Superconvergence error estimates of discontinuous Galerkin time stepping for singularly perturbed parabolic problems

Numerical Algorithms - A parabolic convection-diffusion-reaction problem is discretized by the non-symmetric interior penalty Galerkin (NIPG) method in space and discontinuous Galerkin (DG) method...     

Phase-Transfer Catalysis: Free-Radical Polymerization of Methyl Methacrylate using K2S2O8-Quaternary Ammonium Salt Catalyst System. A Kinetic Study

Abstract

The kinetics of phase-transfer-agent-assisted free-radical polymerization of methyl methacrylate using K₂S₂O₈ as the water-soluble initiator and triethylbenzylammonium chloride (TEBA) as the phase-transfer catalyst (PTC) was investigated in toluene-water biphase media at 60°C. The effect of varying [MMA], [K₂S₂O₈], [TEBA], [H⁺], the ionic strength of the medium, and the temperature on the rate of polymerization (R _p) was studied. R _p was found to be proportional to [MMA]², [K₂S₂O₈]¹, and [TEBA]^0.5. Based on the kinetic results, a mechanism involving initiation of polymerization by phase-transferred S₂O₈ ^2- and termination by Q⁺ (quaternary ammonium ion) is proposed.     

Preparation,spectral characterization,and single crystal X-ray structures of cis and trans isomers of 2,4,6-trifluoroethoxy-1,3,5-triethyl-1,3,5,2λ5, 4λ5, 6λ5-triazatriphosphorinane-2,4,6-trioxide, [ETNP(O)(OCH2CF3)]3

Oxidation of the cis isomer of the λ³-cyclotriphosphazane [EtNP(OCH₂CF₃)]₃ with trimethylamine-N-oxide (TMNO) gives the cis isomer of trioxo-λ⁵-cyclotriphosphazane [EtNP(O)(OCH₂CF₃)]₃; the trans isomer of [EtNP(O)(OCH₂CF₃)]₃ is obtained by the treatment of a cis and trans mixture of [EtNP(OCH₂CF₃)]₃ with aqueous H₂O₂. The two trioxocyclotriphosphazanes have been characterized by elemental analysis, IR, and NMR (¹H, ¹³C, ¹⁹F, and ³¹P) spectroscopy. The solid state structures of both the isomers have been determined by single crystal X-ray diffraction. The six-membered P₃N₃ ring in both the isomers exhibits a twist-boat conformation; in the cis isomer, the trifluoroethoxy substituents lie on the same side of the ring, whereas, in the trans isomer, two trifluoroethoxy groups are on one side of the ring and the third on the other side of the ring. Crystal data for cis-[EtNP(O)(OCH₂CF₃)]₃: monoclinic, P 2₁/ n , a = 13.593(3), b = 9.721(2), c = 17.539(3) Å, β = 99.49(2)°, V = 2286(1) ų, Z = 4, and Final R = 0.047. Crystal data for trans-[EtNP(O)(OCH₂CF₃)]₃: monoclinic, P 2₁/ n , a = 11.685(4), b = 15.115(5), c = 13.233(5) Å, - = 102.21(3)°, V = 2284(1) ų, Z = 4, and Final R = 0.078.     

The parameter uniform numerical method for singularly perturbed parabolic reaction–diffusion problems on equidistributed grids

This article presents the study of singularly perturbed parabolic reaction–diffusion problems with boundary layers. To solve these problems, we use a modified backward Euler finite difference scheme on layer adapted nonuniform meshes at each time level. The nonuniform meshes are obtained by equidistribution of a positive monitor function, which involves the second-order spatial derivative of the singular component of the solution. The equidistributing monitor function at each time level allows us to use this technique to non-linear parabolic problems. The truncation error and the stability analysis are obtained. Parameter–uniform error estimates are derived for the numerical solution. To support the theoretical results, numerical experiments are carried out.     

An investigation of Staudinger reactions involving cis-1,3,5-triazidocyclohexane and tri(alkylamino)phosphines

The reaction of 1,3,5-cis-triazidocyclohexane with the electron-rich tris(dialkylamino)phosphines P(NMe(2))(3) (1) and N(CH(2)CH(2)NMe)(3)P (2b) in acetonitrile for 3 h furnished the corresponding tris-phosphazides 1,3,5-cis-(R(3)PN(3))(3)C(6)H(9), 3a (R(3)P = 1) and 3b (R(3)P = 2b), in 90% and 92% yields, respectively. The same reaction with the relatively electron-poor tris(dialkylamino)phosphine MeC(CH(2)NMe)(3)P (4) for 2 days gave the tris-iminophosphorane, 1,3,5-cis-(R(3)PN)(3)C(6)H(9), 5a (R(3)P = 4), in 60% yield. Compound 3b is a thermally stable solid that did not lose dinitrogen when refluxed in toluene for 24 h or when heated as a neat sample at 100 degrees C /0.5 Torr for 10 h. By contrast, tris-phosphazide 3a decomposed to the tris-iminophosphorane 1,3,5-cis-(R(3)PN)(3)C(6)H(9), 5b (R(3)P = 1), in 3 h in quantitative yield upon heating to 100 degrees C in toluene. Factors influencing the formation of the phosphazides or the iminophosphoranes in these reactions are discussed. The reaction of 3b with 4 equiv of benzoic acid gave [N(CH(2)CH(2)NMe)(3)P=NH(2)]PhCO(2) ([6bH]PhCO(2)) in quantitative yield along with benzene (56% yield) and dinitrogen. The same reaction with 3a gave [(Me(2)N)(3)P=NH(2)]PhCO(2) ([7aH]PhCO(2)) (quantitative yield), benzene (15% yield), and dinitrogen(.) Treatment of [6bH]PhCO(2) with KO(t)Bu afforded N(CH(2)CH(2)NMe)(3)P=NH (6b) in 40% overall yield. Compound 6b upon treatment with PhCH(2)CH(2)Br produced [6bH]Br in 90% yield along with styrene. The new compounds were characterized by analytical and spectroscopic methods, and selected compounds (3b, 5a, and [6bH]Br) were structured by X-ray crystallography. A special feature of 3b is its capability to function as a starting material for 6b, which was not accessible by other synthetic routes.     

Radiation processing of natural polymers: The IAEA contribution

Radiation processing offers a clean and additive-free method for preparation of value-added novel materials based on renewable, non-toxic, and biodegradable natural polymers. Crosslinked natural polymers can be used as hydrogel wound dressings, face cleaning cosmetic masks, adsorbents of toxins, and non-bedsore mats; while low molecular weight products show antibiotic, antioxidant, and plant-growth promoting properties. Recognizing the potential benefits that radiation technology can offer for processing of natural polymers into useful products, the IAEA implemented a coordinated research project (CRP) on “Development of Radiation-processed products of Natural Polymers for application in Agriculture, Healthcare, Industry and Environment”. This CRP was launched at the end of 2007 with participation of 16 MS to help connecting radiation technology and end-users to derive enhanced benefits from these new value-added products of radiation-processed natural materials. In this paper the results of activities in participating MS related to this work will be presented.     

Uniform convergence analysis of hybrid numerical scheme for singularly perturbed problems of mixed type

In this article, we consider a class of singularly perturbed mixed parabolic‐elliptic problems whose solutions possess both boundary and interior layers. To solve these problems, a hybrid numerical scheme is proposed and it is constituted on a special rectangular mesh which consists of a layer resolving piecewise‐uniform Shishkin mesh in the spatial direction and a uniform mesh in the temporal direction. The domain under consideration is partitioned into two subdomains. For the spatial discretization, the proposed scheme is comprised of the classical central difference scheme in the first subdomain and a hybrid finite difference scheme in the second subdomain, whereas the time derivative in the given problem is discretized by the backward‐Euler method. We prove that the method converges uniformly with respect to the perturbation parameter with almost second‐order spatial accuracy in the discrete supremum norm. Numerical results are finally presented to validate the theoretical results.© 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 1931–1960, 2014     

Physicochemical studies of green phosphorescent light-emitting materials from cyclometalated heteroleptic iridium(III) complexes

A series of novel imidazole ligands were synthesized and characterized. Phosphorescence studies of series of heteroleptic cyclometalated iridium(III) complexes reveal that these complexes possess dominantly (3)MLCT and (3)π-π* excited states and the solvent shifts of these complexes are interpreted by Richardt-Dimroth and Marcus solvent functions. The results consistent with prior assignments on the absorption band to a metal-to-ligand charge transfer excited state associated with chelating ligand. Emission kinetic studies exploited that the radiative transition (k(r)), increases with increasing λ(em) and linear correlation exists between ln(k(nr)) and energy gap. Electronic transition theory is applied to study the effect of E(g) and ΔQ(e) on non-radiative transition (k(nr)). With a larger ΔQ(e), favouring vibrational overlap and leading to a larger value for k(nr).     

Physicochemical studies of molecular hyperpolarizability of imidazole derivatives

A series of substituted imidazoles have been synthesized in very good yield under solvent free condition by grinding 1,2-diketone, arylaldehyde, arylamine and ammonium acetate in the presence of molecular iodine as the catalyst. The short reaction time, good yield and easy workup make this protocol practically and economically attractive and the imidazoles are characterized by NMR spectra, X-ray, mass and CHN analysis. The push-pull character of series of imidazoles have been analyzed by the quotient of the occupations of the bonding (π) and anti-bonding (π*) orbitals of the central linking -N=C-C=C- unit. Excellent correlation of the push-pull parameter with the corresponding bond lengths d(CN) and d(CC) strongly recommend both the occupation quotients (π*/π) and the corresponding bond lengths are reasonable sensors for quantifying the push-pull character and for the molecular hyperpolarizability ?(0) of these compounds. To support the experimental results, theoretical calculations (heat of formation, NLO, NBO and vibrational analysis) were also made. Within this context, reasonable conclusions concerning the steric hindrance in the chromospheres, push-pull character, hyperpolarizability of the imidazoles and their application as NLO materials will be drawn.     

Revised structures for fumaritridine and fumaritrine: Two indenobenzazepine type alkaloids

Fumaritridine and fumaritrine are not spirobenzylisoquinolines. Rather, they are indenobenzazepines so that fumaritridine is represented by expression $\text{10}$ and fumaritrine by $\text{11}$. Treatment of dihydroparfumine ($\text{6}$) and dihydroparfumidine ($\text{7}$) uith trifluoroacetic anhydride folloued by quenching with methanol gives $\text{10}$ and $\text{11}$, respectively.