相关论文: On frequencies of small oscillations of some dynam…

In a previous paper (Corrigan-Sasaki), many remarkable properties of classical Calogero and Sutherland systems at equilibrium are reported. For example, the minimum energies, frequencies of small oscillations and the eigenvalues of Lax pair…

We extend some previous results of our work [1] on the error of the averaging method, in the one-frequency case. The new error estimates apply to any separating family of seminorms on the space of the actions; they generalize our previous…

This letter proposes an analytical approach to formulate the power system oscillation frequency under a large disturbance. A fact is revealed that the oscillation frequency is only the function of the oscillation amplitude when the system's…

We report on the possibilities of using the method of normal fundamental systems for solving some problems of oscillation theory. Large elastic dynamical systems with continuous and discrete parameters are considered, which have many…

An astonishingly simple analytical frequency approximation formula for a class of strongly nonlinear oscillators is derived and applied to various example systems yielding useful quick estimates.

Explicit solutions of the classical Calogero (rational with/without harmonic confining potential) and Sutherland (trigonometric potential) systems is obtained by diagonalisation of certain matrices of simple time evolution. The method works…

This article studies typical dynamics and fluctuations for a slow-fast dynamical system perturbed by a small fractional Brownian noise. Based on an ergodic theorem with explicit rates of convergence, which may be of independent interest, we…

Variations of frequency separations of low-degree p-modes are studied over the solar activity cycle. The separations studied are obtained from the frequencies of low-degree p-modes of the Global Oscillation Network Group (GONG). 10.7 cm…

Fluctuations and structure across a wide range of spatial and temporal scales are frequently studied in the solar wind. The properties of the low-frequency fluctuations are of relevance to turbulent energy injection into the plasma and the…

The radiation loss of small amplitude oscillons (very long-living, spatially localized, time dependent solutions) in one dimensional scalar field theories is computed in the small-amplitude expansion analytically using matched asymptotic…

We consider a perturbed integrable system with one frequency, and the approximate dynamics for the actions given by averaging over the angle. The classical theory grants that, for a perturbation of order epsilon, the error of this…

Consider a periodically forced nonlinear system which can be presented as a collection of smaller subsystems with pairwise interactions between them. Each subsystem is assumed to be a massive point moving with friction on a compact surface,…

We study the local structure and the regularity of free boundaries of segregated critical configurations involving the square root of the laplacian. We develop an improvement of flatness theory and, as a consequence of this and Almgren's…

This paper is a review of the dynamics of a system of planets. It includes the study of averaged equations in both non-resonant and resonant systems and shows the great deal of situations in which the angle between the two semi-major axes…

The first part of this paper aims at illustrating the intense scientific activity in the field of stellar rotation although, for sake of shortness, we cannot be exhaustive nor give any details. The second part is devoted to the rotation as…

The small oscillations of an arbitrary scleronomous system subject to time-independent non dissipative forces are discussed. The linearized equations of motion are solved by quadratures. As in the conservative case, the general integral is…

We describe a method for calculating the roots of special functions satisfying second order linear ordinary differential equations. It exploits the recent observation that the solutions of a large class of such equations can be represented…

Numerical simulations show that a massive real scalar field in a nonlinear theory can form long-lived oscillating localized states. For a self-interacting scalar on a fixed background these objects are named oscillons, while for the…

Multiple scattering of wave in strong heterogeneity can cause resonance-like wave anomaly where the signal exhibits low-frequency, high intensity, and slowly propagating wave packet velocity. For example, long period event in volcanic…

Kawaler et al. (1985) present a variational expression for the eigenfrequencies associated with stellar oscillations. We highlight and correct a typographical error in the weight functions appearing in these expressions, and validate the…