Defect of the five-thirds law using the Wiener-Hermite expansion

1989 ◽  
Vol 55 (5-6) ◽  
pp. 1089-1107 ◽  
Author(s):  
Tung -chen Chung ◽  
William C. Meecham
Keyword(s):  
Hermite Expansion

scholarly journals A modified Tikhonov regularization method based on Hermite expansion for solving the Cauchy problem of the Laplace equation

2020 ◽  
Vol 18 (1) ◽  
pp. 1685-1697
Author(s):  
Zhenyu Zhao ◽  
Lei You ◽  
Zehong Meng
Keyword(s):  
Cauchy Problem ◽  
Laplace Equation ◽  
Tikhonov Regularization ◽  
Regularization Method ◽  
Regularization Parameter ◽  
Solution Process ◽  
Tikhonov Regularization Method ◽  
Hermite Expansion ◽  
The Cauchy Problem ◽  
Ill Posed

Abstract In this paper, a Cauchy problem for the Laplace equation is considered. We develop a modified Tikhonov regularization method based on Hermite expansion to deal with the ill posed-ness of the problem. The regularization parameter is determined by a discrepancy principle. For various smoothness conditions, the solution process of the method is uniform and the convergence rate can be obtained self-adaptively. Numerical tests are also carried out to verify the effectiveness of the method.

Analytical analysis of H polarized line-defect modes in two dimensional photonic crystals based on Hermite expansion of Floquet orders

2007 ◽  
Author(s):  
Peyman Sarrafi ◽  
Amir Hossein Atabaki ◽  
Khashayar Mehrany ◽  
Sina Khorasani ◽  
Bizhan Rashidian ◽  
...  
Keyword(s):  
Photonic Crystals ◽  
Two Dimensional ◽  
Line Defect ◽  
Hermite Expansion ◽  
Defect Modes ◽  
Analytical Analysis

Wiener-Hermite Expansion in Model Turbulence at Large Reynolds Numbers

1964 ◽  
Vol 7 (8) ◽  
pp. 1178 ◽  
Author(s):  
William C. Meecham ◽  
Armand Siegel
Keyword(s):  
Reynolds Numbers ◽  
Hermite Expansion

Convergence Analysis of Grad's Hermite Expansion for Linear Kinetic Equations

2020 ◽  
Vol 58 (2) ◽  
pp. 1164-1194
Author(s):  
Neeraj Sarna ◽  
Jan Giesselmann ◽  
Manuel Torrilhon
Keyword(s):  
Convergence Analysis ◽  
Kinetic Equations ◽  
Hermite Expansion ◽  
Linear Kinetic

Analysis of the stochastic point reactor using Wiener-Hermite expansion

2019 ◽  
Vol 134 ◽  
pp. 250-257 ◽  
Author(s):  
Mohamed El-Beltagy ◽  
Adeeb Noor
Keyword(s):  
Hermite Expansion

A practical comparison between the spectral techniques in solving the SDEs

2019 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mohamed El-Beltagy
Keyword(s):  
Infinite Number ◽  
Random Variables ◽  
Nonlinear Problems ◽  
Hermite Expansion ◽  
Content Type ◽  
Spectral Techniques ◽  
Burgers Turbulence ◽  
Non Gaussian ◽  
Convergence Orders ◽  
Lipschitz Conditions

Purpose The paper aims to compare and clarify the differences and between the two well-known decomposition spectral techniques; the Winer–Chaos expansion (WCE) and the Winer–Hermite expansion (WHE). The details of the two decompositions are outlined. The difficulties arise when using the two techniques are also mentioned along with the convergence orders. The reader can also find a collection of references to understand the two decompositions with their origins. The geometrical Brownian motion is considered as an example for an important process with exact solution for the sake of comparison. The two decompositions are found practical in analysing the SDEs. The WCE is, in general, simpler, while WHE is more efficient as it is the limit of WCE when using infinite number of random variables. The Burgers turbulence is considered as a nonlinear example and WHE is shown to be more efficient in detecting the turbulence. In general, WHE is more efficient especially in case of nonlinear and/or non-Gaussian processes. Design/methodology/approach The paper outlined the technical and literature review of the WCE and WHE techniques. Linear and nonlinear processes are compared to outline the comparison along with the convergence of both techniques. Findings The paper shows that both decompositions are practical in solving the stochastic differential equations. The WCE is found simpler and WHE is the limit when using infinite number of random variables in WCE. The WHE is more efficient especially in case of nonlinear problems. Research limitations/implications Applicable for SDEs with square integrable processes and coefficients satisfying Lipschitz conditions. Originality/value This paper fulfils a comparison required by the researchers in the stochastic analysis area. It also introduces a simple efficient technique to model the flow turbulence in the physical domain.

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