Finite Element Solution of Conical Diffraction Problems

This paper is devoted to the numerical study of diffraction by periodic structures of plane waves under oblique incidence. For this situation Maxwell's equations can be reduced to a system of two Helmholtz equations in R ² coupled via quasiperiodic transmission conditions on the piecewise smooth interfaces between different materials. The numerical analysis is based on a strongly elliptic variational formulation of the differential problem in a bounded periodic cell involving nonlocal boundary operators. We obtain existence and uniqueness results for discrete solutions and provide the corresponding error analysis.     

线性分式规划最优解集的求法

本文使用多面集的表示定理，导出了线性分式规划最优解集的结构，并给出确定全部最优解的计算步骤。     

A stability of the steady flow of compressible viscous fluid with respect to initial disturbance (v∞ ≠ 0)

We consider a compressible viscous fluid with the velocity at infinity equal to a strictly non‐zero constant vector in ?³. Under the assumptions on the smallness of the external force and velocity at infinity, Novotny–Padula (Math. Ann. 1997; 308 :439– 489) proved the existence and uniqueness of steady flow in the class of functions possessing some pointwise decay. In this paper, we study stability of the steady flow with respect to the initial disturbance. We proved that if H³‐norm of the initial disturbance is small enough, then the solution to the non‐stationary problem exists uniquely and globally in time, which satisfies a uniform estimate on prescribed velocity at infinity and converges to the steady flow in L_q‐norm for any number q? 2. Copyright © 2006 John Wiley & Sons, Ltd.     

Comparison of growth stress measurements with modelling in thin iron oxide films

High temperature oxidation of metals leads to residual stresses both in the metal and in the growing oxide. In this work, the evolution of this residual stresses is theoretically predicted in the growing oxide layers. The origin of these stresses is based on a microstructural model. Using experimental results providing from the oxidation kinetics, and an analysis proposed to describe the growth strain occurring in the thin layers, a set of equations is established allowing determining the stresses evolution with oxidation time. Then, the model is compared with experimental results obtained on both α-Fe and phosphated α-Fe, oxidised at different temperatures. Numerical data are extracted from experiments either with an asymptotic formulation or with an inverse method. These two methods give good agreement with experiments and allow extracting the model parameters.     

ON THE UNIQUENESS OF THE WEAK SOLUTIONS OF A QUASILINEAR HYPERBOLIC SYSTEM WITH A SINGULAR SOURCE TERM

This paper is a continuation of the authors'previous paper[1].In this paper the authorsprove,assuming additional conditions on the initial data,some results about the existence anduniqueness of the entropy weak solutions of the Cauchy problem for the singular hyperbolicsystem a_t+(au)_x_2au/x=0,u_t+1/2(a~2+u~2)_x=0,x>0,t≥0.     

非线性奇异边值问题的正解

利用锥映射的不动点指数定量，研究了一类非线性奇异边值问题多个正解的存在性问题。在构造的解的存在条件之下，证明了奇异边值问题至少有两个正解的存在性定理。     

On Direct Transformation Approach to Asymptotical Analytical Solutions of Perturbed Partial Differential Equation

In this article, we will derive an equality, where the Taylor series expansion around ε = 0for any asymptotical analytical solution of the perturbed partial differential equation (PDE) with perturbing parameter ε must be admitted.By making use of the equality, we may obtain a transformation, which directly map the analytical solutions of a given unperturbed PDE to the asymptotical analytical solutions of the corresponding perturbed one. The notion of Lie-B(a)cklund symmetries is introduced in order to obtain more transformations. Hence, we can directly create more transformations in virtue of known Lie-B(a)cklund symmetries and recursion operators of corresponding unperturbed equation. The perturbed Burgers equation and the perturbed Korteweg-de Vries (KdV) equation are used as examples.     

Some degenerate and quasilinear parabolic systems not in divergence form

This paper deals with positive solutions of degenerate and quasilinear parabolic systems not in divergence form: u_t=u^p(Δu+av), v_t=v^q(Δv+bu), with null Dirichlet boundary conditions and positive initial conditions, where p, q, a and b are all positive constants. The local existence and uniqueness of classical solution are proved. Moreover, it will be proved that all solutions exist globally if and only if ab?λ₁², where λ₁ is the first eigenvalue of −Δ in Ω with homogeneous Dirichlet boundary condition.     

具连续时滞Liénard方程概周期解的存在唯一性

结合Liapunov泛函，研究了具连续时滞Lienard方程概周期解的存在唯一性和安全一致渐进稳定性。     

Hydrophobicity-induced drying transition in alkanethiol self-assembled monolayer—water interface

During the course of our investigation of the electron transfer properties of some redox species through highly hydrophobic long chain alkanethiol molecules on gold in aqueous and non-aqueous solvents, we obtained some intriguing results such as unusually low interfacial capacitance, very high values of impedance and film resistance, all of which pointed to the possible existence of a nanometer size interfacial gap between the hydrophobic monolayer and aqueous electrolyte. We explain this phenomenon by a model for the alkanethiol monolayer—aqueous electrolyte interface, in which the extremely hydrophobic alkanethiol film repels water molecules adjacent to it and in the process creates a shield between the monolayer film and water. This effectively increases the overall thickness of the dielectric layer that is manifested as an abnormally low value of interfacial capacitance. This behaviour is very much akin to the ‘drying transition’ proposed by Lum, Chandler and Weeks in their theory of length scale dependent hydrophobicity. For small hydrophobic units consisting of apolar solutes, the water molecules can reorganize around them without sacrificing their hydrogen bonds. Since for an extended hydrophobic unit, the existence of hydrogen bonded water structure close to it is geometrically unfavourable, there is a net depletion of water molecules in the vicinity leading to the possible creation of a hydrophobic interfacial gap.