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101.
Kazumi Tanuma 《Journal of Elasticity》2007,89(1-3):5-154
The Stroh formalism is a powerful and elegant mathematical method developed for the analysis of the equations of anisotropic
elasticity. The purpose of this exposition is to introduce the essence of this formalism and demonstrate its effectiveness
in both static and dynamic elasticity. The equations of elasticity are complicated, because they constitute a system and,
particularly for the anisotropic cases, inherit many parameters from the elasticity tensor. The Stroh formalism reveals simple
structures hidden in the equations of anisotropic elasticity and provides a systematic approach to these equations. This exposition
is divided into three chapters. Chapter 1 gives a succinct introduction to the Stroh formalism so that the reader could grasp
the essentials as quickly as possible. In Chapter 2 several important topics in static elasticity, which include fundamental
solutions, piezoelectricity, and inverse boundary value problems, are studied on the basis of the Stroh formalism. Chapter
3 is devoted to Rayleigh waves, for long a topic of utmost importance in nondestructive evaluation, seismology, and materials
science. There we discuss existence, uniqueness, phase velocity, polarization, and perturbation of Rayleigh waves through
the Stroh formalism.
The Table of Contents and Index are also provided as Electronic Supplementary Material for online readers at doi: 相似文献
The Table of Contents and Index are also provided as Electronic Supplementary Material for online readers at doi: 相似文献
102.
Thomas Gorm Theting 《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(1-2):57-92
A class of linear parabolic stochastic boundary value problems of Wick-type is studied. The equations are understood in a weak sense on a suitable stochastic distribution space, and existence and uniqueness results are provided. The paper continues to discuss a numerical method for this type of problem, based on a Galerkin type of approximation. Estimates showing linear convergence in time and space are derived, and rate of convergence results for the stochastic dimension are reported. 相似文献
103.
Bjørnar Larssen 《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(3-4):651-673
We consider optimal control problems for systems described by stochastic differential equations with delay (SDDE). We prove a version of Bellman's principle of optimality (the dynamic programming principle) for a general class of such problems. That the class in general means that both the dynamics and the cost depends on the past in a general way. As an application, we study systems where the value function depends on the past only through some weighted average. For such systems we obtain a Hamilton-Jacobi-Bellman partial differential equation that the value function must solve if it is smooth enough. The weak uniqueness of the SDDEs we consider is our main tool in proving the result. Notions of strong and weak uniqueness for SDDEs are introduced, and we prove that strong uniqueness implies weak uniqueness, just as for ordinary stochastic differential equations. 相似文献
104.
Long Wei 《Applied mathematics and computation》2010,217(4):1632-1638
With the aid of computer symbolic computation system such as Maple, an extended tanh method is applied to determine the exact solutions for some nonlinear problems with variable coefficients. Several new soliton solutions and periodic solutions can be obtained if we taking paraments properly in these solutions. The employed methods are straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics. 相似文献
105.
Neel Patel 《Journal of Differential Equations》2018,264(3):1841-1885
We consider continuation criteria for the three-dimensional relativistic Vlasov–Maxwell system. When the particle density, , is compactly supported at , we prove , where and is arbitrarily small, is a continuation criteria. Our continuation criteria is an improvement in the range to the previously best known criteria due to Kunze [7]. We also consider continuation criteria when has noncompact support. In this regime, Luk–Strain [9] proved that is a continuation criteria for . We improve this result to . Finally, we build on another result by Luk–Strain [8]. The authors proved boundedness of momentum support on a fixed two-dimensional plane is a sufficient continuation criteria. We prove the same result even if the plane varies continuously in time. 相似文献
106.
Kristina E. Lipinska-Kalita Oliver A. Hemmers Patricia E. Kalita Steve Gramsh Thomas Hartmann 《Journal of Physics and Chemistry of Solids》2008,69(9):2268-2273
A review of our recent and ongoing extensive high-pressure synchrotron X-ray diffraction and high-pressure optical spectroscopy studies of nanocrystalline composites is presented. These heterophased, nano-architectured composites consist of amorphous matrices with dispersed nanocrystals or quantum dots. We show how besides compositional variations, additional tuning of these glass-derived nanocomposites can be done by exploiting elevated pressure. We examine stability and pressure-driven phase transitions occurring in nanocrystals as well as structural changes occurring in the glass matrix. Finally, we discuss the influence of the glass matrix of a composite on the structural transformations occurring in the embedded nanocrystals. 相似文献
107.
J. K. Ryo J. A. Jaroniec H. Koodziejczyk M. Jaroniec 《Journal of separation science》1979,2(5):236-242
Thin-layer adsorption chromatography with a multicomponent mobile phase is discussed. A new equation for predicting RM-values in TLC with mixed mobile phases using the RM-ValUeS obtained for pure solvents is proposed. This equation takes into account effects of energetic heterogeneity of the adsorbent surface with regard to adsorbed molecules of solvents and solutes. Experimental verification of this equation is presented for RM-data obtained by TLC using a binary mobile phase. 相似文献
108.
微分连续正则化方法与一维声波方程系数反演问题求解 总被引:4,自引:0,他引:4
本文将求解非线性方程组的微分连续法与求解不问题的Tikhonov正则化方法结合起来,形成了兼有大范围收性与稳定性的“微分连续正则化方法”,给出了方法的收敛性分析,文中最后给出的关于一维波动方程反问题的计算实例表明了方法的有效性。 相似文献
109.
胡朝阳 《高校应用数学学报(A辑)》1994,(4):409-415
本文讨论了一般扰动线性差分方程零解的稳定性和解的有界性,得到了一些新结果,推广了[1]和[2]的相应结果。 相似文献
110.
This paper gives the results of an application of the SWEs (shallow water equations) to a part of the Hamburg harbour area, which is a complex flow domain, using the BFG approach, outlined in Part I. The results of a grid doubling procedure generating the desired computational grid from a coarse initial mesh are also presented. A second class of problems which is addressed, demands time-dependent co-ordinate systems. The problems which are solved are the free surface problem for a moving wave which eventually breaks and for a wave which is reflected by the solid walls of a rectangular basin. 相似文献