High‐order finite difference schemes for numerical solutions of the generalized Burgers–Huxley equation

In this article, up to tenth‐order finite difference schemes are proposed to solve the generalized Burgers–Huxley equation. The schemes based on high‐order differences are presented using Taylor series expansion. To establish the numerical solutions of the corresponding equation, the high‐order schemes in space and a fourth‐order Runge‐Kutta scheme in time have been combined. Numerical experiments have been conducted to demonstrate the high‐order accuracy of the current algorithms with relatively minimal computational effort. The results showed that use of the present approaches in the simulation is very applicable for the solution of the generalized Burgers–Huxley equation. The current results are also seen to be more accurate than some results given in the literature. The proposed algorithms are seen to be very good alternatives to existing approaches for such physical applications. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1313‐1326, 2011     

Guided ion beam and theoretical study of the reactions of Os+ with H2, D2, and HD

Reactions of the third-row transition metal cation Os(+) with H(2), D(2), and HD to form OsH(+) (OsD(+)) were studied using a guided ion beam tandem mass spectrometer. A flow tube ion source produces Os(+) in its (6)D (6s(1)5d(6)) electronic ground state level. Corresponding state-specific reaction cross sections are obtained. The kinetic energy dependences of the cross sections for the endothermic formation of OsH(+) and OsD(+) are analyzed to give a 0 K bond dissociation energy of D(0)(Os(+)-H) = 2.45 ± 0.10 eV. Quantum chemical calculations are performed here at several levels of theory, with B3LYP approaches generally overestimating the experimental bond energy whereas results obtained using BHLYP and CCSD(T), coupled-cluster with single, double, and perturbative triple excitations, levels show good agreement. Theory also provides the electronic structures of these species and the potential energy surfaces for reaction. Results from the reactions with HD provide insight into the reaction mechanism and indicate that Os(+) reacts via a direct reaction. We also compare this third-row transition metal system with the first-row and second-row congeners, Fe(+) and Ru(+), and find that Os(+) reacts more efficiently with dihydrogen, forming a stronger M(+)-H bond. These differences can be attributed to the lanthanide contraction and relativistic effects.     

Guided ion beam and theoretical study of the reactions of Au+ with H2, D2, and HD

Reactions of the late third-row transition metal cation Au(+) with H(2), D(2), and HD are examined using guided ion beam tandem mass spectrometry. A flow tube ion source produces Au(+) in its (1)S (5d(10)) electronic ground state level. Corresponding state-specific reaction cross sections for forming AuH(+) and AuD(+) as a function of kinetic energy are obtained and analyzed to give a 0 K bond dissociation energy of D(0)(Au(+)-H) = 2.13 ± 0.11 eV. Quantum chemical calculations at the B3LYP∕HW+∕6-311+G(3p) and B3LYP∕Def2TZVPP levels performed here show good agreement with the experimental bond energy. Theory also provides the electronic structures of these species and the reactive potential energy surfaces. We also compare this third-row transition metal system with previous results for analogous reactions of the first-row and second-row congeners, Cu(+) and Ag(+). We find that Au(+) has a stronger M(+)-H bond, which can be explained by the lanthanide contraction and relativistic effects that alter the relative size of the valence s and d orbitals. Results from reactions with HD provide insight into the reaction mechanism and indicate that ground state Au(+) reacts largely via a direct mechanism, in concordance with the behavior of the lighter group 11 metal ions, but includes more statistical behavior than these metals as well.     

The synthesis and characterization of copper(II)–<Emphasis Type="Italic">p</Emphasis>-aminosalicylate complexes with diamine ligands

The complexes were synthesized by the reaction between sodium salt of p-aminosalicylic acid (PAS) and Cu(II) for 1 and corresponding ethylenediamine (en) or its derivatives for 2–6. The complexes were characterized by using elemental analyses, FT-IR, UV–Vis, magnetic moment measurements, and thermal analyses techniques. In complex 1[Cu₂(PA)₄(H₂O)₂], two Cu(II) ions were found as bridged by four μ-O:O′ p-aminosalicylato (PA) ligands, forming a cage structure, and two aqua ligands to form dinuclear square-pyramidal geometry around Cu(II) ions. In the complexes 2–6, the PA (anionic form of p-aminosalicylic acid) coordinated to Cu(II) ions as monodentate manner by using its oxygen atom of deprotonated carboxylic acid and ethylenediamine derivatives coordinated to the Cu(II) ions in bidentate manner to form mononuclear octahedral complexes [Cu(PA)₂(L)₂] (L = ethylendiamine, N,N-dimethylethylendiamine, N,N′-dimethylethylendiamine, N,N,N′,N′-tetramethylethylendiamine, and 1,3-propanediamine, for complexes 2, 3, 4, 5, and 6, respectively). In all the complexes OH and NH₂ groups of PA ligands were not coordinated to metals.     

Use of graphite oxide and graphene oxide as catalysts in the synthesis of dipyrromethane and calix[4]pyrrole

Graphite oxide and graphene oxides have been used as solid catalysts for the synthesis of 5,5-dialkyldipyrromethanes and calix[4]pyrroles in organic and aqueous solutions at room temperature.     

Finding a representative nondominated set for multi-objective mixed integer programs

In this paper, we develop algorithms to find small representative sets of nondominated points that are well spread over the nondominated frontiers for multi-objective mixed integer programs. We evaluate the quality of representations of the sets by a Tchebycheff distance-based coverage gap measure. The first algorithm aims to substantially improve the computational efficiency of an existing algorithm that is designed to continue generating new points until the decision maker (DM) finds the generated set satisfactory. The algorithm improves the coverage gap value in each iteration by including the worst represented point into the set. The second algorithm, on the other hand, guarantees to achieve a desired coverage gap value imposed by the DM at the outset. In generating a new point, the algorithm constructs territories around the previously generated points that are inadmissible for the new point based on the desired coverage gap value. The third algorithm brings a holistic approach considering the solution space and the number of representative points that will be generated together. The algorithm first approximates the nondominated set by a hypersurface and uses it to plan the locations of the representative points. We conduct computational experiments on randomly generated instances of multi-objective knapsack, assignment, and mixed integer knapsack problems and show that the algorithms work well.     

Structure preserving model order reduction of shallow water equations

In this paper, we present two different approaches for constructing reduced‐order models (ROMs) for the two‐dimensional shallow water equation (SWE). The first one is based on the noncanonical Hamiltonian/Poisson form of the SWE. After integration in time by the fully implicit average vector field method, ROMs are constructed with proper orthogonal decomposition(POD)/discrete empirical interpolation method that preserves the Hamiltonian structure. In the second approach, the SWE as a partial differential equation with quadratic nonlinearity is integrated in time by the linearly implicit Kahan's method, and ROMs are constructed with the tensorial POD that preserves the linear‐quadratic structure of the SWE. We show that in both approaches, the invariants of the SWE such as the energy, enstrophy, mass and circulation are preserved over a long period of time, leading to stable solutions. We conclude by demonstrating the accuracy and the computational efficiency of the reduced solutions by a numerical test problem.     

On moments of counting distributions satisfying thekth-order recursion and their compound distributions

We present formulas and recurrence formulas commonly used in insurance mathematics for moments of counting distributions given by the kth-order recursion. Moreover, we develop recurrence formulas for moments of compound distributions with those counting distributions satisfying the kth-order recursion. Proceedings of the Seminar on Stability Problems for Stochastic Models, Hajdúszoboszló, Hungary, 1997, Part II.     

Mechanism of combustion dynamics in a backward-facing step stabilized premixed flame

Combustion dynamics leading to thermoacoustic instability in a rearward-facing step stabilized premixed flame is experimentally examined with the objective of investigating the fluid dynamic mechanism that drives heat release rate fluctuations, and how it couples with the acoustic field. The field is probed visually, using linear photodiode arrays that capture the spatiotemporal distribution of CH* and OH*; an equivalence ratio monitor; and a number of pressure sensors. Results show resonance between the acoustic quarter wave mode of the combustion tunnel and a fluid dynamic mode of the wake. Under unstable conditions, the flame is convoluted around a large vortex that extends several step heights downstream. During a typical cycle, while the velocity is decreasing, the vortex grows, and the flame extends downstream around its outer edge. As the velocity reaches its minimum, becoming mostly negative, the vortex reaches its maximum size, and the flame collides with the upper wall; its leading edge folds, trapping reactants pockets, and its trailing edge propagates far upstream of the step. In the next phase, while the velocity is increasing, the heat release grows rapidly as trapped reactant’ pockets are consumed by flames converging towards their centers, and the upstream flame is dislodged back downstream. The heat release rate reaches its maximum halfway into the velocity rise period, leading the maximum velocity by about 90°. In this quarter-wave mode, the pressure leads the velocity by 90° as well, that is, it is in phase with the heat release rate. Numerical modeling results support this mechanism. Equivalence ratio contribution to the instability mechanism is shown to be minor, i.e., heat release dynamics are governed by the cyclical formation of the wake vortex and its interaction with the flame.     

Mathematics Anxiety and Preservice Elementary Teachers' Confidence to Teach Mathematics and Science

Sixty‐five preservice elementary teachers' math anxiety levels and confidence levels to teach elementary mathematics and science were measured. The confidence scores of subjects in different math anxiety groups were compared and the relationships between their math anxiety levels and confidence levels to teach mathematics and science were investigated. The results suggest that low math anxious preservice teachers are more confident to teach elementary mathematics and science than are their peers having higher levels of math anxiety. Negative correlations were found between preservice teachers' math anxiety and their confidence scores to teach elementary mathematics (r = ?.638) and between preservice teachers' math anxiety and their confidence scores to teach elementary science (r = ‐.417). Also, personal math and science teaching self‐efficacy scores of participants were found to be correlated at .01 level (r =.549).