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We perform a detailed study of the dynamics of a nonlinear, one-dimensional oscillator driven by a periodic force under hysteretic damping, whose linear version was originally proposed and analyzed by Bishop in [1]. We first add a small…
This paper investigates resonance transmission in two unidirectionally coupled Duffing oscillators with fractional damping, where the driver is harmonically forced and the receiver is connected through a linear coupling spring. Particular…
For dynamical systems that can be modelled as asymptotically stable linear systems forced by Gaussian noise, this paper develops methods to infer or estimate their modes from observations in real time. The modes can be real or complex. For…
Since Galileo's time, the pendulum has evolved into one of the most exciting physical objects in mathematical modeling due to its vast range of applications for studying various oscillatory dynamics, including bifurcations and chaos, under…
Mechanical dissipation poses an ubiquitous challenge to the performance of nanomechanical devices. Here we analyze the support-induced dissipation of high-stress nanomechanical resonators. We develop a model for this loss mechanism and test…
In this paper problems that arose with the introduction of distance learning in physics at the Technical University of Sofia due to the COVID-19 pandemic and the imposition of video recording of laboratory exercises are indicated. It was…
In a recent article, we have advanced a semiclassical theory of quantum circuits with discrete charge and electrical resistance. In this work, we present a few elementary applications of this theory. For the zero resistance, inductive…
The extension of quantum trajectory theory to incorporate realistic imperfections in the measurement of solid-state qubits is important for quantum computation, particularly for the purposes of state preparation and error-correction as well…
The periodically driven harmonic oscillator with damping is one of the most elementary and trusted models in physics and normally applied in its steady state, disregarding specific initial conditions and associated transients. For example,…
Models of physical systems are used to explain and predict experimental results and observations. When students encounter discrepancies between the actual and expected behavior of a system, they revise their models to include the newly…
We use symmetry considerations to investigate how damped modes affect pattern selection in multi-frequency forced Faraday waves. We classify and tabulate the most important damped modes and determine how the corresponding resonant triad…
The Duffing oscillator is a nonlinear extension of the ubiquitous harmonic oscillator and as such plays an outstanding role in science and technology. Experimentally, the system parameters are determined by a measurement of its response to…
Nonlinear damping, the change in damping rate with the amplitude of oscillations plays an important role in many electrical, mechanical and even biological oscillators. In novel technologies such as carbon nanotubes, graphene membranes or…
We apply adaptive feedback for the partial refrigeration of a mechanical resonator, i.e. with the aim to simultaneously cool the classical thermal motion of more than one vibrational degree of freedom. The feedback is obtained from a neural…
We demonstrate how to derive the exponential decrease of amplitude and an excellent approximation of the energy decay of a weakly damped harmonic oscillator without solving the associated equation of motion and without insight into the…
For the paradigmatic case of the damped quantum harmonic oscillator we present two measurement-based feedback schemes to control the stability of its fixed point. The first scheme feeds back a Pyragas-like time-delayed reference signal and…
We propose a model for frequency-dependent damping in the linear wave equation. After proving well-posedness of the problem, we study qualitative properties of the energy. In the one-dimensional case, we provide an explicit analysis for…
Approximate formulas are derived to describe energy loss in a harmonic oscillator that experiences three distinct damping mechanisms: constant-magnitude (Coulomb), velocity-proportional (Stokes), and velocity-squared (Newton), using…
Inference and prediction under partial knowledge of a physical system is challenging, particularly when multiple confounding sources influence the measured response. Explicitly accounting for these influences in physics-based models is…
We investigate in this paper the superharmonic and subharmonic resonances of forced modified Rayleigh-Duffing oscillator. We analyse this equation by the method of multiple scales and we obtain superharmonic, subharmonic resonances…