Penalty finite element method for Navier–Stokes equations with nonlinear slip boundary conditions

The penalty finite element method for Navier–Stokes equations with nonlinear slip boundary conditions is investigated in this paper. Since this class of nonlinear slip boundary conditions include the subdifferential property, the weak variational formulation is a variational inequality problem of the second kind. Using the penalty finite element approximation, we obtain optimal error estimates between the exact solution and the finite element approximation solution. Finally, we show the numerical results which are in full agreement with the theoretical results. Copyright © 2011 John Wiley & Sons, Ltd.     

An efficient synthesis of pyrazole chalcones under solvent free conditions at room temperature

An easy,safe,solvent free and effective method for the synthesis of pyrazole-substituted chalcones has been achieved by grinding pyrazole aldehydes and acetophenones in the presence of activated barium hydroxide(C-200) in high yield within short span of time.All reactions were carried out just by grinding the two reactants in the presence of activated barium hydroxide(C-200). Results are also compared with sodium hydroxide and potassium hydroxide.     

Dependence of the Constant of the Mark‐Houwink Equation under Theta Conditions on the Bulk of Substituents for Hydrocarbon Polymers

The logarithm of the constant K _θ in the Mark‐Houwink equation under theta conditions was found to be proportional to the molar volume of the substituent groups in the case of vinyl‐ and vinylidene‐type hydrocarbon polymers. This simple empirical relation can be used to estimate K _θ for such polymers.     

Inverse optimization for linearly constrained convex separable programming problems

In this paper, we study inverse optimization for linearly constrained convex separable programming problems that have wide applications in industrial and managerial areas. For a given feasible point of a convex separable program, the inverse optimization is to determine whether the feasible point can be made optimal by adjusting the parameter values in the problem, and when the answer is positive, find the parameter values that have the smallest adjustments. A sufficient and necessary condition is given for a feasible point to be able to become optimal by adjusting parameter values. Inverse optimization formulations are presented with ℓ₁ and ℓ₂ norms. These inverse optimization problems are either linear programming when ℓ₁ norm is used in the formulation, or convex quadratic separable programming when ℓ₂ norm is used.     

Necessary optimality conditions in nondifferentiable vector optimization

The purpose of the present paper is to give necessary optimality conditions for weak Pareto minimun, peints of nondifferentiable vector optimization problems vcing generalized definitions of the upper and lower Dini-Hadamard derivatives. We give two different approaches for such definitions, a global one and a componentwise one     

Direct and inverse problems for electromagnetic scattering by a doubly periodic structure with a partially coated dielectric

Consider the problem of scattering of electromagnetic waves by a doubly periodic Lipschitz structure. The medium above the structure is assumed to be homogenous and lossless with a positive dielectric coefficient. Below the structure there is a perfect conductor with a partially coated dielectric boundary. We first establish the well‐posedness of the direct problem in a proper function space and then obtain a uniqueness result for the inverse problem by extending Isakov's method. Copyright © 2009 John Wiley & Sons, Ltd.     

Entanglement conditions for four-mode states via the uncertainty relations in conjunction with partial transposition

From the Heisenberg uncertainty relation in conjunction with partial transposition, we derive a class of inequalities for detecting entanglements in four-mode states. The sufficient conditions for bipartite entangled states are presented. We also discuss the generalization of the entanglement conditions via the Schrödinger-Robertson indeterminacy relation, which are in general stronger than those based on the Heisenberg uncertainty relation.     

Study on hydrogen sulfide plasma passivation of 790-nm laser diode cavity surface

In order to improve the optical properties of the Ⅲ-Ⅴ laser diodes(LDs) by means of H2S plasma passivation technology,H2S plasma passivation treatment is performed on the GaAs(110) surface.The optimum passivation conditions obtained are 60-W radio frequency(RF)power and 20-min duration.So the laser cavity surfaces axe treated under the optimum passivation conditions.Consequently,compared with unpassivated lasers with only AR/HR-coatings,the catastrophic optical damage (COD) threshold value of the passivated lasers by H2S plasma treatment is increased by 33%,which is almost the same as that of (NH4)2Sx treatment.And the life-test experiment has demonstrated that this passivation method is more stable than(NH4)2Sx solution wet-passivated treatment.     

Inflow conditions for spatial direct numerical simulation of turbulent boundary layers

The inflow conditions for spatial direct numerical simulation (SDNS) of turbulent boundary layers should reflect the characteristics of upstream turbulence, which is a puzzle. In this paper a new method is suggested, in which the flow field obtained by using temporal direct numerical simulation (TDNS) for fully developed turbulent flow (only flow field for a single moment is sufficient) can be used as the inflow of SDNS with a proper transformation. The calculation results confirm that this method is feasible and effective. It is also found that, under a proper time-space transformation, all statistics of the fully developed turbulence obtained by both temporal mode and spatial mode DNS are in excellent agreement with each other, not only qualitatively, but also quantitatively. The normal-wise distributions of mean flow profile, turbulent Mach number and the root mean square (RMS) of the fluctuations of various variables, as well as the Reynolds stresses of the fully developed turbulence obtained by using SDNS, bear similarity in nature. Supported by the National Natural Science Foundation of China (Grant No. 90205021), the China Postdoctoral Science Foundation (Grant No. 20060400707), and the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No. 200328), and partially supported by Liu-Hui Center of Applied Mathematics, Nankai University and Tianjin University     

Weak Entropy Boundary Conditions for Isentropic Gas Dynamics via Kinetic Relaxation

We consider a kinetic BGK model relaxing to isentropic gas dynamics previously introduced by the authors, but with Dirichlet boundary condition on the incoming velocities. We pass to the limit as the relaxation parameter tends to zero by compensated compactness inside the domain, and obtain that the limit satisfies entropy inequalities on the boundary involving weak traces of entropy fluxes. Our method is very general and could be applied to any entropy satisfying BGK model as soon as we have strong compactness of the macroscopic variables inside the domain.