相关论文: Phase Lag Sensitivity Analysis for Numerical Integ…
In the present work, a kind of trigonometric collocation methods based on Lagrange basis polynomials is developed for effectively solving multi-frequency oscillatory second-order differential equations…
In this first of two papers, we present a new method for searching for oscillatory features in the primordial power spectrum. A wide variety of models predict these features in one of two different flavors: logarithmically spaced…
Building oscillator based computing systems with emerging nano-device technologies has become a promising solution for unconventional computing tasks like computer vision and pattern recognition. However, simulation and analysis of these…
We develop an effective description of noise-induced oscillations based on deterministic phase dynamics. The phase equation is constructed to exhibit correct frequency and distribution density of noise-induced oscillations. In the simplest…
Within the expansive domain of optical sciences, achieving the precise characterization of light beams stands as a fundamental pursuit, pivotal for various applications, including telecommunications and imaging technologies. This study…
Sensitivity analysis is a classical and fundamental tool to evaluate the role of a given parameter in a given system characteristic. Because the phase response curve is a fundamental input--output characteristic of oscillators, we developed…
A method is presented for tracing the locus of a specific peak in the frequency response under variation of a parameter. It is applicable to periodic, steady-state vibrations of harmonically forced nonlinear mechanical systems. It operates…
Systems of dynamical elements exhibiting spontaneous rhythms are found in various fields of science and engineering, including physics, chemistry, biology, physiology, and mechanical and electrical engineering. Such dynamical elements are…
We consider the numerical integration of the Gross-Pitaevskii equation with a potential trap given by a time-dependent harmonic potential or a small perturbation thereof. Splitting methods are frequently used with Fourier techniques since…
The resonances of forced dynamical systems occur when either the amplitude of the frequency response undergoes a local maximum (amplitude resonance) or phase lag quadrature takes places (phase resonance). This study focuses on the phase…
Modulation effects such as phasers, flangers and chorus effects are heavily used in conjunction with the electric guitar. Machine learning based emulation of analog modulation units has been investigated in recent years, but most methods…
We introduce a numerical method for the approximation of functions which are analytic on compact intervals, except at the endpoints. This method is based on variable transforms using particular parametrized exponential and…
The exponential fitting technique uses information on the expected behaviour of the solution of a differential problem to define accurate and efficient numerical methods. In particular, exponentially fitted methods are very effective when…
Phase reduction is a general tool widely used to describe forced and interacting self-sustained oscillators. Here we explore the phase coupling functions beyond the usual first-order approximation in the strength of the force. Taking the…
The numerical evaluation of integrals of the form \begin{align*} \int_a^b f(x) e^{ikg(x)}\,dx \end{align*} is an important problem in scientific computing with significant applications in many branches of applied mathematics, science and…
We describe an elementary method for bounding a one-dimensional oscillatory integral in terms of an associated non-oscillatory integral. The bounds obtained are efficient in an appropriate sense and behave well under perturbations of the…
In this paper we revisit some quadrature methods for highly oscillatory integrals of the form $\int_{-1}^1f(x)e^{{\rm i}\omega x}dx, \omega>0$. Exponentially Fitted (EF) rules depend on frequency dependent nodes which start off at the…
We derive a phase-entanglement criterion for two bosonic modes which is immune to number fluc- tuations, using the generalized Moore-Penrose inverse to normalize the phase-quadrature operator. We also obtain a phase-squeezing criterion that…
The phase reduction method for limit cycle oscillators subjected to weak perturbations has significantly contributed to theoretical investigations of rhythmic phenomena. We here propose a generalized phase reduction method that is also…
The phase lag between an applied forcing and a response to that forcing is a fundamen tal parameter in geophysical signal processing. For solid deforming materials, the phase lag between an oscillatory applied stress and the resulting…