Related papers: Instantaneous oscillatory direction and phase for …
We consider a continuum of phase oscillators on the circle interacting through an impulsive instantaneous coupling. In contrast with previous studies on related pulse-coupled models, the stability results obtained in the continuum limit are…
This paper aims to shed some more light on one of the best known phenomena in the field of physics, the Doppler effect, in particular, on its classical version. Although, as mentioned, it is a phenomenon already described more than 150…
Consider the wave equation with heterogeneous coefficients in the homogenization regime. At large times, the wave interacts in a nontrivial way with the heterogeneities, giving rise to effective dispersive effects. The main achievement of…
We formulate a linear phase and frequency response theory for hyperbolic flows, which generalizes phase response theory for autonomous limit cycle oscillators to hyperbolic chaotic dynamics. The theory is based on a shadowing conjecture,…
We develop a timescale synthesis-based probabilistic approach for the modeling of locally stationary signals. Inspired by our previous work, the model involves zero-mean, complex Gaussian wavelet coefficients, whose distribution varies as a…
The manner in which probability amplitudes of paths sum up to form wave functions of orbital angular momentum eigenstates is described. Using a generalization of stationary-phase analysis, distributions are derived that provide a measure of…
Recently, it has been shown (Gavrilov et al., Nonlinear Dyn, 112, 2024) that in a linear solid discrete-continuous system with several slowly time-varying parameters, the amplitude of a strongly localized mode (a trapped wave) can be…
We derive an expression for the phase shift of an atom interferometer in a gravitational field taking into account both the finite duration of the light pulses and the effect of a small perturbing potential added to a stronger uniform…
In the data analysis of oscillatory systems, methods based on phase reconstruction are widely used to characterize phase-locking properties and inferring the phase dynamics. The main component in these studies is an extraction of the phase…
We develop an instanton approach to the non-equilibrium dynamics in one-dimensional random environments. The long time behavior is controlled by rare fluctuations of the disorder potential and, accordingly, by the tail of the distribution…
We consider detecting the evolutionary oscillatory pattern of a signal when it is contaminated by non-stationary noises with complexly time-varying data generating mechanism. A high-dimensional dense progressive periodogram test is proposed…
Amplitude estimation, in its original form, is formulated as phase estimation upon the Grover iterate. Subsequent improvements to the algorithm have eliminated the need for phase estimation and introduced low-depth variants that trade…
We develop a canonical framework for the study of the problem of registration of multiple point processes subjected to warping, known as the problem of separation of amplitude and phase variation. The amplitude variation of a real random…
Transition amplitudes between instantaneous eigenstates of quantum two-level system are evaluated analytically on the basis of a new parametrization of its evolution operator, which has recently been proposed to construct exact solutions.…
In multimode interferometers, the interaction between several modes brings a high level of complexity to the interpretation of its light patterns. With recent advances, it is possible to selectively excite only a couple of modes inside the…
This paper considers sequential adaptive estimation of sparse signals under a constraint on the total sensing effort. The advantage of adaptivity in this context is the ability to focus more resources on regions of space where signal…
The purpose of this paper is to explain a certain dichotomy between the information that the past and future values of a multivariate stochastic process carry about the present. More specifically, vector-valued, second-order stochastic…
Temporal fluctuations in the phase of waves transmitted through a dynamic, strongly scattering, mesoscopic sample are investigated using ultrasonic waves, and compared with theoretical predictions based on circular Gaussian statistics. The…
The extraction of oscillatory components and their properties from different time-frequency representations, such as windowed Fourier transform and wavelet transform, is an important topic in signal processing. The first step in this…
A new method is introduced for analysis of interactions between time-dependent coupled oscillators, based on the signals they generate. It distinguishes unsynchronized dynamics from noise-induced phase slips, and enables the evolution of…