Related papers: Modulated Oscillations in Three Dimensions
Wide-area synchrophasor ambient measurements provide a valuable data source for real-time oscillation mode monitoring and analysis. This paper introduces a novel method for identifying inter-area oscillation modes using wide-area ambient…
We study the behaviour of the spectrum of a family of one-dimensional operators with periodic high-contrast coefficients as the period goes to zero, which may represent e.g. the elastic or electromagnetic response of a two-component…
One-dimensional signal decomposition is a well-established and widely used technique across various scientific fields. It serves as a highly valuable pre-processing step for data analysis. While traditional decomposition techniques often…
We extend the notions of multipole and subsystem symmetries to more general {\it spatially modulated} symmetries. We uncover two instances with exponential and (quasi)-periodic modulations, and provide simple microscopic models in one, two…
We introduce various optimization schemes for highly accurate calculation of the eigenvalues and the eigenfunctions of the one-dimensional anharmonic oscillators. We present several methods of analytically fixing the nonlinear variational…
The entrainment between weakly-coupled nonlinear oscillators, as well as between complex signals such as those representing physiological activity, is frequently assessed in terms of whether a stable relationship is detectable between the…
The full non-linear evolution of the tidal instability is studied numerically in an ellipsoidal fluid domain relevant for planetary cores applications. Our numerical model, based on a finite element method, is first validated by reproducing…
Partially coherent electromagnetic sources with cylindrical symmetry and infinite extent radiating outwards are introduced. Their $3\times3$ cross-spectral density matrix is given through expansions of the field components in terms of basis…
This paper investigates the inverse random source problem for elastic waves in three dimensions, where the source is assumed to be driven by an additive white noise. A novel computational method is proposed for reconstructing the variance…
A number of polarization estimators have been developed for a variety of astrophysical applications to compensate measurements of linear polarization for a bias contributed by the instrumental noise. Most derivations of the estimators…
In this paper we present a study of the non-linear effects of anharmonicity of the potential of the simple pendulum. In a theoretical reminder we highlight that anharmonicity of the potential generates additional harmonics and the…
We propose a simple statistical model of three-dimensionally anisotropic, intermittent, strong Alfv\'enic turbulence, incorporating both critical balance and dynamic alignment. Our model is based on log-Poisson statistics for Elsasser-field…
A mechanism for the localization of spatially periodic, self-organized patterns in anisotropic media which requires systems extended in all three spatial dimensions is presented: When the anisotropy axis is twisted the pattern becomes…
Inequalities are established for certain trilinear scalar-valued functionals. These functionals act on measurable functions of one real variable, are defined by integration over two- or three-dimensional spaces, and are controlled in terms…
A simple model coupling a one-dimensional beam particle to a one-dimensional harmonic oscillator is used to explore complementarity and entanglement. This model, well-known in the inelastic scattering literature, is presented under three…
Concatenated modal interferometers based multipoint sensing system for detection of instantaneous amplitude, frequency, and phase of mechanical vibrations is proposed and demonstrated. The sensor probes are fabricated using identical…
We compute the spectrum of the Feigenbaum period-doubling operator in the space of bounded analytical functions in an ellipse. The spectral properties of the period-doubling operator in this space are not the same as in the space of even…
An estimation method is presented for polynomial phase signals, i.e., those adopting the form of a complex exponential whose phase is polynomial in its indices. Transcending the scope of existing techniques, the proposed estimator can…
Complex systems are often non-stationary, typical indicators are continuously changing statistical properties of time series. In particular, the correlations between different time series fluctuate. Models that describe the multivariate…
Anderson localization of particles -- the complete halt of wave transport through multiple scattering and phase coherence -- is a paradigmatic manifestation of quantum interference in disordered media. In three dimensions, the scaling…