Incorporation of an Allene Unit into α‐Pinene via β‐Elimination

The two double‐bond isomers 3‐iodo‐2,6,6‐trimethylbicyclo[3.1.1]hept‐2‐ene ( 6b ) and 3‐iodo‐4,6,6‐trimethylbicyclo[3.1.1]hept‐2‐ene ( 11 ) were synthesized by reacting 2,6,6‐trimethylbicyclo[3.1.1]heptan‐3‐one ( 9 ) with hydrazine, followed by treatment with I₂ in the presence of Et₃N. Treatment of 11 with t‐BuOK as base in diglyme at 220° resulted in the formation of 9 and 6,6‐dimethyl‐4‐methylidenebicyclo[3.1.1]hept‐2‐ene ( 12 ). For the formation of 9 , the cyclic allene 7 is proposed as an intermediate. Treatment of the second isomer, 6b , with t‐BuOK at 170° gave rise to the diene 12 and the dimerization product 17 . The underlying mechanism of this transformation is discussed. On the basis of density‐functional‐theory (DFT) calculations on the allene 7 and the alkyne 15 , the formation of the latter as the intermediate was excluded.     

Evaluation of two-center overlap integrals using slater type orbitals in terms of bessel type orbitals

Using the definition of STOs in terms of BTOs, we have presented analytical formula for two-center overlap integrals. The obtained formula contains generalized binomial coefficients and Mulliken integrals A_k and B_k. Taking into account the recent advances on the efficient calculation of Mulliken integrals (Harris, Int. J. Quantum Chem., 100 (2004) 142), we have obtained many more satisfactory results for two-center overlap integrals, for arbitrary quantum numbers, scaling parameters, and location of atomic orbitals.PACS No: 31.15.+qAMS Subject Classification: 81V55, 81–08     

Chloroacetonylation of CC double bonds promoted by manganese(III) acetate

The addition of acetylacetone to alkenes was performed using Mn(OAc)₃·2H₂O in the presence of HCl. The intermediate formed was trapped by chloride. Removal of one of the acetyl groups with ammonia under very mild conditions provided compounds derived from chloroacetonylation of the double bonds.     

Fermionic approach to soliton equations

In this paper we exploit the algebraic structure of the soliton equations and find solutions in terms of fermion particles. We show how determinants arise naturally in the fermionic approach to soliton equations. We write the τ-function for charged free fermions in terms of determinants. Examples of how to get soliton, rational and dromion solutions from τ-functions for the various soliton equations are given.     

Structural and electronic properties of InNxP1-x alloy in full range (0 ≤ x ≤1)

We have performed first-principles method to investigate structural and electronic properties of InN_xP_1?x ternary semiconductor alloy in full range (0 ≤ x ≤ 1) using density functional theory. We have used modified Becke–Johnson potential to obtain accurate band gap results. From the electronic band structure calculation we have found that InN_xP_1?x become metal between 47 and 80% of nitrogen concentration. Additional to our band gap calculations, we have also used the band anticrossing model. The band anticrossing model supplies a simple, analytical expression to calculate the physical properties, such as the electronic and optical properties, of III-N_xV_1?x alloys. The knowledge of the electron density of states is required to understand and clarify some properties of materials such as the band structures, bonding character and dielectric function. In order to have a deeper understanding of these properties of the studied materials, the total and partial density of states has been calculated. Finally, we have calculated the total bowing parameter b of studied alloys, together with three contributions b_VD, b_CE, and b_SR due to volume deformation, different atomic electron negativities and structural relaxation, respectively.     

Theoretical calculations on structural and electronic properties of BGaAsBi alloys

The structural and electronic properties of cubic B _x Ga_1?x As_1?y Bi _y alloys with bismuth (Bi) concentration of 0.0625, 0.125, 0.1875 and 0.25 are studied with various boron (B) compositions by means of density functional theory (DFT) within the Wu-Cohen (WC) exchange correlation potential based on generalized gradient approximation (GGA). For all studied alloy structures, we have implemented geometric optimization before the volume optimization calculations. The obtained equilibrium lattice constants and band gap of studied quaternary alloys are investigated for the first time in literature. While the lattice constant behavior changes linearly with boron concentration, increasing small amount of bismuth concentration alter the lattice constant nonlinearly. The present calculation shows that the band gap decreases with increasing bismuth concentration and direct band gap semiconductor alloy became an indirect band gap with increasing boron concentration. From the band offset calculation we have shown that increasing B and Bi concentration in host GaAs reduced the valance band offset in a heterostructure formed by GaAs and studied alloys.     

Gödel type metrics in Einstein–aether theory

Aether theory is introduced to implement the violation of the Lorentz invariance in general relativity. For this purpose a unit timelike vector field is introduced to the theory in addition to the metric tensor. Aether theory contains four free parameters which satisfy some inequalities in order that the theory to be consistent with the observations. We show that the Gödel type of metrics of general relativity are also exact solutions of the Einstein–aether theory. The only field equations are the 3D Maxwell field equations and the parameters are left free except c ₁ ? c ₃ = 1.     

A LES/PDF simulator on block-structured meshes

A block-structured mesh large-eddy simulation (LES)/probability density function (PDF) simulator is developed within the OpenFOAM framework for computational modelling of complex turbulent reacting flows. The LES/PDF solver is a hybrid solution methodology consisting of (i) a finite-volume (FV) method for solving the filtered mass and momentum equations (LES solver), and (ii) a Lagrangian particle-based Monte Carlo algorithm (PDF solver) for solving the modelled transport equation of the filtered joint PDF of compositions. Both the LES and the PDF methods are developed and combined to form a hybrid LES/PDF simulator entirely within the OpenFOAM framework. The in situ adaptive tabulation method [S.B. Pope, Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation, Combust. Theory Model. 1 (1997), pp. 41–63; L. Lu, S.R. Lantz, Z. Ren, and B.S. Pope, Computationally efficient implementation of combustion chemistry in parallel PDF calculations, J. Comput. Phys. 228 (2009), pp. 5490–5525] is incorporated into the new LES/PDF solver for efficient computations of combustion chemistry with detailed reaction kinetics. The method is designed to utilise a block-structured mesh and can readily be extended to unstructured grids. The three-stage velocity interpolation method of Zhang and Haworth [A general mass consistency algorithm for hybrid particle/finite-volume PDF methods, J. Comput. Phys. 194 (2004), pp. 156–193] is adapted to interpolate the LES velocity field onto particle locations accurately and to enforce the consistency between LES and PDF fields at the numerical solution level. The hybrid algorithm is fully parallelised using the conventional domain decomposition approach. A detailed examination of the effects of each stage and the overall performance of the velocity interpolation algorithm is performed. Accurate coupling of the LES and PDF solvers is demonstrated using the one-way coupling methodology. Then the fully two-way coupled LES/PDF solver is successfully applied to simulate the Sandia Flame-D, and a turbulent non-swirling premixed flame and a turbulent swirling stratified flame from the Cambridge turbulent stratified flame series [M.S. Sweeney, S. Hochgreb, M.J. Dunn, and R.S. Barlow, The structure of turbulent stratified and premixed methane/air flames I: Non-swirling flows, Combust. Flame 159 (2012), pp. 2896–2911; M.S. Sweeney, S. Hochgreb, M.J. Dunn, and R.S. Barlow, The structure of turbulent stratified and premixed methane/air flames II: Swirling flows, Combust. Flame 159 (2012), pp. 2912–2929]. It is found that the LES/PDF method is very robust and the results are in good agreement with the experimental data for both flames.     

Bound Analysis Through HDMR for Multivariate Data Modelling - CMMSE

Multivariate data modelling problems consist of a number of nodes with associated function (class) values. The main purpose of these problems is to construct an analytical model to represent the characteristics of the problem under consideration. Because the devices, tools, and/or algorithms used to collect the data may have incapabilities or limited capabilities, the data set is likely to contain unavoidable errors. That is, each component of data is reliable only within an interval which contains the data value. To this end, when an analytical structure is needed for the given data, a band structure should be determined instead of a unique structure. As the multivariance of the given data set increases, divide–and–conquer methods become important in multivariate modelling problems. HDMR based methods allow us to partition the given multivariate data into less variate data sets to reduce the complexity of the given problem. This paper focuses on Interval Factorized HDMR method developed to determine an approximate band structure for a given multivariate data modelling problem having uncertainties on its nodes and function values.