A hybrid DSMC/Navier–Stokes frame to solve mixed rarefied/nonrarefied hypersonic flows over nano‐plate and micro‐cylinder

We extend a hybrid DSMC/Navier–Stokes (NS) approach to unify the DSMC and the NS simulators in one framework capable of solving the mixed non‐equilibrium and near‐equilibrium flow regions efficiently. Furthermore, we use a one‐way state‐based coupling (Dirichlet–Dirichlet boundary‐condition coupling) to transfer the required information from the continuum region to the rarefied one. The current hybrid DSMC–NS frame is applied to the hypersonic flows over nanoflat plate and microcylinder cases. The achieved solutions are compared with the pure DSMC and NS solutions. The results show that the current hybrid approach predicts the surface heat transfer rate and shear stress magnitudes very accurately. Some important conclusions can be drawn from this study. For example, although the shock wave region would be a non‐equilibrium region, it is not necessary to use a pure DSMC simulator to solve it entirely. This is important when the researchers wish to predict the surface properties such as velocity slip, temperature jump, wall heat flux rate, and friction drag magnitudes accurately. Our investigation showed that our hybrid solution time would be at least 40% (for the flat plate) and 35% (for the cylinder) of the time that must be spent by a pure DSMC solver to attain the same accuracy.Copyright © 2013 John Wiley & Sons, Ltd.     

Preyssler heteropolyacid supported on silica coated NiFe2O4 nanoparticles for the catalytic synthesis of bis(dihydropyrimidinone)benzene and 3,4-dihydropyrimidin-2(1H)-ones

A novel magnetic acidic catalyst comprising Preyssler (H14[NaP5W30O110]) heteropoly acid support‐ed on silica coated nickel ferrite nanoparticles (NiFe2O4@SiO2) was prepared. The catalyst was character...     

Multi-component synthesis of highly substituted imidazoles catalyzed by nanorod vanadatesulfuric acid

Nanorod vanadatesulfuric acid (VSA NRs), as a recyclable and eco-benign catalyst, was used for one-pot synthesis of 2,4,5-trisubstituted imidazoles and 1,2,4,5-tetrasubstituted imidazoles using aldehydes, benzil, benzoin or 9,10-phenanthrenequinone and ammonium acetate or aniline under solvent-free conditions providing high to excellent yields. VSA is easily prepared by a simple reaction of chlorosulfonic acid and sodium metavanadate in high purity. As compared with the conventional procedures, the present protocol offers several advantages such as simplicity of procedure, short reaction time, high yields, easy workup, recoverability and reusability of the catalyst and simple purification of the products.     

Optimal subgradient algorithms for large-scale convex optimization in simple domains

This paper describes two optimal subgradient algorithms for solving structured large-scale convex constrained optimization. More specifically, the first algorithm is optimal for smooth problems with Lipschitz continuous gradients and for Lipschitz continuous nonsmooth problems, and the second algorithm is optimal for Lipschitz continuous nonsmooth problems. In addition, we consider two classes of problems: (i) a convex objective with a simple closed convex domain, where the orthogonal projection onto this feasible domain is efficiently available; and (ii) a convex objective with a simple convex functional constraint. If we equip our algorithms with an appropriate prox-function, then the associated subproblem can be solved either in a closed form or by a simple iterative scheme, which is especially important for large-scale problems. We report numerical results for some applications to show the efficiency of the proposed schemes.     

Stochastic optimization of an urban rail timetable under time‐dependent and uncertain demand

Urban rail planning is extremely complex, mainly because it is a decision problem under different uncertainties. In practice, travel demand is generally uncertain, and therefore, the timetabling decisions must be based on accurate estimation. This research addresses the optimization of train timetable at public transit terminals of an urban rail in a stochastic setting. To cope with stochastic fluctuation of arrival rates, a two‐stage stochastic programming model is developed. The objective is to construct a daily train schedule that minimizes the expected waiting time of passengers. Due to the high computational cost of evaluating the expected value objective, the sample average approximation method is applied. The method provided statistical estimations of the optimality gap as well as lower and upper bounds and the associated confidence intervals. Numerical experiments are performed to evaluate the performance of the proposed model and the solution method.     

A modified pseudospectral method for solving trajectory optimization problems with singular arc

This paper presents a direct method based on Legendre–Radau pseudospectral method for efficient and accurate solution of a class of singular optimal control problems. In this scheme, based on a priori knowledge of control, the problem is transformed to a multidomain formulation, in which the switching points appear as unknown parameters. Then, by utilizing Legendre‐Radau pseudospectral method, a nonlinear programming problem is derived which can be solved by the well‐developed parameter optimization algorithms. The main advantages of the present method are its superior accuracy and ability to capture the switching times. Accuracy and performance of the proposed method are examined by means of some numerical experiments. Copyright © 2016 John Wiley & Sons, Ltd.