Search results for "harmonic"

Summary of Trap Properties

2009

Three-dimensional confinement of charged particles requires a potential energy minimum at some region in space, in order that the corresponding force is directed toward that region in all three dimensions. In general, the dependence of the magnitude of this force on the coordinates can have an arbitrary form; however, it is convenient to have a binding force that is harmonic, since this simplifies the analytical description of the particle motion.

A fully manipulable damped driven harmonic oscillator using optical levitation

2020

We implement an experimental system based on optical levitation of a silicone oil droplet to demonstrate a damped driven harmonic oscillator. The apparatus allows us to control all the parameters present in the differential equation that theoretically describes such motion. The damping coefficient and driving force can be manipulated in situ by changing the pressure in the apparatus and by applying a variable electric field. We present two different experimental procedures. First, a transition from the overdamped to underdamped regimes is demonstrated by gradually lowering the air pressure. The characteristic resonance associated with an underdamped driven harmonic oscillator is observed by…

Rotationally symmetric p -harmonic maps fromD2toS2

2013

We consider rotationally symmetric p-harmonic maps from the unit disk D2⊂R2 to the unit sphere S2⊂R3, subject to Dirichlet boundary conditions and with 1<p<∞. We show that the associated energy functional admits a unique minimizer which is of class C∞ in the interior and C1 up to the boundary. We also show that there exist infinitely many global solutions to the associated Euler–Lagrange equation and we completely characterize them.

Maximal function estimates and self-improvement results for Poincaré inequalities

2018

Our main result is an estimate for a sharp maximal function, which implies a Keith–Zhong type self-improvement property of Poincaré inequalities related to differentiable structures on metric measure spaces. As an application, we give structure independent representation for Sobolev norms and universality results for Sobolev spaces. peerReviewed

Real And Positive Filter Based On Circular Harmonic Expansion

1989

A real and positive filter for pattern recognition is presented. The filter, based on the circular harmonic (CH) expansion of a real function, is partially rotation invariant. As it is real and positive, the filter can be recorded on a transparency as an amplitude filter. Computer simulations of character recognition show a partial rotation invariance of about 40°. Optical experiments agree with these results and with acceptable discrimination between different characters. Nevertheless, due to experimental difficulties, the method is onerous for use in general pattern recognition problems.

On Functions of Integrable Mean Oscillation

2005

Given we denote by the modulus of mean oscillation given by where is an arc of , stands for the normalized length of , and . Similarly we denote by the modulus of harmonic oscillation given by where and stand for the Poisson kernel and the Poisson integral of respectively. It is shown that, for each , there exists such that

Deformed Canonical (anti-)commutation relations and non-self-adjoint hamiltonians

2015

Solution of the Skyrme–Hartree–Fock–Bogolyubov equations in the Cartesian deformed harmonic-oscillator basis.

2012

We describe the new version (v2.38j) of the code hfodd which solves the nuclear SkyrmeHartree-Fock or Skyrme-Hartree-Fock-Bogolyubov problem by using the Cartesian deformed harmonic-oscillator basis. In the new version, we have implemented: (i) projection on good angular momentum (for the Hartree-Fock states), (ii) calculation of the GCM kernels, (iii) calculation of matrix elements of the Yukawa interaction, (iv) the BCS solutions for statedependent pairing gaps, (v) the HFB solutions for broken simplex symmetry, (vi) calculation of Bohr deformation parameters, (vii) constraints on the Schiff moments and scalar multipole moments, (viii) the D T transformations and rotations of wave functio…

Bézier Solutions of the Wave Equation

2004

We study polynomial solutions in the Bezier form of the wave equation in dimensions one and two. We explicitly determine which control points of the Bezier solution at two different times fix the solution.

Control of Electron Motion in a Molecular Ion: Dynamical Creation of a Permanent Electric Dipole

2007

The dynamics of a diatomic one-dimensional homonuclear molecule driven by a two-laser field is investigated beyond the usual fixed nuclei approximation. The dynamics of the nuclei is treated by means of Newton equations of motion; the full quantum description is used for the single active electron. The first laser pulse (pump) excites vibrations of the nuclei, while the second very short pulse (probe) has the role of confining the electron around one of the nuclei. We show how to use the radiation scattered in these conditions by the molecule to achieve real-time control of the molecular dynamics.