Generalized alternating-direction collocation methods for parabolic equations. II. Transport equations with application to seawater intrusion problems

The alternating-direction collocation (ADC) method combines the attractive computational features of a collocation spatial approximation and an alternating-direction time marching algorithm. The result is a very efficient solution procedure for parabolic partial differential equations. To date, the methodology has been formulated and demonstrated for second-order parabolic equations with insignificant first-order derivatives. However, when solving transport equations, significant first-order advection components are likely to be present. Therefore, in this paper, the ADC method is formulated and analyzed for the transport equation. The presence of first-order spatial derivatives leads to restrictions that are not present when only second-order derivatives appear in the governing equation. However, the method still appears to be applicable to a wide variety of transport systems. A formulation of the ADC algorithm for the nonlinear system of equations that describes density-dependent fluid flow and solute transport in porous media demonstrates this point. An example of seawater intrusion into coastal aquifers is solved to illustrate the applicability of the method. An alternating-direction collocation solution algorithm has been developed for the general transport equation. The procedure is analogous to that for the model parabolic equations considered by Celia and Pinder [2]. However, the presence of first-order spatial derivatives requires special attention in the ADC formulation and application. With proper implementation, the ADC procedure effectively combines the efficient equation formulation inherent in the collocation method with the efficient equation solving characteristics of alternating-direction time marching algorithms. To demonstrate the viability of the method for problems with complex velocity fields, the procedure was applied to the problem of density-dependent flow and contaminant transport in groundwaters. A standard example of seawater intrusion into coastal aquifers was solved to illustrate the applicability of the method and to demonstrate its potential use in practical problems.     

13C NMR Analysis of some 4-hydroxy-2H-1,2-benzothiazine 1,1-dioxides

The ¹³C nmr spectra of some 4-hydroxy-2H-1,2-benzothiazine 1,1-dioxides I have been recorded and analyzed. Spectroscopic assignments were made on the basis of chemical shift theory, APT and fully coupled ¹³C nmr spectra. Spectral data support the enolic structure of these compounds.     

Synthesis of enantiopure 3-azabicyclo[3.2.0]heptanes by diastereoselective intramolecular [2+2] photocycloaddition reactions on chiral perhydro-1,3-benzoxazines

[2+2] photocycloadditions involving chiral 3-acryloyl-2-vinylperhydro-1,3-benzoxazines derived from (-)-8-aminomenthol are highly diastereoselective reactions. The facial selectivity depends on the type of substitution at the vinyl double bond, and always leads to cis-fused bicyclic derivatives. The de is good for compounds with one substituent at the outer carbon of the double bond at C-2, but only one diastereomer is formed in cyclizations of compounds with two substituents at that position. The elimination of the menthol appendage gives enantiopure 3-azabicyclo[3.2.0]heptanes.     

Stereoselective synthesis of pachastrissamine (jaspine B)

A stereoselective synthesis in enantiopure form of the natural anhydrophytosphingosine pachastrissamine (jaspine B), a metabolite isolated from sponges, is described. The chiral epoxide (R)-glycidol was the starting material. Key steps of this synthesis are a Sharpless asymmetric epoxidation, an intramolecular stereospecific epoxide opening mediated by a trichloroacetimidate group, and the formation of a tetrahydrofuran ring via intramolecular nucleophilic displacement.     

The dominant role of solvent in the sequestering of bile salts by hydrophobic cationic polymeric resins

The binding behavior of sodium cholate, a trihydroxy hydrophobic bile salt, by a polyacrylamide resin with N,N,N-trimethylammonium dodecyl chloride (QPDA12) pendant group was determined with varying buffer conditions and in the presence of 1,2-propanediol as a solvent perturbant. Binding constants extracted from the fit of the binding isotherms to the Langmuir equation were obtained at several temperatures. The temperature dependence of the binding behavior indicated that binding, in comparison with that of the dihydroxy chenodeoxycholate, was weaker due to a smaller positive entropic change, despite a lowered enthalpic barrier. Enthalpy-entropy compensation with a compensation temperature of 285-290 K, characteristic of processes involving water, was found to encompass both the cholate and chenodeoxycholate data under a wide variety of conditions. Previous studies with sodium chenodeoxycholate determined that loss of hydrophobic hydration within the resin dominated the thermodynamics of the binding process, but the observations with sodium cholate revealed that solvent liberation about the bile salt is also a contributor.     

Characterization of Alkane Diol-CD Complexes. Acid Denitrosation of N-Methyl-N-Nitroso-p-Toluenesulphonamide as a Chemical Probe

A study was carried out on the acid denitrosation of N-methyl-N-nitroso-p-toluenesulfonamide (MNTS) in mixed systems made up of linear (geminal and terminal) alkyl diols and β-cyclodextrin (CD). The alkyl diols used allowed us to vary the length of the hydrocarbon chain from 2 to 6 carbon atoms. The observed rate constant, k _obs, decreases in the presence of CD. The inhibition profile decreases as the as the number of carbons in the chain is increased. This behaviour can be interpreted as a consequence of a balance between the complexation processes of MNTS and the alkyl diols by the CD. At a constant CD concentration and increase in the diols concentration decreases the concentration of free cyclodextrin available to complex with MNTS molecules and therefore produces an increases in the observed rate constant. The results were interpreted in terms of two different models; trough the presupposition and non-presupposition of a stoichiometry for the CD-diols complex. Both models agreed quite well and allow us to determine the uncomplexed cyclodextrin concentration in each case as well as the stoichiometry of the complexes. The binding constant for both types of alkane diols increase with increasing the number of carbon in the chain. Besides, the binding constant of the α,ω-alkane diols is higher than for the analog α,β-alkane diols. One of the main consequences of this study is that the acid denitrosation of MNTS can be use to obtain the stochiometry of the CD-diol complexes and to monitor the free cyclodextrin concentration.Electronic Supplementary Material Supplementary material is available for this article at     

Quinazolinone derivatives. Kinetics of the reaction of 2-chloromethyl-3-hydroxy-4-(3H)quinazolinone with nucleophiles

Reaction of 2-Chloromethyl-3-hydroxy-4(3H)quinazolinone ( 1 ) with aliphatic amines and hydroxide follows two different routes affording substituted methyl quinazolinones and a dimer 2 derived from 1 . The former were formed by S_N² reactions while the latter was formed by an inter-molecular nucleophilic displacement. Second-order and third-order rate constants, respectively, were determined, and the kinetic factors influencing both parallel reactions were analysed.     

Monotonicity of ionization energies for three electron lithium-type systems

Although it is quite obvious that an increasing amount of energy is required to remove more and more electrons from an atom, the proof of this observation seems to be a remarkably difficult problem in mathematical physics. Here, by using well-known energy bounds, we show the monotonicity of ionization energies for the simplest nontrivial system, i.e., a nucleus (with infinite mass) and three electrons, which physically corresponds to ionization in the lithium isoelectronic series via the para-channel.PHYMAT, Dept. de math. Univ. de Toulon et du Var F-83130 La Garde, France.On leave from Stranski Institut, TEL 33 Tech. Univ. Berlin D-1000 Berlin 10, F.R.G.Laboratoire propre du Centre Nationale de la Recherche Scientifique.     

Thermodynamic study of perfluorohexane + ether mixtures: VLE, LLE, and H

Vapour–liquid equilibria (VLE), liquid–liquid equilibria (LLE), and excess enthalpies (H^E) of binary mixtures of perfluoro-n-hexane plus an ether (diethyl, dipropyl, dibutyl, butyl methyl, and butyl ethyl ether), have been determined using a head-space gas-chromatographic technique, a turbidimetric apparatus, and a heat-flow calorimeter, respectively. A recently designed titration technique and calculation procedure have been used to obtain H^E from heats of solution. The observed liquid–liquid coexistence curves have been compared with those predicted by the activity coefficients γ_i and their temperature dependence. All mixtures are strongly endothermic (H^E > 0) and show large positive deviations from ideality (G^E > 0), which increase with the size of the ether. Molecular interactions have been examined by calculating and discussing solvation functions and Kirkwood–Buff (KB) integrals. Perfluorohexane proved to be an inert molecule that interacts with ethers more weakly than hexane.     

Bun splitting: a practical cutting stock problem

We describe a new hierarchical 2D-guillotine Cutting Stock Problem. In contrast to the classic cutting stock problem, waste is not an issue. The problem relates to the removal of a defective part and assembly of the remaining parts into homogeneous size blocks. The context is the packing stages of cake manufacturing. The company’s primary objective is to minimise total processing time at the subsequent, packing stage. This objective reduces to one of minimising the number of parts produced when cutting the tray load of buns. We offer a closed form optimization approach to this class of problems for certain cases, without recourse to mathematical programming or heuristics. The methodology is demonstrated through a case study in which the number of parts is reduced by almost a fifth, and the manufacturer’s subsidiary requirement to reduce isolated single bun parts and hence customer complaints is also satisfied.