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21.
Bieniasz LK 《Computational Biology and Chemistry》2003,27(3):315-325
Accurate calculation of concentration gradients at the boundaries is crucial in electrochemical kinetic simulations, owing to the frequent occurrence of gradient-dependent boundary conditions, and the importance of the gradient-dependent electric current. By using the information about higher spatial derivatives of the concentrations, contained in the time-dependent, kinetic reaction-diffusion partial differential equation(s) in one-dimensional space geometry, under appropriate assumptions it is possible to increase the accuracy orders of the conventional, one-sided n-point finite-difference formulae for the concentration gradients at the boundaries, without increasing n. In this way a new class of high order accurate gradient approximations is derived, and tested in simulations of potential-step chronoamperometric and current-step chronopotentiometric transients for the Reinert-Berg system. The new formulae possess advantages over the conventional gradient approximations. For example, they allow one to obtain a third order accuracy by using two space points only, or fourth order accuracy by using three points, and yet they yield smaller errors than the conventional four-point, or five-point formulae, respectively. Needing fewer points, for approximating the gradients with a given accuracy, simplifies also the solution of the linear algebraic equations arising from the application of implicit time integration schemes. 相似文献
22.
In certain species of moths and butterflies iridescent colors arise from subwavelength diffractive surface corrugation of
the wing-scales. The optical properties of such structures depend strongly on wavelength, incidence angle, and state of polarization
of illuminating radiation, and the viewing angle. In this paper, we study the reflection spectra of the wings of the Morpho didius butterfly by simulating a double-layered model of a transverse cross-section comprised of the ground scale and the cover
scale. Each layer contains a certain quasi-periodic arrangement of tree-like subwavelength microstructures. The simulation
is done using a high accuracy nonstandard finite-difference time-domain (FDTD) method in two dimensions. We assume that the
structure is made of a slightly lossy dielectric material. The wavelength dependence of the complex refractive index for the
ground scale of Morpho didius is assumed to be similar to that of Morpho sulkowskyi. The complex refractive index in the latter case was obtained by comparing the computed reflection/transmission spectra with
corresponding experimental measurements at normal incidence. 相似文献
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26.
N. A. Baranov L. I. Turchak 《Computational Mathematics and Mathematical Physics》2007,47(7):1171-1178
A finite-difference method is proposed for solving the Kolmogorov-Feller integro-differential equation. The numerical scheme constructed is an unconditionally stable marching scheme, and the boundary conditions are determined on the basis of an explicit solution to the original equation at boundary points. 相似文献
27.
Hongxing Zheng Lihui Jiang 《International Journal of Infrared and Millimeter Waves》2004,25(5):855-864
This paper deals with the two dimensional (2-D) infrared photonic crystal slab with an air-bridge structure featuring defect waveguides in which the optical propagation properties were obtained by measurements of transmission spectra. 3-D finite-difference time-domain (FDTD) simulations have revealed the appearance of four defect propagation modes for the band structure and transmission spectra in the air-bridge slab. These defect modes were experimentally identified in the measured transmission spectra. 相似文献
28.
In this paper the methods of wave theory based prestack depth migration and their implementation are studied. Using the splitting of wave operator, the wavefield extrapolation equations are deduced and the numerical schemes are presented. The numerical tests for SEG/EAEG model with MPI are performed on the PC-cluster. The numerical re- 相似文献
29.
E. B. Tereshin V. A. Trofimov M. V. Fedotov 《Computational Mathematics and Mathematical Physics》2006,46(1):154-164
Conservative finite-difference schemes are constructed for the problems of self-action of a femtosecond laser pulse and of second-harmonic generation in a one-dimensional nonlinear photonic crystal with nonreflecting boundary conditions. The invariants of the governing equations are found taking into account these conditions. Nonreflecting conditions substantially improve the efficiency of conservative finite-difference schemes used in the modeling of complex nonlinear effects in photonic crystals, which require much smaller steps in space and time than those used in the case of linear propagation. The numerical experiments performed show that the boundary reflects no more than 0.01% of the transmitted energy, which corresponds to the truncation error in the boundary conditions. The amplitude of the reflected pulse is less than that of the pulse transmitted through the boundary by two (and more) orders of magnitude. The simulation is based on the approach proposed by the authors for the given class of problems. 相似文献
30.
Yu. V. Kokhanenko 《International Applied Mechanics》2006,42(9):1045-1051
A thin rectangular sandwich plate with isotropic linear elastic layers is considered. The plate is in a plane-strain state
under uniaxial compression. An exact statement of the buckling problem is given. Its approximate solution is found by the
finite-difference method. The concept of base scheme is used to formulate discrete problems in explicit and compact form.
As an example, the critical parameters of the plate are calculated using a computation optimization procedure. Its efficiency
is demonstrated
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 9, pp. 98–105, September 2006. 相似文献