scispace - formally typeset
Search or ask a question
Topic

Fourier series

About: Fourier series is a research topic. Over the lifetime, 16548 publications have been published within this topic receiving 322486 citations.


Papers
More filters
Journal ArticleDOI
TL;DR: In this paper, a small-scale experiment was conducted (in a 3 m long flume) to study interfacial long-waves in a two-immiscible-fluid system (water and petrol were used).
Abstract: A small-scale experiment was conducted (in a 3 m long flume) to study interfacial long-waves in a two-immiscible-fluid system (water and petrol were used). Experiments and nonlinear theories are compared in terms of wave profiles, phase velocity and mainly frequency--amplitude relationships. As expected, the KdV solitary waves match the experiments for small-amplitude waves for all layer thickness ratios. The characteristics of 'large'-amplitude waves (that is when the crest is close to the critical level - approximately located at mid-depth) asymptotically tend to be predicted by a 'KdV-mKdV' equation containing both quadratic and cubic nonlinear terms. In addition a numerical solution of the complete Euler equations, based on Fourier series expansions, is devised to describe solitary waves of intermediate amplitude. In all cases, solitary interfacial waves in this numerical theory tally with the experimental data. When the layer thicknesses are almost equal (ratio of lower layer to total depth equal to 0.4 or 0.63) both the KdV-mKdV and the numerical solutions match the experimental points.

182 citations

Journal ArticleDOI
TL;DR: In this article, the properties of composite materials with periodic microstructure were analyzed using the Fourier series technique and assuming the homogenization eigenstrain to be piecewise constant, and the coefficients of the overall stiffness tensor of the composite material were expressed analytically in terms of the elastic properties of the constituents.

182 citations

Journal ArticleDOI
TL;DR: The WFS representation is a data smoothing technique that provides the explicit smooth functional estimation of unknown cortical boundary as a linear combination of basis functions and is applied in quantifying the amount of gray matter in a group of high functioning autistic subjects.
Abstract: We present a novel weighted Fourier series (WFS) representation for cortical surfaces. The WFS representation is a data smoothing technique that provides the explicit smooth functional estimation of unknown cortical boundary as a linear combination of basis functions. The basic properties of the representation are investigated in connection with a self-adjoint partial differential equation and the traditional spherical harmonic (SPHARM) representation. To reduce steep computational requirements, a new iterative residual fitting (IRF) algorithm is developed. Its computational and numerical implementation issues are discussed in detail. The computer codes are also available at http://www.stat.wisc.edu/ ~mchung/softwares/weighted-SPHARM/weighted-SPHARM.html . As an illustration, the WFS is applied in quantifying the amount of gray matter in a group of high functioning autistic subjects. Within the WFS framework, cortical thickness and gray matter density are computed and compared

181 citations


Network Information
Related Topics (5)
Boundary value problem
145.3K papers, 2.7M citations
89% related
Differential equation
88K papers, 2M citations
88% related
Eigenvalues and eigenvectors
51.7K papers, 1.1M citations
86% related
Numerical analysis
52.2K papers, 1.2M citations
86% related
Partial differential equation
70.8K papers, 1.6M citations
86% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023270
2022702
2021511
2020510
2019589
2018580