Topic
Fourier series
About: Fourier series is a research topic. Over the lifetime, 16548 publications have been published within this topic receiving 322486 citations.
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TL;DR: In this paper, the authors developed a general formalism for computing simple Cartesian path integrals for harmonic and anharmonic systems, where analytical results can be derived, both imaginary and complex time evolution is discussed.
Abstract: The recently introduced method of partial averaging is developed into a general formalism for computing simple Cartesian path integrals. Examples of its application to both harmonic and anharmonic systems are given. For harmonic systems, where analytical results can be derived, both imaginary and complex time evolution is discussed. For two representative anharmonic systems, Monte Carlo path integral simulations of the imaginary time propagator (statistical density matrix) are presented. Connections with other Cartesian path integral techniques are stressed.
119 citations
TL;DR: The plane-wave-expansion approach dedicated to the simulation of periodic devices has been extended to 1-3 connectivity piezoelectric composite structures and the model is reported and compared to previously published analyses of this problem.
Abstract: The plane-wave-expansion (PWE) approach dedicated to the simulation of periodic devices has been extended to 1-3 connectivity piezoelectric composite structures. The case of simple but actual piezoelectric composite structures is addressed, taking piezoelectricity, acoustic losses, and electrical excitation conditions rigorously into account. The material distribution is represented by using a bidimensional Fourier series and the electromechanical response is simulated using a Bloch-Floquet expansion together with the Fahmy-Adler formulation of the Christoffel problem. Application of the model to 1-3 connectivity piezoelectric composites is reported and compared to previously published analyses of this problem.
118 citations
TL;DR: In this article, a theory of Fourier coefficients for modular forms on the split exceptional group G2 over ℚ was developed, where the coefficients are derived from the Fourier coefficient theory of modular forms.
Abstract: We develop a theory of Fourier coefficients for modular forms on the split exceptional group G2 over ℚ.
118 citations
Journal Article•
TL;DR: In this paper, a method of finding a first approximation to a crustal magnetization distribution from inversion of satellite magnetic anomaly data is described, where magnetization is expressed as a Fourier series in a segment of spherical shell.
Abstract: A method of finding a first approximation to a crustal magnetization distribution from inversion of satellite magnetic anomaly data is described. Magnetization is expressed as a Fourier series in a segment of spherical shell. Input to this procedure is an equivalent source representation of the observed anomaly field. Instability of the inversion occurs when high frequency noise is present in the input data, or when the series is carried to an excessively high wave number. Preliminary results are given for the United States and adjacent areas.
118 citations
TL;DR: In this paper, a new method for the analysis of high frequency vibrations is presented in which the vibration of each component of the system is represented in terms of a homogeneous random wave field.
118 citations