Convergence analysis of a coupled method for time‐dependent convection‐diffusion equations

The coupling of two locally mass conservative methods is formulated and analyzed for the time‐dependent convection‐diffusion problem. Finite volume method is used in some subdomains and interior penalty discontinuous Galerkin method is used in other subdomains. Numerical examples show the advantages of the proposed hybrid method, namely an accurate approximation obtained at a reduced computational cost. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 30: 133–157, 2014     

General linear methods for y′′?=?f?(y?(t))

In this paper we consider the family of General Linear Methods (GLMs) for the numerical solution of special second order Ordinary Differential Equations (ODEs) of the type y????=?f(y(t)), with the aim to provide a unifying approach for the analysis of the properties of consistency, zero-stability and convergence. This class of methods properly includes all the classical methods already considered in the literature (e.g. linear multistep methods, Runge?CKutta?CNystr?m methods, two-step hybrid methods and two-step Runge?CKutta?CNystr?m methods) as special cases. We deal with formulation of GLMs and present some general results regarding consistency, zero-stability and convergence. The approach we use is the natural extension of the GLMs theory developed for first order ODEs.     

Factorization of analytic functions by means of Koenig's theorem and Toeplitz computations

Summary. By providing a matrix version of Koenig's theorem we reduce the problem of evaluating the coefficients of a monic factor r(z) of degree h of a power series f(z) to that of approximating the first h entries in the first column of the inverse of an Toeplitz matrix in block Hessenberg form for sufficiently large values of n. This matrix is reduced to a band matrix if f(z) is a polynomial. We prove that the factorization problem can be also reduced to solving a matrix equation for an matrix X, where is a matrix power series whose coefficients are Toeplitz matrices. The function is reduced to a matrix polynomial of degree 2 if f(z) is a polynomial of degreeN and . These reductions allow us to devise a suitable algorithm, based on cyclic reduction and on the concept of displacement rank, for generating a sequence of vectors that quadratically converges to the vector having as components the coefficients of the factor r(z). In the case of a polynomial f(z) of degree N, the cost of computing the entries of given is arithmetic operations, where is the cost of solving an Toeplitz-like system. In the case of analytic functions the cost depends on the numerical degree of the power series involved in the computation. From the numerical experiments performed with several test polynomials and power series, the algorithm has shown good numerical properties and promises to be a good candidate for implementing polynomial root-finders based on recursive splitting strategies. Applications to solving spectral factorization problems and Markov chains are also shown. Received September 9, 1998 / Revised version received November 14, 1999 / Published online February 5, 2001     

Strong convergence of the discontinuous Galerkin scheme for the low regularity miscible displacement equations

Strong convergence of the numerical solution to a weak solution is proved for a nonlinear coupled flow and transport problem arising in porous media. The method combines a mixed finite element method for the pressure and velocity with an interior penalty discontinuous Galerkin method in space for the concentration. Using functional tools specific to broken Sobolev spaces, the convergence of the broken gradient of the numerical concentration to the weak solution is obtained in the L² norm. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 489–513, 2017     

Preparation and Characterization of Activated Carbon – nFe3O4, Activated Carbon – nSiO2 and Activated Carbon – nZnO Hybrid Materials

The preparation and physicochemical characterization of activated carbon, nano metal oxides, and activated carbon – nFe₃O₄, activated carbon – nSiO₂ and activated carbon – nZnO hybrid materials has been undertaken. The materials have been characterized by scanning and transmission electron microscopy, x‐ray diffraction, CNH analysis and Fourier transform infrared spectroscopy. Surface area and porosity, ash content, pH, and point of zero charge were also measured. The results showed that the surfaces of activated carbon, nSiO₂, activated carbon – nFe₃O₄, activated carbon – nSiO₂ and activated carbon – nZnO are suitable for the sorption of cationic complexes while the surfaces of nFe₃O₄ and nZnO are favourable to the sorption of anionic complexes of heavy metals. Results also showed that the composition of the activated carbon and nano metal oxides increased the surface and micropore areas of nano metal oxides due to the large number of micropores and crevices on the surface of the hybrid materials.     

Optical soliton perturbation in non-Kerr law media: Traveling wave solution

This paper analyses the dynamics of soliton propagation through optical fibers with non-Kerr law nonlinearities. The governing nonlinear Schrödinger equation is integrated in the presence of perturbation terms. The traveling wave hypothesis is used to carry out the integration. Domain restrictions on the soliton parameters are identified in the process. The five forms of nonlinearity that are studied are Kerr-law, power-law, parabolic-law, dual-power law and the log-law nonlinearity. Numerical simulations are presented for each of these nonlinear media.     

Monitoring the Evolution of Asynchrony between Mean Arterial Pressure and Mean Cerebral Blood Flow via Cross-Entropy Methods

Cerebrovascular control is carried out by multiple nonlinear mechanisms imposing a certain degree of coupling between mean arterial pressure (MAP) and mean cerebral blood flow (MCBF). We explored the ability of two nonlinear tools in the information domain, namely cross-approximate entropy (CApEn) and cross-sample entropy (CSampEn), to assess the degree of asynchrony between the spontaneous fluctuations of MAP and MCBF. CApEn and CSampEn were computed as a function of the translation time. The analysis was carried out in 23 subjects undergoing recordings at rest in supine position (REST) and during active standing (STAND), before and after surgical aortic valve replacement (SAVR). We found that at REST the degree of asynchrony raised, and the rate of increase in asynchrony with the translation time decreased after SAVR. These results are likely the consequence of the limited variability of MAP observed after surgery at REST, more than the consequence of a modified cerebrovascular control, given that the observed differences disappeared during STAND. CApEn and CSampEn can be utilized fruitfully in the context of the evaluation of cerebrovascular control via the noninvasive acquisition of the spontaneous MAP and MCBF variability.     

Efficient microwave combinatorial parallel and nonparallel synthesis of N-alkylated glycine methyl esters as peptide building blocks

An easy and convenient microwave-assisted synthesis of N-alkylated glycine methyl esters is described. Parallel and nonparallel combinatorial methods are described and compared. The described reactions are reductive alkylations of several aldehydes and glycine methyl ester in the presence of NaBH3CN. Good yields and short reaction times are the main aspects of these procedures.     

Hierarchical self-assembly in molecularly ordered phenylene-bridged mesoporous organosilica nanofilaments.

Herein we report on the mechanism of formation of a hybrid phenylene-bridged hexagonally ordered mesoporous organosilica with crystal-like walls (CW-Ph-HMM). Electron microscopy and X-Ray diffraction studies indicate that the formation of CW-Ph-HMM involves the surfactant-mediated hydrothermal transformation of an amorphous organosilica precursor and that the final product is hierarchically ordered. Significantly, the material is in the form of submicrometre-thick sheets that consist of co-aligned aggregates of needle-like particles (up to 500 nm in length and 50 nm in width). The results suggest that preferential growth along the channel direction of the hexagonally ordered mesostructure is coupled with the propagation of molecular periodicity in the pore walls. Together, these factors give rise to the growth of highly anisotropic primary nanofilaments that become co-aligned to produce micrometer-thick sheets consisting of a periodic array of mesoscopic channels oriented perpendicular to the surface of the flake-like particles.     

Synthesis of Dendritic Metalloporphyrins with Distal H‐Bond Donors as Model Systems for Hemoglobin

We report the synthesis of the first‐ (G1) and second‐generation (G2) dendritic Fe^II porphyrins 1?Fe – 4?Fe (G1) and 6?Fe (G2) bearing distal H‐bond donors ideally positioned for stabilization of Fe^II? O₂ adducts by H‐bonding (Fig. 1). A first approach towards the construction of these novel biomimetic systems failed unexpectedly: the Suzuki cross‐coupling between appropriately functionalized Zn^II porphyrins and ortho‐ethynylated aryl derivatives, serving as anchors for the distal H‐bond donor moieties, was unsuccessful (Schemes 1, 3, and 5), presumably due to steric hindrance resulting from unfavorable coordination of the ethynyl residue to the Pd species in the catalytic cycle (Scheme 6). The target molecules were finally prepared by a route in which the ortho‐ethynylated meso‐aryl ring is introduced during porphyrin construction in a mixed condensation involving the two dipyrrylmethanes 33 and 34 , and aldehyde 36 (Schemes 7 and 8). Following attachment of the dendrons (Scheme 11), the distal H‐bond donors were introduced by Sonogashira cross‐coupling (Scheme 12), and subsequent metallation afforded the dendritic Fe^II porphyrins 1?Fe – 6?Fe . ¹H‐NMR Spectroscopy proved the location of the H‐bond donor moiety atop the porphyrin surface, and X‐ray crystal‐structure analysis of model system 45 (Fig. 2) revealed that this moiety would not sterically interfere with gas binding. With 1,2‐dimethyl‐1H‐imidazole (DiMeIm) as ligand, the dendritic Fe^II porphyrins formed five‐coordinate high‐spin complexes (Figs. 3 and 4) and addition of CO led reversibly to the corresponding stable six‐coordinate gas complexes (Fig. 6). Oxygenation, however, did not result in defined Fe^II? O₂ complexes as rapid decomposition to Fe^III species took place immediately, even in the case of the G2 dendrimer 6?Fe (DiMeIm) (Fig. 7). In contrast, stable gas adducts are formed between dendritic Co^II porphyrins and O₂ in the presence of DiMeIm as axial ligand, as revealed by electron paramagnetic resonance (EPR). The possible stabilization of these complexes through H‐bonding involving the distal ligand is currently under investigation in multidimensional and multifrequency pulse EPR experiments.