex formation: For 4-phenyl- (II), 2,6- dimethoxy- (V), 2,4-diphenyl- (VI), and radicals VII, IX, and X the linear relationships between log k1 and log (T/η) have a slope of from 0.5 ± 0.05 to 0.8 ± 0.05. The k1-1 versus η relationships for these radicals are not straight lines. The recombination of these six radicals is limited by translational and rotational diffusion. With the aid of theoretical models, the k1 versus η relationships have been used to derive the steric factor f in radical recombination and the angle θ between the axis and the solid angle generatrix. The solid angle defines the reaction spot on the radical-sphere surface. The recombination of the 2,6-diphenyl-4-diphenylmethylphenoxy radical (VIII) takes place in the region intermediate between the diffusion and the kinetic ones, and the relationship between log k1 and log (T/η) for this radical has a plateau portion. The log k-1 versus log (T/η) relationships have precisely the same form as the corresponding k1 relationships, which is quite in line with the theory of diffusion-controlled reversible recombination reactions.  相似文献   
468.
Rates and thermodynamic data have been obtained for the reversible self-termination reaction: Involving aromatic 2-(4′dimethylaminophenyl)indandione-1,3-yl (I), 2-(4′diphenylaminophenyl)indandione-1,3-yl (II), and 2,6 di-tert-butyl-4-(β-phthalylvinyl)-phenoxyl (III) radicals in different solvents. The type of solvent does not tangibly affect the 2k1 of Radical(I), obviously due to a compensation effect. The log(2k1) versus solvent parameter ET(30) curves for the recombination of radicals (II) and (III) have been found to be V shaped, the minimum corresponding to chloroform. The intensive solvation of Radical (II) by chloroform converts the initially diffusion-controlled recombination of the radical into an activated reaction. The log (2k?1) of the dimer of Radical (I) has been found to be a linear function of the Kirkwood parameter (ε - 1)/(2ε + 1), the dissociation rate increasing with the dielectic constant of the solvent. The investigation revealed an isokinetic relationship for the decay of the dimer of Radical (I), an isokinetic temperature β = 408 K and isoequilibrium relationship for the reversible recombination of Radical (I) with β° = 651 K. For Radical (I) dimer decay In(2k?1) = const + 0.8 In K, where K is the equilibrium constant of this reversible reaction. The transition state of Radical (I) dimer dissociation reaction looks more like a pair of radicals than the initial dimer. The role of specific solvation in radical self-termination reactions is discussed.  相似文献   
469.
The kinetics of the reversible recombination of the 2-phenyl- (I), 2-p-methoxyphenyl-(II), and 2-p-nitrophenyl-3-oxo-2,3-dihydrobenzothiophene-2-yl (III) radicals have been investigated. Recombination rate constants of R(I–III) have been determined in different solvents (2k1 ~ 109 M?1 s?1). The rate of reaction (I) with R(I–III) decreases with increasing solvent viscosity η. In the toluene-vaseline oil mixture (2 ? η ? 120 cP) the recombination of R(I–III) is molecular mobility limited. The thermodynamic parameters of reaction (I) have been determined: ΔH0 = 20–30 kcal/mol. Activation volumes ΔV for recombination of R(II) have been measured. In n-propanol ΔV is equal to the viscous flow activation volume of the solvent ΔV. In toluene and chloroform ΔV < ΔV. For the last two solvents the activation volumes of the cage reaction have been estimated ΔV = ?(2–3) cm3/mol. Visible-range absorption spectra and ESR spectra have been recorded for R(I–III). The role of cage effect in the reactivity anisotropy averaging of R(I–III) is discussed. The potential of the high-pressure tests for deriving information about the elementary act of a fast bimolecular reaction is considered.  相似文献   
470.
The decay kinetics of aryloxy and semiquinone radicals in the presence of copper ions in aqueous solutions has been studied by means of the flash photolysis technique. The radicals are involved in electron transfer reactions and those leading to the formation of intermediate complexes with copper ions. The complexes of p-benzosemiquinone anion radicals and 2-hydroxyphenoxy radicals with cupric ions decay in bimolecular self-reactions at a much slower rate than the original radicals. The increased stability of the complexes compared with the initial radicals is attributed to partial delocalization of the unpaired electron over the electron shell of copper and to steric hindrances in the self-reactions of complexes.  相似文献   
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