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71.
We consider the plane-strain buckling of a cylindrical shellof arbitrary thickness which is made of a Varga material andis subjected to an external hydrostatic pressure on its outersurface. The WKB method is used to solve the eigenvalue problemthat results from the linear bifurcation analysis. We show thatthe circular cross-section buckles into a non-circular shapeat a value of µ1 which depends on A1/A2 and a mode number,where A1 and A2 are the undeformed inner and outer radii, andµ1 is the ratio of the deformed inner radius to A1. Inthe large mode number limit, we find that the dependence ofµ1 on A1/A2 has a boundary layer structure: it is constantover almost the entire region of 0 < A1/A2 < 1 and decreasessharply from this constant value to unity as A1/A2 tends tounity. Our asymptotic results for A1 1 = O(1) and A1 1 = O(1/n) are shown to agree with the numerical resultsobtained by using the compound matrix method. 相似文献
72.
73.
该文讨论一类带有奇异系数的双重调和方程{△^2u-μu/|x|^s=f(x,u),x∈Ω,u=δu/δv=0,x∈δΩ,这里Ω包含R^N是包含0的有界光滑区域,u∈H0^2(Ω),μ∈R是参数,0≤s≤2,△^2=△△表示双重拉普拉斯算子,当f(x,u)=u^p,p=2N/N-4时,上述问题就是一个临界双重调和问题,该文运用Sobolev-Hardy不等式和变分方法,得到它的解的存在性的一些结果。 相似文献
74.
We treat here of the question of absorbing boundary conditionsfor nonlinear diffusion equations. We use the conditions designedfor the linear equation, we prove them to be well posed forthe nonlinear problem, and through numerical experiments thatthey are well suited for reactiondiffusion equations. 相似文献
75.
76.
A group representation of radiation propagation in an anisotropic medium is developed. The system of wave equations for electromagnetic potentials, obtained from the Maxwell equations with account for the constitutive equations, has been factorized. It is shown that the linear differential operator of the factorized system is orthogonal in transparent crystals and unitary in gyrotropic ones and is represented through the momentum operator. On the basis of the commutation relations for the components of this operator, the eigenvalue problem has been solved and the expression for the change in the radiant energy in the crystal in the form of spherical waves has been obtained. The dependences of the ray and phase velocities and the polarization vectors of waves on the birefringence anisotropy and gyrotropy as well as on the angular momentum, displacement current, and bound charge determining them have been analyzed. It has been established that in the general case of gyrotropic crystals where the nonreciprocity phenomenon takes place and in magnetoelectrics Maxwell equations are represented in a form similar to the Dirac equations and the electromagnetic radiation is correctly described by means of bispinors and is quantized as fermions. 相似文献
77.
Hubert Grudziński 《Reports on Mathematical Physics》2004,53(2):317-328
The eigenvalues and eigenfunctions of an elementary 3-fermion 2-body operator 3P2g∧I1A3∑1≤i≤j≤3P2g(i, j)A3 acting on a 3-particle antisymmetric finite-dimensional Hilbert space have been found. Here Pg2 denotes the projection operator onto a 2-particle antisymmetric function g2, while A3 denotes the 3-particle antisymmetrizing operator. 相似文献
78.
Anuj Mittal Swaminathan Sivaram 《Journal of polymer science. Part A, Polymer chemistry》2005,43(21):4996-5008
A tridentate ligand, BPIEP: 2,6‐bis[1‐(2,6‐diisopropyl phenylimino) ethyl] pyridine, having central pyridine unit and two peripheral imine coordination sites was effectively employed in controlled/“living” radical polymerization of MMA at 90°C in toluene as solvent, CuIBr as catalyst, and ethyl‐2‐bromoisobutyrate (EBiB) as initiator resulting in well‐defined polymers with polydispersities Mw/Mn ≤ 1.23. The rate of polymerization follows first‐order kinetics, kapp = 3.4 × 10?5 s?1, indicating the presence of low radical concentration ([P*] ≤ 10?8) throughout the reaction. The polymerization rate attains a maximum at a ligand‐to‐metal ratio of 2:1 in toluene at 90°C. The solvent concentration (v/v, with respect to monomer) has a significant effect on the polymerization kinetics. The polymerization is faster in polar solvents like, diphenylether, and anisole, as compared to toluene. Increasing the monomer concentration in toluene resulted in a better control of polymerization. The molecular weights (Mn,SEC) increased linearly with conversion and were found to be higher than predicted molecular (Mn,Cal). However, the polydispersity remained narrow, i.e., ≤1.23. The initiator efficiency at lower monomer concentration approaches a value of 0.7 in 110 min as compared to 0.5 in 330 min at higher monomer concentration. The aging of the copper salt complexed with BPIEP had a beneficial effect and resulted in polymers with narrow polydispersitities and higher conversion. PMMA obtained at room temperature in toluene (33%, v/v) gave PDI of 1.22 (Mn = 8500) in 48 h whereas, at 50°C the PDI is 1.18 (Mn = 10,300), which is achieved in 23 h. The plot of lnkapp versus 1/T gave an apparent activation energy of polymerization as (ΔE≠app) 58.29 KJ/mol and enthalpy of equilibrium (ΔH0eq) to 28.8 KJ/mol. Reverse ATRP of MMA was successfully performed using AIBN in bulk as well as solution. The controlled nature of the polymerization reaction was established through kinetic studies and chain extension experiments. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 4996–5008, 2005 相似文献
79.
80.
Hiroto Kudo Nobuhito Ito Keiji Nakajima Masami Ochiai Tadatomi Nishikubo 《Journal of polymer science. Part A, Polymer chemistry》2007,45(19):4421-4429
The polyaddition of fluorine‐containing bis(epoxide)s and fluorine‐containing triazine di(aryl ether)s were examined to give the corresponding fluorine‐containing poly(cyanurate)s. It was observed that the synthesized fluoropolymers had good thermal stabilities and good film‐forming properties. The glass transition temperatures (Tg's) and refractive‐indices (nD's) of synthesized polymers were determined by differential scanning calorimetry and ellipsometry, respectively, and it was found that the values of Tg's and nD's were supported by their fluorine containing ratios and skeletons. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4421–4429, 2007 相似文献