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For classical solutions of the incompressible Navier-Stokes equations (NSE) the energybalance between kinetic energy, work done by external forces, and viscous dissipation holds rigorously true. It is shown in this paper that standard Galerkin approximations violate energy balance in the case of plane Couette flow, whereas Poiseuille flow turns out to be energy consistent at any cutoff. The main reason for this discrepancy is seen in the different boundary conditions between the stationary linear shear flow and its disturbances. In our analysis, essentially, we introduce an auxiliary external force field which enforces the finite dimensional Galerkin approximation to fulfil the NSE. It is exemplarily demonstrated how the energy discrepancy decreases when the number of disturbed modes is increased which couple to the stationary shear flow. 相似文献
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Alexander Tsalik 《Mathematical Methods in the Applied Sciences》1995,18(9):697-708
This paper contains new representations of the 3D elasticity and thermoelasticity problems, expressed in terms of regular quaternion functions, which in 3D and 4D have properties analogous to those of complex analytical functions in 2D. The known and some new results, described in the paper, are used to formulate boundary 3D problems, related to the theory. The formulae obtained are very similar to those given by Muskhelishvili for 2D boundary problems. The obtained representations can be used for development of a 3D boundary element method in numerical analysis. 相似文献
79.
P. Dawson J. W. Haas III K. B. Alexander J. Thompson T. L. Ferrell 《Surface science》1991,250(1-3):L383-L388
The intensity of surface enhanced Raman scattering from benzoic acid derivatives on mildly roughened, thermally evaporated Ag films shows a remarkably strong dependence on metal grain size. Large grained (slowly deposited) films give a superior response, by up to a factor of 10, to small grained (quickly deposited) films, with films of intermediate grain size yielding intermediate results. The optical field amplification underlying the enhancement mechanism is due to the excitation of surface plasmon polaritons (SPPs). Since surface roughness characteristics, as determined by STM, remain relatively constant as a function of deposition rate, it is argued that the contrast in Raman scattering is due to differences in elastic grain boundary scattering of SPPs (leading to different degrees of internal SPP damping), rather than differences in the interaction of SPPs with surface inhomogeneities. 相似文献
80.
Alexander L. Rosenberg 《Communications in Mathematical Physics》1992,144(1):41-51
The goal of this work is to describe the irreducible representations of the quantum Heisenberg algebra and the unitary irreducible representation of one of its real forms. The solution of this problem is obtained through the investigation of theleft spectrum of the quantum Heisenberg algebra using the result about spectra of generic algebras of skew differential operators (cf. [R]). 相似文献