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11.
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
12.
考虑一个奇异摄动罗宾问题在Bakhvalov-Shishkin网格上的迎风差分策略,得到在改进的Shishkin网格上迎风策略是关于ε一致的一阶L∞模收敛的.数值实验证实了此理论结果,显示估计是稳健的. 相似文献
13.
Heterogeneity is typically the result of space variability of soil parameters at different scales. Soil anisotropy may be defined as the spatial persistence in some direction only, across coarse-grid elements, of heterogeneous structures with different characteristic lengths in different directions. One can account for the effect of these structures by upscaling soil properties. Analyzing flow in a strongly anisotropic structured soil at different scales evidences how transverse dispersion reduces to a subscale process, leading to mixing within the conductive structures. 相似文献
14.
Patrick Guidotti 《Mathematische Nachrichten》2004,272(1):32-45
We consider elliptic and parabolic problems in unbounded domains. We give general existence and regularity results in Besov spaces and semi‐explicit representation formulas via operator‐valued fundamental solutions which turn out to be a powerful tool to derive a series of qualitative results about the solutions. We give a sample of possible applications including asymptotic behavior in the large, singular perturbations, exact boundary conditions on artificial boundaries and validity of maximum principles. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
15.
Luis L. Bonilla 《Journal of statistical physics》1987,46(3-4):659-678
A nonlinear Fokker-Planck equation is derived to describe the cooperative behavior of general stochastic systems interacting via mean-field couplings, in the limit of an infinite number of such systems. Disordered systems are also considered. In the weak-noise limit; a general result yields the possibility of having bifurcations from stationary solutions of the nonlinear Fokker-Planck equation into stable time-dependent solutions. The latter are interpreted as non-equilibrium probability distributions (states), and the bifurcations to them as nonequilibrium phase transitions. In the thermodynamic limit, results for three models are given for illustrative purposes. A model of self-synchronization of nonlinear oscillators presents a Hopf bifurcation to a time-periodic probability density, which can be analyzed for any value of the noise. The effects of disorder are illustrated by a simplified version of the Sompolinsky-Zippelius model of spin-glasses. Finally, results for the Fukuyama-Lee-Fisher model of charge-density waves are given. A singular perturbation analysis shows that the depinning transition is a bifurcation problem modified by the disorder noise due to impurities. Far from the bifurcation point, the CDW is either pinned or free, obeying (to leading order) the Grüner-Zawadowki-Chaikin equation. Near the bifurcation, the disorder noise drastically modifies the pattern, giving a quenched average of the CDW current which is constant. Critical exponents are found to depend on the noise, and they are larger than Fisher's values for the two probability distributions considered. 相似文献
16.
一类具有非局部反应扩散方程的奇摄动问题 总被引:7,自引:0,他引:7
本文讨论一类具非局部反应扩散方程的奇摄动初始边值问题,利用迭代法及微分不等式,研究了初始边值问题的存在唯一及其渐近性态。 相似文献
17.
High even order generalizations of the traditional upwind method are introduced to solve second order ODE-BVPs without recasting
the problem as a first order system. Both theoretical analysis and numerical comparison with central difference schemes of
the same order show that these new methods may avoid typical oscillations and achieve high accuracy. Singular perturbation
problems are taken into account to emphasize the main features of the proposed methods.
AMS subject classification (2000) 65L10, 65L12, 65L50 相似文献
18.
本文研究了催化反应非线性奇摄动边值问题.利用微分不等式理论和方法,得到了问题的解的任意次近似渐近估计. 相似文献
19.
In this paper, based on the Lame function and Jacobi elliptic function, the perturbation method is appliedto some nonlinear evolution equations to derive their multi-order solutions. 相似文献
20.
B. Ananthanarayan 《Pramana》2003,61(5):911-920
A review of chiral perturbation theory and recent developments on the comparison of its predictions with experiment is presented.
Some interesting topics with scope for further elaboration are touched upon. 相似文献