118,798 research outputs found
Dynamics of coupled vortices in layered magnetic nanodots
The spin dynamics are calculated for a model system consisting of
magnetically soft, layered nanomagnets, in which two ferromagnetic (F)
cylindrical dots, each with a magnetic vortex ground state, are separated by a
non-magnetic spacer (N). This permits a study of the effects of interlayer
magnetostatic interactions on the vortex dynamics. The system was explored by
applying the equations of motion for the vortex core positions. The restoring
force was calculated taking into account the magnetostatic interactions
assuming a realistic surface charge free spin distribution. For tri-layer F/N/F
dots with opposite chiralities and the same core polarizations (lowest energy
state), two eigenmodes are predicted analytically and confirmed via
micromagnetic simulations. One mode is in the sub-GHz range for submicron dot
diameters and corresponds to quasi-circular rotation of the cores about the dot
center. A second mode is in the MHz range corresponding to a small amplitude
rotation of the mean core position. The eigenfrequencies depend strongly on the
geometrical parameters of the system, suggesting that magnetostatic effects
play a dominant role in determining the vortex dynamics.Comment: One PDF file including text and 4 figure
Minimal Committee Problem for Inconsistent Systems of Linear Inequalities on the Plane
A representation of an arbitrary system of strict linear inequalities in R^n
as a system of points is proposed. The representation is obtained by using a
so-called polarity. Based on this representation an algorithm for constructing
a committee solution of an inconsistent plane system of linear inequalities is
given. A solution of two problems on minimal committee of a plane system is
proposed. The obtained solutions to these problems can be found by means of the
proposed algorithm.Comment: 29 pages, 2 figure
Electronic optics in graphene in the semiclassical approximation
We study above-barrier scattering of Dirac electrons by a smooth
electrostatic potential combined with a coordinate-dependent mass in graphene.
We assume that the potential and mass are sufficiently smooth, so that we can
define a small dimensionless semiclassical parameter . This electronic
optics setup naturally leads to focusing and the formation of caustics, which
are singularities in the density of trajectories. We construct a semiclassical
approximation for the wavefunction in all points, placing particular emphasis
on the region near the caustic, where the maximum of the intensity lies.
Because of the matrix character of the Dirac equation, this wavefunction
contains a nontrivial semiclassical phase, which is absent for a scalar wave
equation and which influences the focusing. We carefully discuss the three
steps in our semiclassical approach: the adiabatic reduction of the matrix
equation to an effective scalar equation, the construction of the wavefunction
using the Maslov canonical operator and the application of the uniform
approximation to the integral expression for the wavefunction in the vicinity
of a caustic. We consider several numerical examples and show that our
semiclassical results are in very good agreement with the results of
tight-binding calculations. In particular, we show that the semiclassical phase
can have a pronounced effect on the position of the focus and its intensity.Comment: 103 pages, 11 figure
Chain configurations in light nuclei
The model of nuclear matter built from alpha-particles is proposed. The
strong deformed shape for doubly even N=Z nuclides from carbon to magnesium has
been determined according to this model. In this paper we undertake very simple
approach, which assumes the existence of low lying chain configurations.Comment: 6 pages, 5 figure
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