Related papers: Studies on Frequency Response Optimized Integrator…
We address two aspects of the dynamics of the forced Duffing oscillator which are relevant to the technology of micromechanical devices and, at the same time, have intrinsic significance to the field of nonlinear oscillating systems. First,…
This paper discusses and summarizes some results on complex variables that are very useful in fractional-order systems analysis and design, specifically when the system is analyzed in the frequency domain. The author hopes that this…
The operator fidelity is a measure of the information-theoretic distinguishability between perturbed and unperturbed evolutions. The response of this measure to the perturbation may be formulated in terms of the operator fidelity…
We consider frequency fluctuations in self-sustained oscillators based on nonlinear underdamped resonators. An important type of such resonators are nano- and micro-electro-mechanical systems. Various noise sources are considered, with the…
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…
Based on the previously proposed notions of action operators and of quantum integrability, frequency operators are introduced in a fully quantum-mechanical setting. They are conceptually useful because a new formulation can be given to…
We construct new, efficient, and accurate high-order finite differencing operators which satisfy summation by parts. Since these operators are not uniquely defined, we consider several optimization criteria: minimizing the bandwidth, the…
This article addresses the weak convergence of numerical methods for Brownian dynamics. Typical analyses of numerical methods for stochastic differential equations focus on properties such as the weak order which estimates the asymptotic…
Timing detection is the first step and very important in wireless communication systems. Timing detection performance is usually affected by the frequency offset. Therefore, it is a challenge to design the synchronization signal in massive…
In the stability analysis of an equilibrium, given by a stationary point of a functional F[n] (free energy functional, e.g.), the second derivative of F[n] plays the essential role. If the system in equilibrium is subject to the…
This paper deals with the numerical integration of Hamiltonian systems in which a stiff anharmonic potential causes highly oscillatory solution behavior with solution-dependent frequencies. The impulse method, which uses micro- and…
This contribution deals with identification of fractional-order dynamical systems. We consider systems whose mathematical description is a three-member differential equation in which the orders of derivatives can be real numbers. We give a…
We have investigated temporal fluctuation of superconducting qubits via the time-resolved measurement for an IBM Quantum system. We found that the qubit error rate abruptly changes during specific time intervals. Each high error state…
We study non-parametric frequency-domain system identification from a finite-sample perspective. We assume an open loop scenario where the excitation input is periodic and consider the Empirical Transfer Function Estimate (ETFE), where the…
The precise motion control of a multi-degree of freedom~(DOF) robot manipulator is always challenging due to its nonlinear dynamics, disturbances, and uncertainties. Because most manipulators are controlled by digital signals, a novel…
The dynamics of power grids are governed by a large number of nonlinear differential and algebraic equations (DAEs). To safely operate the system, operators need to check that the states described by these DAEs stay within prescribed limits…
Willems' fundamental lemma enables data-driven analysis and control by characterizing an unknown system's behavior directly in terms of measured data. In this work, we extend a recent frequency-domain variant of this result--previously…
Real life signals are in general non--stationary and non--linear. The development of methods able to extract their hidden features in a fast and reliable way is of high importance in many research fields. In this work we tackle the problem…
Properties of the response functions for a two-dimensional quartic oscillator are studied based on the diagonalization of the Hamiltonian in a large model space. In particular, response functions corresponding to a given momentum transfer…
This paper addresses the problem of efficiently computing higher-order variational integrators in simulation and trajectory optimization of mechanical systems as those often found in robotic applications. We develop $O(n)$ algorithms to…