The purpose of this note is to state without proof certain. results on polynomial approximation to harmonic functions whose proofs will appear elsewhere later. In the plane of the complex variable z = x + iy, a (real) function u(z) harmonic in the interior of the Jordan curve C and continuous in the corresponding closed region C can be represented in C by a uniformly convergent series of harmon...

We investigate the evolution of the many-body wave function of a quantum system with time-varying effective mass, confined by a harmonic potential with time-varying frequency in the presence of a uniform time-varying magnetic field, and perturbed by a time-dependent uniform electric field. It is found that the wave function is comprised of a phase factor times the solution to the unperturbed ti...

We use the simulated plane wave section method to separate specular reflections and diffraction events. We show that plane wave sections naturally separate specular and diffracted events and allow us to use plane-wave distruction filters to suppress specular events resulting in plane-wave sections of diffractions. A synthetic example demonstrates the effectiveness of our method in imaging fault...

We present a new and efficient method to obtain a Gamow shell-model basis and matrix elements generated by realistic nucleon-nucleon interactions. We derive a self-consistent Hartree-Fock potential from the renormalized NLO interaction model. The corresponding Gamow one-body eigenstates are generated in a plane wave basis in order to build a Gamow shell-model set of basis states for the closed ...

Harmonic perturbations are studied for a plane parallel model for the solar magnetic atmosphere. In the present model, the magnetic field lines are horizontal, the sound speed and the Alfvén speed are constants. It is known that in this model, analytical solutions can be obtained for linearized perturbations. The harmonic perturbations can either propagate as MHD modes modified by the action of...

Trefftz methods are finite element-type schemes whose test and trial functions are (locally) solutions of the targeted differential equation. They are particularly popular for time-harmonic wave problems, as their trial spaces contain oscillating basis functions and may achieve better approximation properties than classical piecewise-polynomial spaces. We review the construction and properties ...

In the frame of random matrix theory, it was shown, that relaxation projection initial plane wave with vector q is described by equation motion memory function which corresponds to complex dynamical Young modulus E(ω). harmonic scalar model displacements absence energy dissipation, Ioffe-Regel crossover arises universally in amorphous systems dimension d≥3. Vibrations above are related diffusiv...

The interaction of a weakly nonlinear Alfvénic pulse with an Alfvén speed inhomogeneity in the direction perpendicular to the magnetic field is investigated. Identically to the phase mixing experienced by a harmonic Alfvén wave, sharp transverse gradients are generated in the pulse by the inhomogeneity. In the initial stage of the evolution of an initially plane Alfvénic pulse, the transverse g...

The interaction of a weakly nonlinear Alfvénic pulse with an Alfvén speed inhomogeneity in the direction perpendicular to the magnetic field is investigated. Identical to the phase mixing experienced by a harmonic Alfvén wave, sharp transverse gradients are generated in the pulse by the inhomogeneity. In the initial stage of the evolution of an initially plane Alfvénic pulse, the transverse gra...

Controlling the directionality of spin waves is a key ingredient in wave-based computing methods such as magnonics. In this Letter, we demonstrate particular aspect by using an all-optical pointlike source continuous based on frequency comb rapid demagnetization. The emitted contain range $k$ vectors and detuning applied magnetic field slightly off ferromagnetic resonance (FMR), observe $\maths...