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1.
Various tests have been carried out in order to compare the performances of several methods used to solve the non-symmetric linear systems of equations arising from implicit discretizations of CFD problems, namely the scalar advection-diffusion equation and the compressible Euler equations. The iterative schemes under consideration belong to three families of algorithms: relaxation (Jacobi and Gauss-Seidel), gradient and Newton methods. Two gradient methods have been selected: a Krylov subspace iteration method (GMRES) and a non-symmetric extension of the conjugate gradient method (CGS). Finally, a quasi-Newton method has also been considered (Broyden). The aim of this paper is to provide indications of which appears to be the most adequate method according to the particular circumstances as well as to discuss the implementation aspects of each scheme. 相似文献
2.
We have synthesized a homologous series of azoesters consisting of a coumaryl moiety as the end group. Eleven derivatives of this series exhibit mesomorphism. The nematic mesophase is exhibited from ethyl homologue onward, while the smectic phase commences at the pentyl derivative and is exhibited along with the nematic phase up to the hexadecyl derivative. The N-I transition temperatures curves show the usual odd-even effect. All the compounds in this series are thermally stable and exhibit a wide mesomorphic range of nearly 120°C. Their thermal stabilities and other characteristics are discussed. 相似文献
3.
Thomas Lorenz 《Set-Valued Analysis》2008,16(1):1-50
The mutational equations of Aubin extend ordinary differential equations to metric spaces (with compact balls). In first-order
geometric evolutions, however, the topological boundary need not be continuous in the sense of Painlevé–Kuratowski. So this
paper suggests a generalization of Aubin’s mutational equations that extends classical notions of dynamical systems and functional
analysis beyond the traditional border of vector spaces: Distribution-like solutions are introduced in a set just supplied
with a countable family of (possibly non-symmetric) distance functions. Moreover their existence is proved by means of Euler
approximations and a form of “weak” sequential compactness (although no continuous linear forms are available beyond topological
vector spaces). This general framework is applied to a first-order geometric example, i.e. compact subsets of ℝ
N
evolving according to the nonlocal properties of both the current set and its proximal normal cones. Here neither regularity
assumptions about the boundaries nor the inclusion principle are required. In particular, we specify sufficient conditions
for the uniqueness of these solutions.
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5.
It is well-known that Bi-CG can be adapted so that the operations withA
T can be avoided, and hybrid methods can be constructed in which it is attempted to further improve the convergence behaviour. Examples of this are CGS, Bi-CGSTAB, and the more general BiCGstab(l) method. In this paper it is shown that BiCGstab(l) can be implemented in different ways. Each of the suggested approaches has its own advantages and disadvantages. Our implementations allow for combinations of Bi-CG with arbitrary polynomial methods. The choice for a specific implementation can also be made for reasons of numerical stability. This aspect receives much attention. Various effects have been illustrated by numerical examples. 相似文献
6.
Deformations possible (i.e., those satisfying the governing three-dimensional equations of equilibrium and the incompressibility
constraint) within a class of non-symmetric deformations for a neo-Hookean nonlinearly elastic body were determined in [1],
where it was found that only three special cases of the class of deformation fields considered could be solutions. One of
these is the trivial solution, one the solution describing radially symmetric deformation, and the other a (non-symmetric,
non-homogeneous) deformation contained within a family of universal deformations. In this paper, the results reported in [1]
are shown to hold for a substantially broadened deformation field.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
7.
The interaction of four parallel non-symmetric permeable cracks in a piezoelectric/piezomagnetic composite plane subjected to anti-plane shear stress loading was studied by the Schmidt method. The problem was formulated through a Fourier transform into four pairs of dual integral equations, in which unknown variables are jumps of displacements across the crack surfaces. To solve the dual integral equations, the jumps of displacements across the crack surfaces were directly expanded as a series of Jacobi polynomials. Finally, the relationships among the electric displacement, magnetic flux and stress fields near the crack tips were obtained. The results show that the stress, the electric displacement and the magnetic flux intensity factors at the crack tips depend on the lengths and spacing of cracks. It was also revealed that the crack shielding effect is present in piezoelectric/piezomagnetic composites. 相似文献
8.
Four symmetric and non-symmetric chiral liquid crystal dimers containing trifluoromethyl groups, termed as TFBA-PD-TFBA, UEBBA-PD-TFBA, UEBA-PD-TFBA and UEA-PD-TFBA, respectively, have been synthesised and characterised. UEA-PD-TFBA exhibited chiral nematic phase, whereas the other three dimers displayed chiral smectic A phase. X-ray diffraction (XRD) has revealed the structure of the smectic A phase for TFBA-PD-TFBA to be intercalated, whereas that for UEBBA-PD-TFBA and UEBA-PD-TFBA to be monolayer and interdigitated, respectively. In addition, the weaker peak corresponding to a shorter layer spacing was observed for UEBBA-PD-TFBA and UEBA-PD-TFBA. Considering the results of XRD measurements and computer simulations, the structural model corresponding to the shorter layer spacing is assigned as horseshoe-like shape. The absence of smectic behaviour for UEA-PD-TFBA reveals that the weaker aromatic–aromatic interactions cannot stabilise the smectic A phase. 相似文献
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10.
Nakao’s stochastic integrals for continuous additive functionals of zero energy are extended from the symmetric Dirichlet forms setting to the non-symmetric Dirichlet forms setting.It? ’s formula in terms of the extended stochastic integrals is obtained. 相似文献