Analysis of electromagnetic fields in inhomogeneous media by fourier series expansion methods

The model for the angular orientational energy (AOE) has been extended to hexagonal submonolayer domains of Ag electrodeposited at a constant overpotential on a C(0001) surface. These domains which are characterized by an epitaxy angle θ=15±5° and an Ag−Ag distance d Ag−Ag =0.330± 0.016 nm, can be considered as precursors of 3D Ag crystal formation, according to a Volmer-Weber type mechanism. Calculations are based upon a simple Hamiltonian evaluated by introducing the concept of the commensurable unit cell. A Fourier series expansion for the substrate potential was used. Results from the model predict the existence of a commensurable cell in agreement with the experimental data derived from STM imaging.

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Fourier-series expansion of the dark-energy equation of state

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/stz1229 ◽

2019 ◽

Vol 487 (1) ◽

pp. 729-736 ◽

Cited By ~ 4

Author(s):

David Tamayo ◽

J Alberto Vázquez

Keyword(s):

Fourier Series ◽

Dark Energy ◽

Equation Of State ◽

Series Expansion ◽

Energy Equation ◽

Fourier Series Expansion

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Predicting Apple Firmness and Soluble Solids Content Based on Hyperspectral Scattering Imaging Using Fourier Series Expansion

Transactions of the ASABE ◽

10.13031/trans.11890 ◽

2017 ◽

Vol 60 (4) ◽

pp. 1053-1062

Author(s):

Wei Wang ◽

Min Huang ◽

Qibing Zhu

Keyword(s):

Fourier Series ◽

Least Squares ◽

Series Expansion ◽

Fourier Coefficients ◽

Expansion Method ◽

Soluble Solids ◽

Fourier Series Expansion ◽

Support Vector ◽

Soluble Solids Content ◽

Solids Content

Abstract. This article reports on using a Fourier series expansion method to extract features from hyperspectral scattering profiles for apple fruit firmness and soluble solids content (SSC) prediction. Hyperspectral scattering images of ‘Golden Delicious’ (GD), ‘Jonagold’ (JG), and ‘Delicious’ (RD) apples, harvested in 2009 and 2010, were acquired using an online hyperspectral imaging system over the wavelength region of 500 to 1000 nm. The moment method and Fourier series expansion method were used to analyze the scattering profiles of apples. The zeroth-first order moment (Z-FOM) spectra and Fourier coefficients were extracted from each apple, which were then used for developing fruit firmness and SSC prediction models using partial least squares (PLS) and least squares support vector machine (LSSVM). The PLS models based on the Fourier coefficients improved the standard errors of prediction (SEP) by 4.8% to 19.9% for firmness and by 2.4% to 13.5% for SSC, compared with the PLS models using the Z-FOM spectra. The LSSVM models for the prediction set of Fourier coefficients achieved better SEP results, with improvements of 4.4% to 11.3% for firmness and 2.8% to 16.5% for SSC over the LSSVM models for the Z-FOM spectra data and 3.7% to 12.6% for firmness and 5.4% to 8.6% for SSC over the PLS models for the Fourier coefficients. Experiments showed that Fourier series expansion provides a simple, fast, and effective means for improving Keywords: Apples, Firmness, Fourier series expansion, Hyperspectral scattering imaging, Least squares support vector machine, Partial least squares, Soluble solids content.

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