Structural and dynamical studies of poly(vinyl alcohol) gels by high-resolution solid-state C NMR spectroscopy

The ¹³C CP/MAS NMR spectra of isotactic, syndiotactic and atactic poly(vinyl alcohol) (PVA) gels were measured in order to clarify the structure of the immobile component of PVA gel. In the ¹³C CP/MAS NMR spectra, the three CH carbon peaks I, II and III (at about 77, 71 and 65 ppm) were clearly observed, which originate from the formation of strong intermolecular or intramolecular hydrogen bonds between hydroxyl groups like solid PVA. It has been assigned that these peaks originate from the crosslinked region in the gel state. On the basis of the experimental results, intermolecular hydrogen bonds play an important role in the formation of the crosslinked-region in the gel state. Further, the effect of PVA's tacticity on the amount of the crosslinked regions by intermolecular interactions was discussed. In addition, molecular motion in the immobile and mobile region of PVA gel was discussed through the observation of ¹³C spin-lattice relaxation time T₁.     

Chemistry of 5(2H)-isoxazolones: Novel conversion of positional isomers

Reactions of 4-arylidene-3-methyl-5(4H)-isoxazolones with nucleophiles lead to 4-substituted-benzyl-3-methyl-5(2H)-isoxazolones. Formation of 5(4H)- and 5(2H)-isoxazolone derivatives have been observed when 4-substituted-arylidene-3-rriethyl-5(4H)-isoxazolones are reacted with methyl magnesium iodide. Oxidation of 4-substituted-benzyl-3-methyl-5(2H)-isoxazolones with manganic acetate and pyridinium chlorochromate, gives 4,4′-bis[4-substituted-benzyl-3-methyl-5(4H)-isoxazolone]. Oxidation of 4-substituted-benzyl-3-methyl-5(2H)-isoxazolones with metachloroperbenzoic acid gives 4-hydroxy-4-substituted-benzyl-3-methyl-5(4H)-isoxazolones and reactions of the same substrates with N-bromosuccinimide furnish 4-bromo-4-substitutedbenzyl-3-methyl-5(4H)isoxazolones.     

Interfacial organizations of gel phospholipid and cholesterol in bovine lung surfactant films

Pulmonary surfactants stabilize the lung by way of reducing surface tension at the air-lung interface of the alveolus. 31P NMR, thin-layer chromatography, and electrospray ionization mass spectroscopy of bovine lipid extract surfactant (BLES) confirmed dipalmitoylphosphatidylcholine (DPPC) to be the major phospholipid species, with significant amounts of palmitoyl-oleoylphosphatidylcholine, palmitoyl-myristoylphosphatidylcholine, and palmitoyl-oleoylphosphatidylglycerol. BLES and DPPC spread at the air-water interface were studied through surface pressure area, fluorescence, and Brewster angle microscopy measurements. Langmuir-Blodgett films of monomolecular films, deposited on mica, were characterized by atomic force microscopy. BLES films displayed shape, size, and vertical height profiles distinct from those of DPPC alone. Calcium ions in the subphase altered BLES film domain structure. The addition of cholesterol (4 mol %) resulted in the destabilization of compressed BLES films at higher surface pressures (>40 mN m-1) and the formation of multilayered structures, apparently consisting of stacked monolayers. The studies suggested potential roles for individual surfactant lipid components in supramolecular arrangements, which could be the contributing factors in pulmonary surfactant to attain low surface tension at the air-water interface.     

On approximation theorems for controllability of non-linear parabolic problems

^** Email: anil{at}math.iitb.ac.in^*** Email: mcj{at}math.iitb.ac.in^**** Email: akp{at}math.iitb.ac.in In this paper, we consider the following control system governedby the non-linear parabolic differential equation of the form: [graphic: see PDF] where A is a linear operator with dense domain and f(t, y)is a non-linear function. We have proved that under Lipschitzcontinuity assumption on the non-linear function f(t, y), theset of admissible controls is non-empty. The optimal pair (u^*,y^*) is then obtained as the limit of the optimal pair sequence{(u_n^*, y_n^*)}, where u_n^* is a minimizer of the unconstrainedproblem involving a penalty function arising from the controllabilityconstraint and y_n^* is the solution of the parabolic non-linearsystem defined above. Subsequently, we give approximation theoremswhich guarantee the convergence of the numerical schemes tooptimal pair sequence. We also present numerical experimentwhich shows the applicability of our result.     

Physicochemical studies of octadecyl-trimethyl-ammonium bromide: a critical assessment of its solution behavior with reference to formation of micelle, and microemulsion with n-butanol and n-heptane

Octadecyl-trimethyl-ammonium bromide (C18TAB) is a much less studied representative in the alkyltrimethylammonium halide surfactant series. A comprehensive study of its normal and reverse micelle (microemulsion) formation has been herein conducted by the methods of conductometry, tensiometry, fluorimetry, and microcalorimetry. The energetics of its air/liquid interfacial adsorption and self-association in aqueous solution have been examined. The phase behavior of its combinations with water, n-butanol, and n-heptane in the formation of microemulsions have been investigated with identification of a variety of phases. The energetics of formation of water dispersion in oil (w/o) has been evaluated from dilution experiments conducted at different temperatures. From the results, structural parameters of the droplets have been determined at different [water]/[surfactant] mole ratios (omega) and temperatures. The w/o dispersions have evidenced both volume- and temperature-induced conductance percolation. The results have been treated in light of the Scaling equations, and the associated parameters for the process have been determined. The activation energies for the temperature-induced percolation process of the w/o dispersion have been evaluated and assessed.     

A priori error estimates of expanded mixed FEM for Kirchhoff type parabolic equation

Numerical Algorithms - For a nonlinear nonlocal parabolic problem containing the elastic energy coefficients, an expanded mixed finite element method using lowest order RT spaces is discussed in...     

Mixed finite element method for a strongly damped wave equation

A mixed finite element Galerkin method is analyzed for a strongly damped wave equation. Optimal error estimates in L²‐norm for the velocity and stress are derived using usual energy argument, while those for displacement are based on the nonstandard energy formulation of Baker. Both a semi‐discrete scheme and a second‐order implicit‐time discretization method are discussed, and it is shown that the results are valid for all t > 0. © 2001 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 17: 105–119, 2001     

Expanded mixed FEM with lowest order RT elements for nonlinear and nonlocal parabolic problems

In this paper, an expanded mixed finite element method with lowest order Raviart Thomas elements is developed and analyzed for a class of nonlinear and nonlocal parabolic problems. After obtaining some regularity results for the exact solution, a priori error estimates for the semidiscrete problem are established. Based on a linearized backward Euler method, a complete discrete scheme is proposed and a variant of Brouwer’s fixed point theorem is used to derive an existence of a fully discrete solution. Further, a priori error estimates for the fully discrete scheme are established. Finally, numerical experiments are conducted to confirm our theoretical findings.     

<Emphasis Type="Italic">hp</Emphasis>-Discontinuous Galerkin methods for strongly nonlinear elliptic boundary value problems

In this paper, we have analyzed a one parameter family of hp-discontinuous Galerkin methods for strongly nonlinear elliptic boundary value problems with Dirichlet boundary conditions. These methods depend on the values of the parameter , where θ = + 1 corresponds to the nonsymmetric and θ = −1 corresponds to the symmetric interior penalty methods when and f(u,∇u) = −f, that is, for the Poisson problem. The error estimate in the broken H ¹ norm, which is optimal in h (mesh size) and suboptimal in p (degree of approximation) is derived using piecewise polynomials of degree p ≥ 2, when the solution . In the case of linear elliptic problems also, this estimate is optimal in h and suboptimal in p. Further, optimal error estimate in the L ² norm when θ = −1 is derived. Numerical experiments are presented to illustrate the theoretical results. Supported by DST-DAAD (PPP-05) project.     

An -local discontinuous Galerkin method for some quasilinear elliptic boundary value problems of nonmonotone type

In this paper, an -local discontinuous Galerkin method is applied to a class of quasilinear elliptic boundary value problems which are of nonmonotone type. On -quasiuniform meshes, using the Brouwer fixed point theorem, it is shown that the discrete problem has a solution, and then using Lipschitz continuity of the discrete solution map, uniqueness is also proved. A priori error estimates in broken norm and norm which are optimal in , suboptimal in are derived. These results are exactly the same as in the case of linear elliptic boundary value problems. Numerical experiments are provided to illustrate the theoretical results.