Analysis of plane and axisymmetric flows of incompressible fluids with the stream tube method: Numerical simulation by trust-region optimization algorithm

New concepts for the study of incompressible plane or axisymmetric flows are analysed by the stream tube method. Flows without eddies and pure vortex flows are considered in a transformed domain where the mapped streamlines are rectilinear or circular. The transformation between the physical domain and the computational domain is an unknown of the problem. In order to solve the non-linear set of relevant equations, we present a new algorithm based on a trust region technique which is effective for non-convex optimization problems. Experimental results show that the new algorithm is more robust compared to the Newton-Raphson method.     

A theorem on integer flows on cartesian products of graphs

It is shown that the Cartesian product of two nontrivial connected graphs admits a nowhere‐zero 4‐flow. If both factors are bipartite, then the product admits a nowhere‐zero 3‐flow. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 93–98, 2003     

架起传统与现代的桥梁--建筑历史与理论课程体系教学改革的思考

重新审视建筑历史理论教学的目标、内容、教学方式和手段，通过对国内几座有影响的建筑院校的调研，比较各个院校在这些问题及途径上的异同，分析其利弊，以期促进建筑历史与理论课程体系教学的建设和改革．     

Overloaded elution band profiles of ionizable compounds in reversed‐phase liquid chromatography: Influence of the competition between the neutral and the ionic species

The parameters that affect the shape of the band profiles of acido‐basic compounds under moderately overloaded conditions (sample size less than 500 nmol for a conventional column) in RPLC are discussed. Only analytes that have a single pK_a are considered. In the buffer mobile phase used for their elution, their dissociation may, under certain conditions, cause a significant pH perturbation during the passage of the band. Two consecutive injections (3.3 and 10 μL) of each one of three sample solutions (0.5, 5, and 50 mM) of ten compounds were injected on five C₁₈‐bonded packing materials, including the 5 μm Xterra‐C₁₈ (121 Å), 5 μm Gemini‐C₁₈ (110 Å), 5 μm Luna‐C₁₈(2) (93 Å), 3.5 μm Extend‐C₁₈ (80 Å), and 2.7 μm Halo‐C₁₈ (90 Å). The mobile phase was an aqueous solution of methanol buffered at a constant _W^WpH of 6, with a phosphate buffer. The total concentration of the phosphate groups was constant at 50 mM. The methanol concentration was adjusted to keep all the retention factors between 1 and 10. The compounds injected were phenol, caffeine, 3‐phenyl 1‐propanol, 2‐phenyl butyric acid, amphetamine, aniline, benzylamine, p‐toluidine, procainamidium chloride, and propranololium chloride. Depending on the relative values of the analyte pK_a and the buffer solution pH, these analytes elute as the neutral, the cationic, or the anionic species. The influence of structural parameters such as the charge, the size, and the hydrophobicity of the analytes on the shape of its overloaded band profile is discussed. Simple but general rules predict these shapes. An original adsorption model is proposed that accounts for the unusual peak shapes observed when the analyte is partially dissociated in the buffer solution during its elution.     

Geometry and electronic structure of a heterometallic cluster Mo<Subscript>2</Subscript>Mg<Subscript>2</Subscript> in different oxidation states of Mo: a DFT study

Reduction of tetranuclear heterometallic complex Mo₂Mg₂ was simulated using the B3LYP and PBE density functional methods. The results of geometry calculations of the initial complex [Mo^VIO₂Mg(MeOH)₂(OMe)₄]₂ and a partially reduced Mo^V complex are in good agreement with experimental data. The reduced Mo^III complex is characterized by a decrease in the binding energy of aqua ligands. Structural rearrangement of the complex with release of a coordination position at the Mo atoms requires small energy expenditure. One can assume that the reduction of the polynuclear complex causes overcrowding of its coordination sphere, which favors formation of dinitrogen complexes. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 441–457, March, 2008.     

Linearized and rational approximation method for solving non‐linear Burgers' equation

A new numerical method called linearized and rational approximation method is presented to solve non‐linear evolution equations. The utility of the method is demonstrated for the case of differentiation of functions involving steep gradients. The solution of Burgers' equation is presented to illustrate the effectiveness of the technique for the solution of non‐linear evolution equations exhibiting nearly discontinuous solutions. Copyright © 2004 John Wiley & Sons, Ltd.     

Calculation of impulsively started incompressible viscous flows

The paper's focus is the calculation of unsteady incompressible 2D flows past airfoils. In the framework of the primitive variable Navier–Stokes equations, the initial and boundary conditions must be assigned so as to be compatible, to assure the correct prediction of the flow evolution. This requirement, typical of all incompressible flows, viscous or inviscid, is often violated when modelling the flow past immersed bodies impulsively started from rest. Its fulfillment can however be restored by means of a procedure enforcing compatibility, consisting in a pre‐processing of the initial velocity field, here described in detail. Numerical solutions for an impulsively started multiple airfoil have been obtained using a finite element incremental projection method. The spatial discretization chosen for the velocity and pressure are of different order to satisfy the inf–sup condition and obtain a smooth pressure field. Results are provided to illustrate the effect of employing or not the compatibility procedure, and are found in good agreement with those obtained with a non‐primitive variable solver. In addition, we introduce a post‐processing procedure to evaluate an alternative pressure field which is found to be more accurate than the one resulting from the projection method. This is achieved by considering an appropriate ‘unsplit’ version of the momentum equation, where the velocity solution of the projection method is substituted. Copyright © 2004 John Wiley & Sons, Ltd.     

Passive control of the flow around a square cylinder using porous media

The passive control of bluff body flows using porous media is investigated by means of the penalization method. This method is used to create intermediate porous media between solid obstacles and the fluid in order to modify the boundary layer behaviour. The study covers a wide range of two‐dimensional flows from low transitional flow to fully established turbulence by direct numerical simulation of incompressible Navier–Stokes equations. A parametric study is performed to illustrate the effect of the porous layer permeability and thickness on the passive control. The numerical results reveal the ability of porous media to both regularize the flow and to reduce the drag forces up to 30%. Copyright © 2004 John Wiley & Sons, Ltd.     

Damage and fracture evaluation of granular composite materials by digital image correlation method

This paper presents the applications of digital image correlation technique to the mesoscopic damage and fracture study of some granular based composite materials including steelfiber reinforced concrete, sandstone and crystal-polymer composite. The deformation fields of the composite materials resulted from stress localization were obtained by the correlation computation of the surface images with loading steps and thus the related damage prediction and fracture parameters were evaluated. The correlation searching could be performed either directly based on the gray levels of the digital images or from the wavelet transform (WT) coefficients of the transform spectrum. The latter was developed by the authors and showed higher resolution and sensitivity to the singularity detection. Because the displacement components came from the rough surfaces of the composite materials without any coats of gratings or fringes of optical interferometry, both surface profiles and the deformation fields of the composites were visualized which was helpful to compare each other to analyze the damage of those heterogeneous materials. The project supported by the National Natural Science Foundation of China (10125211 and 10072002), the Scientific Committee of Yunnan Province for the Program of Steel Fiber Reinforced Concrete, and the Institute of Chemical Materials, CAEP at Mianyang