Related papers: Driven damped harmonic oscillator revisited: energ…
We present an approximate analytic expression for thermonuclear reaction rate of charged particles when the cross section contains a single narrow or wide resonance described by a Breit-Wigner shape. The resulting expression is uniformly…
This paper revisits the resonant behavior of a harmonically-forced Duffing oscillator with a specific attention to phase resonance and to its relation with amplitude resonance. To this end, the different families of resonances, namely…
The paper discusses the relationships between electrical and affine differential geometry quantities, establishing a link between frequency and time derivatives of voltage, through the utilization of affine geometric invariants. Based on…
We discover that the energy-integral of time-delay is an adiabatic invariant in quantum scattering theory and corresponds classically to the phase space volume. The integral thus found provides a quantization condition for resonances,…
Energy dissipation rate is an important parameter for nearly every experiment on turbulent flow. Mathematically precise relationships between energy dissipation rate and other measurable statistics for the case of anisotropic turbulence are…
We calculate the change of the properties of a resonator, when coupled to a semiclassical spin by means of the magnetic field. Starting with the Lagrangian of the complete system, we provide an analytical expression for the linear response…
We investigate the energy distribution and quantum thermodynamics in periodically driven polaritonic systems in the stationary state at room temperature. Specifically, we consider an exciton strongly coupled to a harmonic oscillator and…
The global entropy generation rate in the zero-mean oscillatory flow of a Maxwell fluid in a pipe is analyzed with the aim at determining its behavior at resonant flow conditions. This quantity is calculated explicitly using the analytic…
Motivated by numerically modeling surface waves for inviscid Euler equations, we analyze linear models for damped water waves and establish decay properties for the energy for sufficiently regular initial configurations. Our findings give…
A closed expression for the density operator of the damped harmonic oscillator is extracted from the master equation based on the Lindblad theory for open quantum systems. The entropy and effective temperature of the system are subsequently…
Under appropriate assumptions the energy of wave equations with damping and variable coefficients $c(x)u_{tt}-\hbox{div}(b(x)\nabla u)+a(x)u_t =h(x)$ has been shown to decay. Determining the rate of decay for the higher order energies…
We explored vibrations of a single-degree of freedom oscillator with a magneto-rheological damper subjected to kinematic excitations. Using fast and slow scales decoupling procedure we derived an effective damping coefficient in the limit…
We give a physically compelling definition of the instantaneous reactive energy density associated with an arbitrary transient electromagnetic field in vacuum.
We investigate parametric autoresonance: a persisting phase locking which occurs when the driving frequency of a parametrically excited nonlinear oscillator slowly varies with time. In this regime, the resonant excitation is continuous and…
We present a complete set of analytical and invariant expressions for the steady-state density matrix of atoms in a resonant radiation field with arbitrary intensity and polarization. The field drives the closed dipole transition with…
We comment of the widespread belief among some undergraduate students that the amplitude of any harmonic oscillator in the presence of any type of friction, decays exponentially in time. To dispel that notion, we compare the amplitude decay…
Mechanical resonances are used in a wide variety of devices; from smart phone accelerometers to computer clocks and from wireless communication filters to atomic force microscope sensors. Frequency stability, a critical performance metric,…
We prove integrated local energy decay for the damped wave equation on stationary, asymptotically flat space-times in (1 + 3) dimensions. Local energy decay constitutes a powerful tool in the study of dispersive partial differential…
This paper presents a stable finite element approximation for the acoustic wave equation on second-order form, with perfectly matched layers (PML) at the boundaries. Energy estimates are derived for varying PML damping for both the discrete…
It is shown that the single-step periodic signal (periodic telegraph signal) can not produce coherent stochastic resonance for diffusion on a segment with one absorbing and one reflecting end points while the multi-step periodic signal…