Related papers: Harmonic analysis of oscillators through standard …
In this article we obtained the harmonic oscillator solution for quaternionic quantum mechanics ($\mathbbm{H}$QM) in the real Hilbert space, both in the analytic method and in the algebraic method. The quaternionic solutions have many…
In the following, we discuss nonlinear simulations of nonlinear dynamical systems, which are applied in technical and biological models. We deal with different ideas to overcome the treatment of the nonlinearities and discuss a novel…
We present a methodology for numerically integrating ordinary differential equations containing rapidly oscillatory terms. This challenge is distinct from that for differential equations which have rapidly oscillatory solutions: here the…
We point out a rather effective approach for solving the time-dependent harmonic oscillator $\ddot q=-\omega^2 q$ under various regularity assumptions. Where $\omega(t )$ is $C^1$ this is reduced to Hamilton equation for the angle variable…
In this paper we give a general solution to the problem of the damped harmonic oscillator under the influence of an arbitrary time-dependent external force. We employ simple methods accessible for beginners and useful for undergraduate…
The model we deal with is the mathematical model for mutually penetrating continua one of which is the carrying medium obeying the wave equation whereas the other one is the oscillating inclusion described by the equation for oscillators.…
In this paper, we present a novel estimation and control strategy to balance a formation of discrete-time oscillators on a circle. We consider the case in which each oscillator only gathers noisy proximity measurements, whose range is lower…
We solve explicitly the two-dimensional harmonic oscillator and the harmonic oscillator in a background magnetic field in noncommutative phase-space without making use of any type of representation. A key observation that we make is that…
We consider a set of N linearly coupled harmonic oscillators and show that the diagonalization of this problem can be put in geometrical terms. The matrix techniques developed here allowed for solutions in both the classical and quantum…
Periodic recurrence is a prominent behavioural of many biological phenomena, including cell cycle and circadian rhythms. Although deterministic models are commonly used to represent the dynamics of periodic phenomena, it is known that they…
Robust online estimation of oscillation frequency belongs to classical problems of system identification and adaptive control. The given harmonic signal can be noisy and with varying amplitude at the same time, as in the case of damped…
We investigate the effects of dichotomous noise added to a classical harmonic oscillator in the form of stochastic time-dependent gain and loss states, whose durations are sampled from two distinct exponential waiting time distributions.…
In a recent paper a slightly modified version of the Bateman system, originally proposed to describe a damped harmonic oscillator, was proposed. This system is really different from the Bateman's one, in the sense that this latter cannot be…
We present here a simple analytical model for self-oscillations in nano-electro-mechanical systems. We show that a field emission self-oscillator can be described by a lumped electrical circuit and that this approach is generalizable to…
Periodically driven parametric oscillators offer a convenient way to simulate classical Ising spins. When many parametric oscillators are coupled dissipatively, they can be analogous to networks of Ising spins, forming an effective coherent…
We study the continuity/discontinuity of the effective boundary condition for periodic homogenization of oscillating Dirichlet data for nonlinear divergence form equations and linear systems. For linear systems we show continuity, for…
The one-dimensional Schr\"{o}dinger equation with the singular harmonic oscillator is investigated. The Hermiticity of the operators related to observable physical quantities is used as a criterion to show that the attractive or repulsive…
In this paper, we consider a class of highly oscillatory Hamiltonian systems which involve a scaling parameter $\varepsilon\in(0,1]$. The problem arises from many physical models in some limit parameter regime or from some time-compressed…
We propose homotopy analysis method in combination with Galerkin projections to approximate the natural response of non-smooth oscillators with discontinuities of type Heaviside, signum, modulus etc. While constructing the homotopy, we…
We show that the equivalent linearization technique, when used properly, enables us to calculate frequency corrections of weakly nonlinear oscillators beyond the first order in nonlinearity. We illustrate the method by applying it to the…