Damped oscillators: A continuous model for velocity dependent drag

Polynomial Chaos Expansions For Damped Oscillators

Uncertainty quantification is the state-of-the-art framework dealing with uncertainties arising in all kind of real-life problems. One of the framework’s functions is to propagate uncertainties from the stochastic input factors to the output quantities of interest, hence the name uncertainty propagation. To this end, polynomial chaos expansions (PCE) have been effectively used in a wide variety...

Damped Harmonic Oscillators in the Holomorphic Representation

Quantum dynamical semigroups are applied to the study of the time evolution of harmonic oscillators, both bosonic and fermionic. Explicit expressions for the density matrices describing the states of these systems are derived using the holomorphic representation. Bosonic and fermionic degrees of freedom are then put together to form a supersymmetric oscillator; the conditions that assure supers...

Hyperchaotic circuit with damped harmonic oscillators

A simple fourth-order hyperchaotic circuit with damped harmonic oscillators is described. ANP3 and PSpice simulations including an eigenvalue study of the linearized Jacobian are presented together with a hardware implementation. The circuit contains two inductors with series resistance. two ideal capacitors and one non-linear active conductor. The Lyapunov exponents are presented to confirm th...

Optimal Phase-Control Strategy for Damped-Driven Duffing Oscillators.

Phase-control techniques of chaos aim to extract periodic behaviors from chaotic systems by applying weak harmonic perturbations with a suitably chosen phase. However, little is known about the best strategy for selecting adequate perturbations to reach desired states. Here we use experimental measures and numerical simulations to assess the benefits of controlling individually the three terms ...

The Velocity Dependence of Aerodynamic Drag: a Primer for Mathematicians