China
Africa
Explore chapters and articles related to this topic
Bifurcation and Chaos
Published in Wai-Kai Chen, Feedback, Nonlinear, and Distributed Circuits, 2018
Michael Peter Kennedy, Vandenberghe Lieven
A quasiperiodic function is one that may be expressed as a countable sum of periodic functions with incommensurate frequencies, i.e., frequencies that are not rationally related. For example, X(t) = sin(t) + sin(2πt) is a quasiperiodic signal. In the time domain, a quasiperiodic signal may look like an amplitude-or phase-modulated waveform.
Plasmon polaritons in 3D graphene periodic structure
Published in Electromagnetics, 2022
Lei Zhang, Lijun Wang, Daqing Liu, Xingfang Jiang, Yong He, Ning Ma
where G(x, y, z) is a quasiperiodic function, i.e., G(x + a, y, z) = G(x, y + a, z) = G(x, y, z + a) = G(x, y, z), except at the interfaces,
Stability of three-dimensional icosahedral quasicrystals in multi-component systems
Published in Philosophical Magazine, 2020
In detail, using the n-dimensional periodic structure and the projection matrix, any d-dimensional quasiperiodic function can be expanded aswhere the Fourier coefficient can be easily obtained by using the n-dimensional -inner product, , with and . , , is the reciprocal primitive vector which satisfies the dual relationship, . Furthermore, the function is the inverse Fourier transform of the Fourier coefficient . From the expansion Equation (5), the d-dimensional quasiperiodic structure can be also treated as a hyperplane of an n-dimensional periodic structure whose orientation is determined by the projection matrix . In order to describe the position of the quasilattice in d-dimensional Fourier space, the notation is utilised to replace in Equation (5). With this notation, the projection method has the following form,where . Despite being similar to the common Fourier series, it should be emphasised that the distribution of is not a periodic lattice. Similarly, the order parameter in multi-component systems can be expanded as follows,where has the same definition as Equation (6).