Wave generation in a computation domain

One of the possible methods to deal with the reflecting waves at the incident boundary in numerical modeling is to generate waves in the computation domain and absorb the outgoing waves at the incident boundary. A source function is introduced into the momentum equation of Boussinesq equations for generating wave in a computation domain in this paper. Typical numerical examples are given for the verification of the proposed method. Numerical examination for the wave diffraction through a breakwater gap shows that the proposed method is especially useful for multidirectional waves.     

Fully-developed pipe and planar flows of multimode viscoelastic fluids

Two solutions are presented for fully-developed pipe and planar flows of multimode viscoelastic models. The fluids have a Newtonian solvent contribution and the polymer modes are described by the Phan-Thien—Tanner (PTT), the FENE-P or the Giesekus equation. The first solution is exact and can handle any number of modes, but is only semi-analytical. The second solution, which is presented only for the PTT model with a linear stress coefficient and the FENE-P model, can also handle any number of modes. It is based on a truncated series expansion and is completely analytical, but provides only an approximated solution. The complexity of the multimode solutions is investigated first with the exact semi-analytical method and it is shown that at high Deborah number flows the high-order stresses can become as important as the stress of the first mode. It is also under these conditions that the approximated analytical solution deviates from the exact semi-analytical solution. A criterion for the accurate use of the approximated solution is presented. Fortran codes are provided to obtain these solutions at the internet address at the end.     

Global exponential stability for nonautonomous cellular neural networks with delays

In this Letter, by utilizing Lyapunov functional method and Halanay inequalities, we analyze global exponential stability of nonautonomous cellular neural networks with delay. Several new sufficient conditions ensuring global exponential stability of the network are obtained. The results given here extend and improve the earlier publications. An example is given to demonstrate the effectiveness of the obtained results.     

A new generalized algebra method and its application in the (2 + 1) dimensional Boiti–Leon–Pempinelli equation

In the present paper, some types of general solutions of a first-order nonlinear ordinary differential equation with six degree are given and a new generalized algebra method is presented to find more exact solutions of nonlinear differential equations. As an application of the method and the solutions of this equation, we choose the (2 + 1) dimensional Boiti Leon Pempinelli equation to illustrate the validity and advantages of the method. As a consequence, more new types and general solutions are found which include rational solutions and irrational solutions and so on. The new method can also be applied to other nonlinear differential equations in mathematical physics.     

Enantioselective olefin epoxidation using novel biphenyl and binaphthyl azepines and azepinium salts

Homologous biphenyl and (diastereomeric) binaphthyl tertiary azepines and quaternary iminium salts were prepared from (S)- and (R)-3,3-dimethylbutan-2-amine. Both the amines and iminium ions behave as effective catalysts for the enantioselective epoxidation of unfunctionalized olefins (ee up to 87%).     

The quadratic trace identity for constructing Hamiltonian structures of the multicomponent equation hierarchies

The quadratic trace identity is presented, which is devoted to constructing the Hamiltonian structures of some multicomponent equation hierarchies.     

Hβ-沸石的氧化物改性对由β-甲基萘选择性合成2,6-二甲基萘反应的影响

Ｈβ－沸石的氧化物改性对由β－甲基萘选择性合成２，６－二甲基萘反应的影响栗同林刘希尧１）（北京燕山石化公司研究院北京１０２５４９）王祥生（大连理工大学工业催化研究所大连１１６０１２）关键词β－甲基萘β沸石氧化物改性歧化烷基化分类号Ｏ６４３．３２在Ｃ－...     

Control of mesoporous structure of aerogels derived from cresol-formaldehyde

Polycondensation of a cresol mixture (C(m)) with formaldehyde (F) in basic aqueous solutions leads to formation of highly cross-linked C(m)F aquagels that can be supercritically dried with carbon dioxide to form organic C(m)F aerogels. Aerogels synthesized with different catalyst contents and reactant concentrations are characterized by low-temperature nitrogen adsorption. The present experimental results suggest that the C(m)F aerogels are typical mesoporous materials and have almost no micropores in bulk. The microstructure of the organic C(m)F aerogels can be controlled and tailored effectively by varying synthesis conditions during the initial sol-gel process. C(m)F organic aerogels with specific surface area as high as 627 m(2)/g and corresponding pore volume 2.06 ml/g have been obtained with a dominant pore size of 30 nm. C(m)F organic aerogels with peaky pore size distributions concentrated at 11 nm have also been prepared.