On Double Chebyshev Series Approximation

Basu, Nirabhra

doi:10.1137/0710045

Cited by 27 publications

(23 citation statements)

References 5 publications

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“…Our data closely matched with Chebyshev series bivariate polynomial function [15] of order 6, which is given as in Equation (4). Variable x in the equation corresponds to the initial Stokes number and variable y corresponds to time.…”

Section: Is the Number Of Grid Points And Msupporting

confidence: 57%

Direct numerical simulation of preferential particle concentration in decaying turbulence under the influence of magnetic field

Kondaraju

Lee

2010

Numerical Methods in Fluids

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We present the preferential concentration of particles in the decaying turbulence. The change in Kolmogorov time scales with the decaying turbulence leads to the change in the maximum preferential concentration of particles of different sizes. We show a correlation for standard deviation of concentration with both time and the initial Stokes number for turbulence which is decaying under the influence of magnetic field. This allows us to predict the change in the maximum concentration of particles corresponding to the initial Stokes number. Spatial distribution of solid particles in fluid has interested many researchers because of the compressible motion shown by the particles even in the incompressible flows. Inhomogeneous distribution of particles is the consequence of the difference in densities between the particles and the fluid. This clustering behavior of particles has physical applications including rain generation, [1], pollutant distribution and combustion [2], and planet formation [3]. Many experiments and numerical simulations have been conducted to understand this phenomenon, known as preferential

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Section: Is the Number Of Grid Points And Msupporting

confidence: 57%

Direct numerical simulation of preferential particle concentration in decaying turbulence under the influence of magnetic field

Kondaraju

Lee

2010

Numerical Methods in Fluids

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“…Since the function yit) is Recalling matrix representations (4), (6), (8) and (15), substituting in equation (2) and simplifying the resulting equation, we get…”

Section: Methods For Solutionmentioning

confidence: 99%

Chebyshev series solutions of Fredholm integral equations

Sezer

Doğan

1996

International Journal of Mathematical Education in Science and

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A matrix method for approximately solving certain linear and non-linear Fredholm integral equations of the second kind is presented. The solution involves a truncated Chebyshev series approximation. The method is based on first taking the truncated Chebyshev series expansions of the functions in equation and then substituting their matrix forms into the equation. Thereby the equation reduces to a matrix equation, which corresponds to a linear or non-linear system of algebraic equations with unknown Chebyshev coefficients. In addition, some equations considered by other authors are solved in terms of Chebyshev polynomials and the results are compared.

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“…where K 3C and K 5C are again the same with the coefficients used in expansion (15). By analyzing the resulting circuit, the phasor amplitudẽ i out;2x 1 Àx 2 can be determined and thus the current i out;2x 1 Àx 2 : Fig.…”

Section: Appendixmentioning

confidence: 99%

“…Caution should be exercised when selecting the expansion interval [-A,A], which, by definition, should be equal to the excitation signal's amplitude. If a nonlinearity is controlled by two or more voltages, multidimensional Chebyshev expansions can be applied [15].…”

Section: Chebyshev Seriesmentioning

confidence: 99%

Large and small signal distortion analysis using modified Volterra series

Sarkas

Mavridis

Papamichail

et al. 2007

Analog Integr Circ Sig Process

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A new approach to the Volterra analysis of analog circuits is presented. Volterra analysis is widely used for the calculation of harmonic and intermodulation distortion products. However, the analysis is limited to circuits experiencing small signal excitations and becomes inaccurate when the input signal amplitude increases, especially when MOS transistors are involved. In this paper, we analyze the cause of this drawback, which is no other than the Taylor series' convergence properties. Moreover, we propose a solution, by calculating the nonlinearity coefficients using a different type of polynomial expansion, the Chebyshev series. This replacement improves significantly the capabilities of Volterra analysis. We also present results comparing Chebyshev series with other types of polynomial expansions. Finally, we apply the proposed method to analyze the intermodulation distortion (IMD) of a CMOS RF power amplifier, both in the small and the large signal regimes.

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On Double Chebyshev Series Approximation

Cited by 27 publications

References 5 publications

Direct numerical simulation of preferential particle concentration in decaying turbulence under the influence of magnetic field

Direct numerical simulation of preferential particle concentration in decaying turbulence under the influence of magnetic field

Chebyshev series solutions of Fredholm integral equations

Large and small signal distortion analysis using modified Volterra series

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