Search results for "harmonic"

The Egan problem on the pull-in range of type 2 PLLs

2021

In 1981, famous engineer William F. Egan conjectured that a higher-order type 2 PLL with an infinite hold-in range also has an infinite pull-in range, and supported his conjecture with some third-order PLL implementations. Although it is known that for the second-order type 2 PLLs the hold-in range and the pull-in range are both infinite, the present paper shows that the Egan conjecture may be not valid in general. We provide an implementation of the third-order type 2 PLL, which has an infinite hold-in range and experiences stable oscillations. This implementation and the Egan conjecture naturally pose a problem, which we will call the Egan problem: to determine a class of type 2 PLLs for …

Superharmonic functions are locally renormalized solutions

2011

Abstract We show that different notions of solutions to measure data problems involving p-Laplace type operators and nonnegative source measures are locally essentially equivalent. As an application we characterize singular solutions of multidimensional Riccati type partial differential equations.

Multi-particle azimuthal correlations in p-Pb and Pb-Pb collisions at the CERN Large Hadron Collider

2014

Measurements of multi-particle azimuthal correlations (cumulants) for charged particles in p-Pb and Pb-Pb collisions are presented. They help address the question of whether there is evidence for global, flow-like, azimuthal correlations in the p-Pb system. Comparisons are made to measurements from the larger Pb-Pb system, where such evidence is established. In particular, the second harmonic two-particle cumulants are found to decrease with multiplicity, characteristic of a dominance of few-particle correlations in p-Pb collisions. However, when a $|\Delta \eta|$ gap is placed to suppress such correlations, the two-particle cumulants begin to rise at high-multiplicity, indicating the prese…

Complex Dynamics in a Harmonically Excited Lennard-Jones Oscillator: Microcantilever-Sample Interaction in Scanning Probe Microscopes1

1998

In this paper we model the microcantilever-sample interaction in an atomic force microscope (AFM) via a Lennard-Jones potential and consider the dynamical behavior of a harmonically forced system. Using nonlinear analysis techniques on attracting limit sets, we numerically verify the presence of chaotic invariant sets. The chaotic behavior appears to be generated via a cascade of period doubling, whose occurrence has been studied as a function of the system parameters. As expected, the chaotic attractors are obtained for values of parameters predicted by Melnikov theory. Moreover, the numerical analysis can be fruitfully employed to analyze the region of the parameter space where no theoret…

Self-Trapping of Magnetic Oscillation Modes in Landau Flux-Closure Structures

2005

We investigated the magnetodynamics in rectangular Permalloy platelets by means of time-resolved x-ray photoemission microscopy. 10 nm thick platelets of size 16 x 32 microm were excited by an oscillatory field along the short side of the sample with a fundamental frequency of 500 MHz and considerable contributions of higher harmonics. Under the influence of the oscillatory field, the Néel wall in the initial classical Landau pattern shifts away from the center, corresponding to an induced magnetic moment perpendicular to the exciting field. This phenomenon is explained by a self-trapping effect of the dominating spin-wave mode when the system is excited just below the resonance frequency. …

Scaling property of variational perturbation expansion for a general anharmonic oscillator with xp-potential

1995

We prove a powerful scaling property for the extremality condition in the recently developed variational perturbation theory which converts divergent perturbation expansions into exponentially fast convergent ones. The proof is given for the energy eigenvalues of an anharmonic oscillator with an arbitrary $x^p$-potential. The scaling property greatly increases the accuracy of the results.

Phase transition systematics in BiVO4 by means of high-pressure–high-temperature Raman experiments

2018

We report here high-pressure--high-temperature Raman experiments performed on ${\text{BiVO}}_{4}$. We characterized the fergusonite and scheelite phases (powder and single crystal samples) and the zircon polymorph (nanopowder). The experimental results are supported by ab initio calculations, which, in addition, provide the vibrational patterns. The temperature and pressure behavior of the fergusonite lattice modes reflects the distortions associated with the ferroelastic instability. The linear coefficients of the zircon phase are in sharp contrast to the behavior observed in the fergusonite phase. The boundary of the fergusonite-to-scheelite second-order phase transition is given by ${T}_…

Light-Driven Extremely Nonlinear Bulk Photogalvanic Currents

2021

We predict the generation of bulk photocurrents in materials driven by bichromatic fields that arc circularly polarized and corotating. The nonlinear photocurrents have a fully controllable directionality and amplitude without requiring carrier-envelope-phase stabilization or few-cycle pulses, and can be generated with photon energies much smaller than the band gap (reducing heating in the photoconversion process). We demonstrate with ab initio calculations that the photocurrent generation mechanism is universal and arises in gaped materials (Si, diamond, MgO, hBN), in semimetals (graphene), and in two- and three-dimensional systems. Photocurrents are shown to rely on sub-laser-cycle asymme…

Phragmén-Lindelöf's and Lindelöf's theorems

1985

Magnetic field uniformity in neutron electric dipole moment experiments

2019

© 2019 American Physical Society. Magnetic-field uniformity is of the utmost importance in experiments to measure the electric dipole moment of the neutron. A general parametrization of the magnetic field in terms of harmonic polynomial modes is proposed, going beyond the linear-gradients approximation. We review the main undesirable effects of nonuniformities: depolarization of ultracold neutrons and Larmor frequency shifts of neutrons and mercury atoms. The theoretical predictions for these effects were verified by dedicated measurements with the single-chamber neutron electric-dipole-moment apparatus installed at the Paul Scherrer Institute. ispartof: Physical Review A vol:99 issue:4 sta…