Study on a Cross Diffusion Parabolic System

This paper considers a kind of strongly coupled cross diffusion parabolic system,which can be usedas the multi-dimensional Lyumkis energy transport model in semiconductor science.The global existence andlarge time behavior are obtained for smooth solution to the initial boundary value problem.When the initialdata are a small perturbation of an isothermal stationary solution,the smooth solution of the problem under theinsulating boundary condition,converges to that stationary solution exponentially fast as time goes to infinity.     

Development of a finite-element analysis methodology for the propagation of delaminations in composite structures

Analysing the collapse of skin-stiffened structures requires capturing the critical phenomenon of skin-stiffener separation, which can be considered analogous to interlaminar cracking. This paper presents the development of a numerical approach for simulating the propagation of interlaminar cracks in composite structures. A degradation methodology was introduced in MSC.Marc, which involved the modelling of a structure with shell layers connected by user-defined multiple-point constraints (MPCs). User subroutines were written that employ the virtual crack closure technique (VCCT) to determine the onset of crack growth and modify the properties of the user-defined MPCs to simulate crack propagation. Methodologies for the release of failing MPCs are presented and are discussed with reference to the VCCT assumption of self-similar crack growth. The numerical results obtained by using the release methodologies are then compared with experimental data for a double-cantilever beam specimen. Based on this comparison, recommendations for the future development of the degradation model are made, especially with reference to developing an approach for the collapse analysis of fuselage-representative structures. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 1, pp. 15–42, January–February, 2007.     

THE LARGE TIME BEHAVIOR OF SPECTRAL APPROXIMATION FOR A CLASS OF PSEUDOPARABOLIC VISCOUS DIFFUSION EQUATION

The asymptotic behavior of the solutions to a class of pseudoparabolic viscous diffusion equation with periodic initial condition is studied by using the spectral method. The semidiscrete Fourier approximate solution of the problem is constructed and the error estiation between spectral approximate solution and exact solution on large time is also obtained. The existence of the approximate attractor AN and the upper semicontinuity d(AN,A)→0 are proved.     

Side‐chain crystallization behavior of graft copolymers consisting of an amorphous main chain and crystalline side chains. II. Poly(n‐hexyl methacrylate)‐graft‐poly(ethylene glycol)

The phase behavior and crystallization of graft copolymers consisting of poly(n‐hexyl methacrylate) (PHMA) as an amorphous main chain and poly(ethylene glycol) (PEG) as crystallizable side chains (HMAx with 15 ≤ x ≤ 73, where x represents the weight percentage of PEG) were investigated. Small‐angle X‐ray scattering profiles measured above the melting temperature of PEG suggested that a microdomain structure with segregated PHMA and PEG domains was formed in HMA40 and HMA46. This phase behavior was qualitatively described by a calculated phase diagram based on the mean‐field theory. Because of the segregation of PEG into microdomains, the crystallization temperature of the PEG side chains in HMAx was higher than that in poly(methyl acrylate)‐graft‐poly(ethylene glycol) having a similar value of x, which was considered to be in a disordered state above the melting temperature. In HMAx with x ≤ 40, PEG crystallization was strongly restricted, probably because the PEG microdomains were isolated in the PHMA matrix. As a result, the growth of PEG spherulite was not observed because the PEG crystallization occurred after vitrification of the PHMA segregated domains. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 129–137, 2007     

3族新的不含紧优与几乎紧优的有向双环网络无限族

给出了3族新的不含紧优与几乎紧优的有向双环网络.     

端面泵浦掺Yb3+双包层光纤激光器

从双包层光纤激光器的速率方程出发，得到了光纤中泵浦光与激光的功率分布、输出功率与泵浦功率的关系、腔镜反射率及光纤长度对输出功率的影响。研究结果表明：输出激光功率与光纤长度及后腔镜反射率有很强的依赖关系，存在一个输出功率最大的最佳光纤长度。后腔镜反射率越大，输出激光功率越小；当光纤长度较短时，在输出端放置反射镜使泵浦光高反射，可以提高输出功率和效率。通过对端面泵浦掺Yb3+双包层光纤激光器进行理论分析和实验研究，得到输出激光的中心波长为1088.3nm，斜率效率为33.7%，最大输出功率为1.75W。     

MOCVD生长的GaN单晶膜透射光谱研究

采用MOCVD技术在Al2O3(0001)衬底上生长了GaN薄膜，使用透射光谱、光致发光光谱和X射线双晶衍射三种技术测试了五类GaN薄膜样品，实验结果表明：GaN薄膜透射谱反映出的GaN质量与X射线双晶衍射测量的结果一致，即透射率越大，半高宽越小，结晶质量越好；而X射线双晶衍射峰半高宽最小的样品，其PL谱的带边峰却很弱，这说明PL谱反映样品的光学性能与X射线双晶衍射获得的结晶质量不存在简单的对应关系，同时还报导了一种特殊工艺生长的高阻GaN样品的RBS／沟道结果。     

Application of the stabilization method to interacting resonances

The stabilization method is applied to the case of interacting resonances in the photo-dissociation of van der Waals clusters composed by a rare gas atom bound to a dihalogen molecule. The study of an illustrative two-dimensional model consisting in a T-shaped NeI₂ molecule shows the adequacy of the method whenever the projection of the stabilization wave functions on the assumed prepared initial state is accounted for. The agreement of the fragmentation cross-sections with some previous results using the effective resolvent method and accurate close-coupling calculations is excellent. The method reveals its utility as a complementary tool since allows, through the analysis of the stabilization wave function in terms of zero-order levels, a precise characterization of the resonant states involved. Received 5 April 2002 / Received in final form 24 May 2002 Published online 19 July 2002     

Generalized double affine Hecke algebras of rank 1 and quantized del Pezzo surfaces

Let D be a simply laced Dynkin diagram of rank r whose affinization has the shape of a star (i.e., D₄,E₆,E₇,E₈). To such a diagram one can attach a group G whose generators correspond to the legs of the affinization, have orders equal to the leg lengths plus 1, and the product of the generators is 1. The group G is then a 2-dimensional crystallographic group: G=Z??Z², where ? is 2, 3, 4, and 6, respectively. In this paper, we define a flat deformation H(t,q) of the group algebra C[G] of this group, by replacing the relations saying that the generators have prescribed orders by their deformations, saying that the generators satisfy monic polynomial equations of these orders with arbitrary roots (which are deformation parameters). The algebra H(t,q) for D₄ is the Cherednik algebra of type C^∨C₁, which was studied by Noumi, Sahi, and Stokman, and controls Askey-Wilson polynomials. We prove that H(t,q) is the universal deformation of the twisted group algebra of G, and that this deformation is compatible with certain filtrations on C[G]. We also show that if q is a root of unity, then for generic t the algebra H(t,q) is an Azumaya algebra, and its center is the function algebra on an affine del Pezzo surface. For generic q, the spherical subalgebra eH(t,q)e provides a quantization of such surfaces. We also discuss connections of H(t,q) with preprojective algebras and Painlevé VI.     

Surface characterization and barrier properties of plasma‐modified polyethersulfone/layered silicate nanocomposites

This study describes the preparation of polyethersulfone (PES)/layered silicate nanocomposites (PLSNs) by mixing PES polymer chain into organically‐modified layered silicate in 1‐methyl‐2‐pyrrolidinone (NMP) solution. Both X‐ray diffraction data and transmission electron microscopy images of PLSNs indicate that the silicate layers were almost exfoliated and randomly distributed into the PES matrix. The mechanical and barrier properties of PLSNs show remarkable enhancement in the storage modulus and water/oxygen permeability when compared with that of neat PES matrix. Surfaces modification of PES and PLSN films with various treated times, system pressures, and radio frequency (RF) powers were performed using a mixture of oxygen (O₂) and nitrogen (N₂) plasmas. The topographical and physical properties of plasma‐modified PES and PLSN surfaces were investigated using scanning probe microscopy (SPM), contact‐angle measurements, and X‐ray photoelectron spectroscopy (XPS). These results indicate that the surface roughness of PLSNs with the same condition of plasma modification is lower than that of neat PES matrix and is probably due to the increase of stiffness with the presence of inorganic layered silicates in PES matrix. The surface properties of the PES and PLSNs are also changed from hydrophobic to hydrophilic. The XPS spectra suggest that the exposure of the PES and PLSNs to the plasmas led to the combination of etching reactions of polymer surface initiated by plasma and the following addition reactions of new oxygen‐ and nitrogen‐containing functional groups onto polymer surfaces to change their surface properties. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3185–3194, 2006