AN IMPROVED NAVIER–STOKES PROCEDURE FOR ANALYSIS OF TWO-DIMENSIONAL AEROFOILS IN LAMINAR AND TURBULENT FLOWS

An accurate and robust Navier–Stokes procedure to predict the complex flow about an aerofoil has been developed. Much improvement over existing methods is achieved in various aspects of the solution procedure. The computational grid generated by conformal mapping, which is not only orthogonal but aligned with the inviscid streamlines, keeps the equations simple and minimizes the error due to false diffusion. Formal second-order accuracy is ensured by employing the QUICK scheme for the convective derivatives in the full Navier–Stokes and turbulence transport equations. To treat the separated region properly and to better resolve the flow field in the wake, the two-layer k–ε turbulence model is incorporated. The onset of transition is triggered in a unique fashion to warrant the smooth transition to turbulent flow. Sample calculations for various aerofoil sections show that the prediction is improved substantially over those by existing methods. The details of the flow extending to the wake, such as the surface pressure distribution, C_Lmax, the velocity fields and the Reynolds stress profiles, are found to be in excellent agreement with the data. © 1997 John Wiley & Sons, Ltd.     

Cayley–Dickson Procedure, Relativistic Wave Equations and Supersymmetric Oscillators

The relativistic first-order wave equations for massive particles with spin 0,1,1/2 are formulated in terms of a factorization of the Klein–Fock equation by means of the algebra of octonions. An analogous method applied to Hamiltonian of the quantum isotropic oscillator leads to the natural generalization of the model. The class of supersymmetric oscillators with dimension N7 associated with te algebras of the Cayley–Dickson series is introduced.     

One-pot enyne metathesis/Diels-Alder reaction for the construction of highly functionalized novel polycyclic aza-compounds

Various tricyclic dienes were synthesized via enyne metathesis using the first generation Grubbs catalyst. The enyne metathesis proceeded smoothly in refluxing CH₂Cl₂ with a low catalyst loading (3.0 mol %), giving good yields (72-89%) of the tricyclic products 6 and 16. The resulting 1,3-dienes are suitable precursors of polycyclic structures via a Diels-Alder process. One-pot RCM/Diels-Alder reactions of the enyne products with dienophiles proceeded smoothly to afford polycyclic compounds as a single cycloadduct. The structures of the Diels-Alder adducts were determined by ¹H NMR spectra and X-ray analysis. The cycloadducts were formed via the approach of the dienophiles towards the diene in endo mode.     

Use of statistical measures for analyzing RNA secondary structures

With more and more RNA secondary structures accumulated, the need for comparing different RNA secondary structures often arises in function prediction and evolutionary analysis. Numerous efficient algorithms were developed for comparing different RNA secondary structures, but challenges remain. In this article, a new statistical measure extending the notion of relative entropy based on the proposed stochastic model is evaluated for RNA secondary structures. The results obtained from several experiments on real datasets have shown the effectiveness of the proposed approach. Moreover, the time complexity of our method is favorable by comparing with that of the existing methods which solve the similar problem.     

Reply to “Comment on Aromatic‐Backbone Interactions in Model α‐Helical Peptides”

In response to Van Mourik's comments on our paper (J Comput Chem 2007, 28, 1208.) we present an extended version of our rotation method. We also prove that intramolecular interaction energies as well the basis set superposition errors calculated with our rotation method are comparable with those obtained by the counterpoise method of Boys and Bernardi (Mol Phys 1970, 19, 533). In intramolecular interaction energy calculations, if the interacting groups are in proximity, our rotation method is recommended to avoid artificial interactions, which can be induced by fragmentation. © 2007 Wiley Periodicals, Inc.J Comput Chem, 2008     

A green and novel procedure for the preparation of ionic liquid

A green and novel procedure is described for the preparation of a series of ionic liquid containing alkylimidazolium-based or N-alkylpyridinium-based cations and hexafluorophosphate-based or tetrafluoroborate-based anions in one-pot solvent-free conditions to give excellent yields with shortened time.     

Numerical convergence on adaptive grids for control volume methods

An adaptive technique for control‐volume methods applied to second order elliptic equations in two dimensions is presented. The discretization method applies to initially Cartesian grids aligned with the principal directions of the conductivity tensor. The convergence behavior of this method is investigated numerically. For solutions with low Sobolev regularity, the found L² convergence order is two for the potential and one for the flow density. The system of linear equations is better conditioned for the adaptive grids than for uniform grids. The test runs indicate that a pure flux‐based refinement criterion is preferable.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008     

Fast search algorithms for computational protein design

One of the main challenges in computational protein design (CPD) is the huge size of the protein sequence and conformational space that has to be computationally explored. Recently, we showed that state‐of‐the‐art combinatorial optimization technologies based on Cost Function Network (CFN) processing allow speeding up provable rigid backbone protein design methods by several orders of magnitudes. Building up on this, we improved and injected CFN technology into the well‐established CPD package Osprey to allow all Osprey CPD algorithms to benefit from associated speedups. Because Osprey fundamentally relies on the ability of to produce conformations in increasing order of energy, we defined new strategies combining CFN lower bounds, with new side‐chain positioning‐based branching scheme. Beyond the speedups obtained in the new ‐CFN combination, this novel branching scheme enables a much faster enumeration of suboptimal sequences, far beyond what is reachable without it. Together with the immediate and important speedups provided by CFN technology, these developments directly benefit to all the algorithms that previously relied on the DEE/ combination inside Osprey* and make it possible to solve larger CPD problems with provable algorithms. © 2016 Wiley Periodicals, Inc.     

A greedy meshless local Petrov–Galerkin methodbased on radial basis functions

The meshless local Petrov–Galerkin (MLPG) method with global radial basis functions (RBF) as trial approximation leads to a full final linear system and a large condition number. This makes MLPG less efficient when the number of data points is increased. We can overcome this drawback if we avoid using more points from the data site than absolutely necessary. In this article, we equip the MLPG method with the greedy sparse approximation technique of (Schaback, Numercail Algorithms 67 (2014), 531–547) and use it for numerical solution of partial differential equations. This scheme uses as few neighbor nodal values as possible and allows to control the consistency error by explicit calculation. Whatever the given RBF is, the final system is sparse and the algorithm is well‐conditioned. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 847–861, 2016