1,971 research outputs found
Topological monodromy as an obstruction to Hamiltonization of nonholonomic systems: pro or contra?
The phenomenon of a topological monodromy in integrable Hamiltonian and
nonholonomic systems is discussed. An efficient method for computing and
visualizing the monodromy is developed. The comparative analysis of the
topological monodromy is given for the rolling ellipsoid of revolution problem
in two cases, namely, on a smooth and on a rough plane. The first of these
systems is Hamiltonian, the second is nonholonomic. We show that, from the
viewpoint of monodromy, there is no difference between the two systems, and
thus disprove the conjecture by Cushman and Duistermaat stating that the
topological monodromy gives a topological obstruction for Hamiltonization of
the rolling ellipsoid of revolution on a rough plane.Comment: 31 pages, 11 figure
On the New Notion of the Set-Expectation for a Random Set of Events
The paper introduces new notion for the set-valued mean set of a random set. The means are defined as families of sets that minimize mean distances to the random set. The distances are determined by metrics in spaces of sets or by suitable generalizations. Some examples illustrate the use of the new definitions.mean random set, metrics in set space, mean distance, Aumann expectation, Frechet expectation, Hausdorff metric, random finite set, mean set, set-median, set-expectation
Magnetoelectric domain wall dynamics and its implications for magnetoelectric memory
Domain wall dynamics in a magnetoelectric antiferromagnet is analyzed, and
its implications for magnetoelectric memory applications are discussed.
CrO is used in the estimates of the materials parameters. It is found
that the domain wall mobility has a maximum as a function of the electric field
due to the gyrotropic coupling induced by it. In CrO the maximal
mobility of 0.1 m/(sOe) is reached at V/nm. Fields of
this order may be too weak to overcome the intrinsic depinning field, which is
estimated for B-doped CrO. These major drawbacks for device
implementation can be overcome by applying a small in-plane shear strain, which
blocks the domain wall precession. Domain wall mobility of about 0.7
m/(sOe) can then be achieved at V/nm. A split-gate scheme is
proposed for the domain-wall controlled bit element; its extension to
multiple-gate linear arrays can offer advantages in memory density,
programmability, and logic functionality.Comment: 5 pages, 2 figures, revised and corrected version, accepted in
Applied Physics Letter
Colossal infrared and terahertz magneto-optical activity in a two-dimensional Dirac material
When two-dimensional electron gases (2DEGs) are exposed to magnetic field,
they resonantly absorb electromagnetic radiation via electronic transitions
between Landau levels (LLs). In 2DEGs with a Dirac spectrum, such as graphene,
theory predicts an exceptionally high infrared magneto-absorption, even at zero
doping. However, the measured LL magneto-optical effects in graphene have been
much weaker than expected because of imperfections in the samples available so
far for such experiments. Here we measure magneto-transmission and Faraday
rotation in high-mobility encapsulated monolayer graphene using a custom
designed setup for magneto-infrared microspectroscopy. Our results show a
strongly enhanced magneto-optical activity in the infrared and terahertz ranges
characterized by a maximum allowed (50%) absorption of light, a 100% magnetic
circular dichroism as well as a record high Faraday rotation. Considering that
sizeable effects have been already observed at routinely achievable magnetic
fields, our findings demonstrate a new potential of magnetic tuning in 2D Dirac
materials for long-wavelength optoelectronics and plasmonics.Comment: 14 pages, 4 figure
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