相关论文: Frequency map analysis and quasiperiodic decomposi…
A set of semi-analytical techniques based on Fourier analysis is used to solve wave scattering problems in variously shaped waveguides with varying normal admittance boundary conditions. Key components are newly developed conformal mapping…
We describe a method for analyzing the phase space structures of Hamiltonian systems. This method is based on a time-frequency decomposition of a trajectory using wavelets. The ridges of the time-frequency landscape of a trajectory, also…
This paper introduces the Frequency-Domain Differential Corrector (FDDC), a model-agnostic approach for constructing quasi-periodic orbits (QPOs) across a range of dynamical regimes. In contrast to existing methods that explicitly enforce…
Quasi-integrable Hamiltonian systems are of great interest in many research fields of physics and mathematics. In these systems, the phase space has regular and chaotic trajectories. These trajectories depend in part on the magnitude of…
Time-frequency (TF) analysis is a powerful tool for exploring ultrafast dynamics in atoms and molecules. While some TF methods have demonstrated their usefulness and potential in several of quantum systems, a systematic comparison among…
Phase-space analysis or time-frequency analysis can be thought as Fourier analysis simultaneously both in time and in frequency, originating from signal processing and quantum mechanics. On groups having unitary Fourier transform, we…
This paper develops a harmonic-domain framework for systems with variable fundamental frequency. A variable-frequency sliding Fourier decomposition is introduced in the phase domain, together with necessary and sufficient conditions for…
We derive a systematic high-frequency expansion for the effective Hamiltonian and the micromotion operator of periodically driven quantum systems. Our approach is based on the block diagonalization of the quasienergy operator in the…
Traditional resolvent analysis is a powerful framework for identifying the most amplified input-output structures in fluid flows from a stationary base state. Extending this resolvent analysis to periodic base flows poses computational…
The paper develops a method for discrete computational Fourier analysis of functions defined on quasicrystals and other almost periodic sets. A key point is to build the analysis around the emerging theory of quasicrystals and diffraction…
Analyzing time series in the frequency domain enables the development of powerful tools for investigating the second-order characteristics of multivariate processes. Parameters like the spectral density matrix and its inverse, the coherence…
Area preserving maps provide the simplest and most accurate means to visualize and quantify the behavior of nonlinear systems. Convenience of the mapping equations of motion for investigation of transition to chaotic behavior in dynamics of…
Frequently, transient changes in physiological signals, such as ECG morphology, precede or follow a rate change. Current methods for visualizing morphology allow only the tracking of preselected changes, severely limiting analytical…
For a long time, many methods are developed to make temporal signal analyses based on time series. However, for geographical systems, spatial signal analyses are as important as temporal signal analyses. Nonstationary spatial and temporal…
New experimental techniques based on non-linear ultrafast spectroscopies have been developed over the last few years, and have been demonstrated to provide powerful probes of quantum dynamics in different types of molecular aggregates,…
The frequency response analysis describes the steady-state responses of a system to sinusoidal inputs at different frequencies, providing control engineers with an effective tool for designing control systems in the frequency domain.…
We introduce multi-frequency vector diffusion maps (MFVDM), a new framework for organizing and analyzing high dimensional datasets. The new method is a mathematical and algorithmic generalization of vector diffusion maps (VDM) and other…
Galactic all-sky maps at very disparate frequencies, like in the radio and $\gamma$-ray regime, show similar morphological structures. This mutual information reflects the imprint of the various physical components of the interstellar…
We describe an analytical method for computing the orbital parameters of a planet from the periodogram of a radial velocity signal. The method is very efficient and provides a good approximation of the orbital parameters. The accuracy is…
Triadic interactions are the fundamental mechanism of energy transfer in fluid flows. This work introduces bispectral mode decomposition as a direct means of educing flow structures that are associated with triadic interactions from…