Synthesis of pyrrolo-pyrrolo-pyrazines via the Pd/C-catalyzed cyclization of N-propargyl pyrrolinyl-pyrrole derivatives

A novel and efficient synthesis of N-substituted dipyrrolo[1,2-a:2′,1′-c]pyrazine derivatives has been developed. The synthetic strategy relies on the synthesis of 4′,5′-dihydro-1H,3′H-2,2′-bipyrrole, followed by the reaction with propargyl bromide. Various substituents were introduced to the alkyne functionality using the Sonogashira coupling reaction. Aromatization of the dihydropyrrole ring followed by an intramolecular cyclization reaction between the alkyne functionality and the pyrrole nitrogen atom was catalyzed by Pd/C at high temperature to furnish the desired dipyrrolo-pyrazine skeleton.     

Dynamic analysis and synchronization control of an unusual chaotic system with exponential term and coexisting attractors

This paper reports a new four-dimensional chaotic system consisting of an exponential nonlinear term, two quadratic nonlinear terms and five linear terms. The system has only one equilibrium and performs stability, periodicity and chaos with the variation of the parameters. It losses its stability with the occurrence of Hopf bifurcation and goes into chaos via period-doubling bifurcation. One more interesting feature of the system is that it can generate multiple coexisting attractors for different initial conditions, such as two strange attractors with one limit cycle, one strange attractor with two limit cycles, etc. The dynamic properties of the system are presented by numerical simulation includes bifurcation diagrams, Lyapunov exponent spectrum and phase portraits. An electronic circuit is constructed to implement the chaotic attractor of the system. Based on the linear quadratic regulator (LQR) method, the synchronization control of the system is investigated.     

On the Coupling Time of the Heat-Bath Process for the Fortuin–Kasteleyn Random–Cluster Model

We consider the coupling from the past implementation of the random–cluster heat-bath process, and study its random running time, or coupling time. We focus on hypercubic lattices embedded on tori, in dimensions one to three, with cluster fugacity at least one. We make a number of conjectures regarding the asymptotic behaviour of the coupling time, motivated by rigorous results in one dimension and Monte Carlo simulations in dimensions two and three. Amongst our findings, we observe that, for generic parameter values, the distribution of the appropriately standardized coupling time converges to a Gumbel distribution, and that the standard deviation of the coupling time is asymptotic to an explicit universal constant multiple of the relaxation time. Perhaps surprisingly, we observe these results to hold both off criticality, where the coupling time closely mimics the coupon collector’s problem, and also at the critical point, provided the cluster fugacity is below the value at which the transition becomes discontinuous. Finally, we consider analogous questions for the single-spin Ising heat-bath process.     

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.     

A novel polysiloxane-based polymer as a gel agent for gel–VRLA batteries

In this study, a novel polysiloxane-based gel agent (PSGA) was synthesized by using poly(dimethylsiloxane-co-alkylmethylsiloxane) and used as a gel agent for gel–valve-regulated lead–acid batteries. A PSGA was characterized by Fourier transform infrared, zeta meter, scanning electron microscopy, and energy-dispersive X-ray analysis. The electrochemical characterization of the gel system for the optimization of some parameters, such as concentration of gel agent, stirring rate, and agitation time, was conducted by cyclic voltammetric and electrochemical impedance spectroscopic analyses. The optimum concentration of the gel agent was determined as 6 wt% of the PSGA to form the best gel structure. The mechanical parameters related to the formation of a suitable gel structure were also investigated. The optimum stirring rate and agitation time were determined as 500 rpm and 2.5 h, respectively. The charge–discharge tests were applied to the gel system, and the highest capacity was determined in the PSGA-based gel system as 10 mAh at the end of the 100th cycle. The capacity of non-gelled system was the lowest.     

Some solutions of the Gauss–Bonnet gravity with scalar field in four dimensions

We give all exact solutions of the Einstein–Gauss–Bonnet Field Equations coupled with a scalar field in four dimensions under certain assumptions. The main assumption we make in this work is to take the second covariant derivative of the coupling function proportional to the spacetime metric tensor. Although this assumption simplifies the field equations considerably, to obtain exact solutions we assume also that the spacetime metric is conformally flat. Then we obtain a class of exact solutions.     

Synthesis and structure of new systems containing pyramidalized double bonds

Syn- andanti-isomers of substituted tetracyclo[6.2.2.2^3.6.1^2.7]tetradeca-2(7)-ene have been synthesized. In thesyn-isomers steric interactions between cyclopropane hydrogen atoms lead to a pyramidalization of the C(sp²) atoms of the central double bond. The parameters from three crystal structures are compared with geometry optimized structures using PCWIN, MM3, and MOPAC. Plots of X-ray distances versus theoretically optimized distances give correlation coefficients between 0.91 and 0.97. Analysis of the discrepancies suggest modifications in some molecular mechanics parameters are needed to model the solid state structures.     

Cartesian Expressions for Surface and Regular Solid Spherical Harmonics Using Binomial Coefficients and Its Use in the Evaluation of Multicenter Integrals

In this study, we present cartesian expressions for surface and regular solid spherical harmonics using binomial coefficients. The obtained results are useful for the calculation of multicenter molecular integrals over Slater type orbitals, especially for large values of quantum numbers. The main advantage of presented formulae in the evaluation of multicenter integrals is discussed.     

Upper and lower bounds on the control field and the quality of achieved optimally controlled quantum molecular motion

A large class of problems in optimally controlled quantum or classical molecular dynamics has multiple solutions for the control field amplitude. A denumerably infinite number of solutions may exist depending on the structure of the design cost functional. This fact has been recently proved with the aid of perturbation theory by considering the electric field as the perturbating agent. In carrying out this analysis, an eigenvalue (i.e., a spectral parameter) appears which gives the degree of deviation of the control objective from its desired value. In this work, we develop a scheme to construct upper and lower bounds for the field amplitude and spectral parameter for each member of the denumerably infinite set of control solutions. The bounds can be tightened if desired. The analysis here is primarily restricted to the weak field regime, although the bounds for the strong field nonlinear case are also presented.