64,970 research outputs found
On the rational subset problem for groups
We use language theory to study the rational subset problem for groups and
monoids. We show that the decidability of this problem is preserved under graph
of groups constructions with finite edge groups. In particular, it passes
through free products amalgamated over finite subgroups and HNN extensions with
finite associated subgroups. We provide a simple proof of a result of
Grunschlag showing that the decidability of this problem is a virtual property.
We prove further that the problem is decidable for a direct product of a group
G with a monoid M if and only if membership is uniformly decidable for
G-automata subsets of M. It follows that a direct product of a free group with
any abelian group or commutative monoid has decidable rational subset
membership.Comment: 19 page
Vortex rectification effects in films with periodic asymmetric pinning
We study the transport of vortices excited by an ac current in an Al film
with an array of nanoengineered asymmetric antidots. The vortex response to the
ac current is investigated by detailed measurements of the voltage output as a
function of ac current amplitude, magnetic field and temperature. The
measurements revealed pronounced voltage rectification effects which are mainly
characterized by the two critical depinning forces of the asymmetric potential.
The shape of the net dc voltage as a function of the excitation amplitude
indicates that our vortex ratchet behaves in a way very different from standard
overdamped models. Rather, as demonstrated by the observed output signal, the
repinning force, necessary to stop vortex motion, is considerably smaller than
the depinning force, resembling the behavior of the so-called inertia ratchets.
Calculations based on an underdamped ratchet model provide a very good fit to
the experimental data.Comment: 5 pages, 4 figure
Dipole-induced vortex ratchets in superconducting films with arrays of micromagnets
We investigate the transport properties of superconducting films with
periodic arrays of in-plane magnetized micromagnets. Two different magnetic
textures are studied: a square array of magnetic bars and a close-packed array
of triangular microrings. As confirmed by MFM imaging, the magnetic state of
both systems can be adjusted to produce arrays of almost point-like magnetic
dipoles. By carrying out transport measurements with ac drive, we observed
experimentally a recently predicted ratchet effect induced by the interaction
between superconducting vortices and the magnetic dipoles. Moreover, we find
that these magnetic textures produce vortex-antivortex patterns, which have a
crucial role on the transport properties of this hybrid system.Comment: 4 pages, 4 figure
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