Related papers: Incorporating Damped Harmonic Oscillator in DSGE M…

The Dicke model, which describes the coupling of an ensemble of spins to a harmonic oscillator, is known for its superradiant phase transition, which can both be observed in the ground state in a purely Hamiltonian setting, as well as in…

Discrete-time systems under aperiodic sampling may serve as a modeling abstraction for a multitude of problems arising in cyber-physical and networked control systems. Recently, model- and data-based stability conditions for such systems…

By using the Feynman-Hibbs prescription for the evolution amplitude, we quantize the system of a damped harmonic oscillator coupled to its time-reversed image, known as Bateman's dual system. The time-dependent quantum states of such a…

We derive a posteriori error estimates for the the scalar wave equation discretized in space by continuous finite elements and in time by the explicit leapfrog scheme. Our analysis combines the idea of invoking extra time-regularity for the…

We consider the question of when it is possible to force a degenerate scalar oscillatory integral to decay as fast as a nondegenerate one by restricting the support to the region where the Hessian determinant of the phase is bounded below.…

In this article, results from the previous paper (I) are applied to calculations of squeezed states for such well-known systems as the harmonic oscillator, free particle, linear potential, oscillator with a uniform driving force, and…

Power system dynamic state estimation (DSE) remains an active research area. This is driven by the absence of accurate models, the increasing availability of fast-sampled, time-synchronized measurements, and the advances in the capability,…

Dynamic systems described by differential equations often involve feedback among system components. When there are time delays for components to sense and respond to feedback, delay differential equation (DDE) models are commonly used. This…

We propose a new estimator for the Generalised Dynamic Factor Model (GDFM) that simplifies estimation by avoiding frequency-domain methods. Our key theoretical insight shows that under reasonable conditions the dynamic common component can…

This paper explores the novel concept of damping controller coordination, which aims to minimize the Total Action metric by identifying an optimal switching combination (on/off) of these controllers. The metric is rooted in power system…

Geometric numerical integration has recently been exploited to design symplectic accelerated optimization algorithms by simulating the Lagrangian and Hamiltonian systems from the variational framework introduced in Wibisono et al. In this…

We consider the nonlinear Duffing oscillator in presence of fractional damping which is characteristic in different physical situations. The system is studied with a smaller and larger damping parameter value, that we call the underdamped…

This paper deals with the phase noise affecting communication systems, where local oscillators are employed to obtain reference signals for carrier and timing synchronizations. The most common discrete-time phase noise channel model is…

Building oscillator based computing systems with emerging nano-device technologies has become a promising solution for unconventional computing tasks like computer vision and pattern recognition. However, simulation and analysis of these…

We investigate the effects of numerical damping for oscillator simulation with spline methods. Numerical damping results in an artificial loss of energy and leads therefore to unreliable results in the simulation of autonomous systems, as…

The time-dependent fields obtained by solving partial differential equations in two and more dimensions quickly overwhelm the analytical capabilities of the human brain. A meaningful insight into the temporal behaviour can be obtained by…

Distributed lag models (DLMs) express the cumulative and delayed dependence between pairs of time-indexed response and explanatory variables. In practical application, users of DLMs examine the estimated influence of a series of lagged…

The overdamped dynamics of a particle is in general affected by its interaction with the surrounding medium, especially out of equilibrium, and when the latter develops spatial and temporal correlations. Here we consider the case in which…

Dynamic Mode Decomposition (DMD) is a data-driven technique to identify a low dimensional linear time invariant dynamics underlying high-dimensional data. For systems in which such underlying low-dimensional dynamics is time-varying, a…

We present a new time discretization scheme adapted to the structure of GENERIC systems. The scheme is variational in nature and is based on a conditional incremental minimization. The GENERIC structure of the scheme provides stability and…