scholarly journals Evaluation of Densities and Distributions via Hermite and Generalized Laguerre Series Employing High-Order Expansion Coefficients Determined Recursively via Moments or Cumulants

1985 ◽  
Author(s):  
Albert H. Nuttall
Keyword(s):  
High Order ◽  
Laguerre Series ◽  
Order Expansion ◽  
Expansion Coefficients ◽  
High Order Expansion

High-order expansion of the solution of preliminary orbit determination problem

2012 ◽  
Vol 112 (3) ◽  
pp. 331-352 ◽  
Author(s):  
Roberto Armellin ◽  
Pierluigi Di Lizia ◽  
Michele Lavagna
Keyword(s):  
Orbit Determination ◽  
High Order ◽  
Order Expansion ◽  
High Order Expansion

scholarly journals ASYMPTOTIC EXPANSIONS FOR HIGH-CONTRAST ELLIPTIC EQUATIONS

2013 ◽  
Vol 24 (03) ◽  
pp. 465-494 ◽  
Author(s):  
VICTOR M. CALO ◽  
YALCHIN EFENDIEV ◽  
JUAN GALVIS
Keyword(s):  
Contrast Media ◽  
Elliptic Equations ◽  
Multiscale Model ◽  
High Order ◽  
High Contrast ◽  
Rigorous Analysis ◽  
Order Expansion ◽  
Mesh Resolution ◽  
Local Solutions ◽  
High Order Expansion

In this paper, we present a high-order expansion for elliptic equations in high-contrast media. The background conductivity is taken to be one and we assume the medium contains high (or low) conductivity inclusions. We derive an asymptotic expansion with respect to the contrast and provide a procedure to compute the terms in the expansion. The computation of the expansion does not depend on the contrast which is important for simulations. The latter allows avoiding increased mesh resolution around high conductivity features. This work is partly motivated by our earlier work in [Domain decomposition preconditioners for multiscale flows in high-contrast media, Multiscale Model Simul.8 (2010) 1461–1483] where we design efficient numerical procedures for solving high-contrast problems. These multiscale approaches require local solutions and our proposed high-order expansion can be used to approximate these local solutions inexpensively. In the case of a large-number of inclusions, the proposed analysis can help to design localization techniques for computing the terms in the expansion. In the paper, we present a rigorous analysis of the proposed high-order expansion and estimate the remainder of it. We consider both high- and low-conductivity inclusions.

scholarly journals Texture, Piezoelectricity and Ferroelectricity

1995 ◽  
Vol 23 (4) ◽  
pp. 221-236 ◽  
Author(s):  
L. Fuentes ◽  
O. Raymond
Keyword(s):  
Distribution Function ◽  
Barium Titanate ◽  
Texture Analysis ◽  
Technological Process ◽  
Orientation Distribution Function ◽  
Orientation Distribution ◽  
Odd Order ◽  
Order Expansion ◽  
Orientation Distributions ◽  
Expansion Coefficients

A Quantitative Texture Analysis approach to polycrystal piezoelectric and ferroelectric phenomena is given. Monocrystal longitudinal piezoelectric moduli are expanded in Bunge's symmetry- adapted functional bases. Suitable expansion coefficients are given. Orientation Distribution Function based algorithms for polycrystal piezo-moduli prediction are presented. Significant odd-order expansion terms are calculated and their relation to ghost phenomena is commented. Polycrystal ferroelectricity is characterized. Quantitative describers associated to crystallographic and electric orientation distributions are presented and related. Their evolution during heat and poling processes is discussed. Two computer-simulated examples are analyzed: (a) Texture-modulated longitudinal piezo-modulus is calculated for an ideal quartz single-component texture. (b) Barium titanate fibre texture transformation during a hypothetical technological process is investigated.

Closed-Loop Identification Using Laguerre Series Expansions for Second-Order Plus Time Delay Model

2013 ◽  
Vol 416-417 ◽  
pp. 822-833
Author(s):  
Qi Bing Jin ◽  
Si Nian Li ◽  
Qie Liu ◽  
Qi Wang
Keyword(s):  
Time Delay ◽  
Closed Loop ◽  
Second Order ◽  
High Order ◽  
Series Expansions ◽  
Delay Model ◽  
Order Process ◽  
High Order Process ◽  
Laguerre Series ◽  
Closed Loop Identification

In this paper, a simple yet robust closed-loop identification method based on step response is presented. By approximating the process response firstly using Laguerre series expansions, a high-order process transfer function can be obtained. Then, a linear two-step reduction technique is used to reduce the high-order process to a second-order plus time delay model based on the frequency response data. This method is robust to measurement noise and it also does not need any numerical technique or iterative optimization. Simulation examples show the effectiveness of the proposed method for different process models. Comparison of identification performance between different methods is also illustrated in this work.

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