2,085 research outputs found
Multipartite hypergraphs achieving equality in Ryser's conjecture
A famous conjecture of Ryser is that in an -partite hypergraph the
covering number is at most times the matching number. If true, this is
known to be sharp for for which there exists a projective plane of order
. We show that the conjecture, if true, is also sharp for the smallest
previously open value, namely . For , we find the minimal
number of edges in an intersecting -partite hypergraph that has
covering number at least . We find that is achieved only by linear
hypergraphs for , but that this is not the case for . We
also improve the general lower bound on , showing that .
We show that a stronger form of Ryser's conjecture that was used to prove the
case fails for all . We also prove a fractional version of the
following stronger form of Ryser's conjecture: in an -partite hypergraph
there exists a set of size at most , contained either in one side of
the hypergraph or in an edge, whose removal reduces the matching number by 1.Comment: Minor revisions after referee feedbac
Magnetization patterns in ferromagnetic nano-elements as functions of complex variable
Assumption of certain hierarchy of soft ferromagnet energy terms, realized in
small enough flat nano-elements, allows to obtain explicit expressions for
their magnetization distributions. By minimising the energy terms sequentially,
from most to the least important, magnetization distributions are expressed as
solutions of Riemann-Hilbert boundary value problem for a function of complex
variable. A number of free parameters, corresponding to positions of vortices
and anti-vortices, still remain in the expression. These parameters can be
found by computing and minimizing the total magnetic energy of the particle
with no approximations. Thus, the presented approach is a factory of realistic
Ritz functions for analytical micromagnetic calculations. These functions are
so versatile, that they may even find applications on their own (e.g. for
fitting magnetic microscopy images). Examples are given for multi-vortex
magnetization distributions in circular cylinder, and for 2-dimensional domain
walls in thin magnetic strips.Comment: 4 pages, 3 figures, 2 refs added, fixed typo
Magnetostatic bias in multilayer microwires: theory and experiments
The hysteresis curves of multilayer microwires consisting of a soft magnetic
nucleus, intermediate non-magnetic layers, and an external hard magnetic layer
are investigated. The magnetostatic interaction between magnetic layers is
proved to give rise to an antiferromagnetic-like coupling resulting in a
magnetostatic bias in the hysteresis curves of the soft nucleus. This
magnetostatic biasing effect is investigated in terms of the microwire
geometry. The experimental results are interpreted considering an analytical
model taking into account the magnetostatic interaction between the magnetic
layers.Comment: 6 pages, 7 figure
Domain wall motion in thin ferromagnetic nanotubes: Analytic results
Dynamics of magnetization domain walls (DWs) in thin ferromagnetic nanotubes subject to weak longitudinal external fields is addressed analytically in the regimes of strong and weak penalization. Exact solutions for the DW profiles and formulas for the DW propagation velocity are derived in both regimes. In particular, the DW speed is shown to depend nonlinearly on the nanotube radius
Finite-size versus Surface effects in nanoparticles
We study the finite-size and surface effects on the thermal and spatial
behaviors of the magnetisation of a small magnetic particle. We consider two
systems: 1) A box-shaped isotropic particle of simple cubic structure with
either periodic or free boundary conditions. This case is treated analytically
using the isotropic model of D-component spin vectors in the limit , including the magnetic field. 2) A more realistic particle (-FeO) of ellipsoidal (or spherical) shape with open boundaries.
The magnetic state in this particle is described by the anisotropic classical
Dirac-Heisenberg model including exchange and dipolar interactions, and bulk
and surface anisotropy. This case is dealt with by the classical Monte Carlo
technique. It is shown that in both systems finite-size effects yield a
positive contribution to the magnetisation while surface effects render a
larger and negative contribution, leading to a net decrease of the
magnetisation of the small particle with respect to the bulk system. In the
system 2) the difference between the two contributions is enhanced by surface
anisotropy. The latter also leads to non saturation of the magnetisation at low
temperatures, showing that the magnetic order in the core of the particle is
perturbed by the magnetic disorder on the surface. This is confirmed by the
profile of the magnetisation.Comment: 6 pages of RevTex including 4 Figures, invited paper to 3rd
EuroConference on Magnetic Properties of Fine Nanoparticles, Barcelona,
October 9
Scaling relations for magnetic nanoparticles
A detailed investigation of the scaling relations recently proposed by [J.
d'Albuquerque e Castro, D. Altbir, J. C. Retamal, and P. Vargas, Phys. Rev.
Lett. 88, 237202 (2002)] to study the magnetic properties of nanoparticles is
presented. Analytical expressions for the total energy of three characteristic
internal configurations of the particles are obtained, in terms of which the
behavior of the magnetic phase diagram for those particles upon scaling of the
exchange interaction is discussed. The exponent in scaling relations is
shown to be dependent on the geometry of the vortex core, and results for
specific cases are presented.Comment: 6 pages, 4 figure
Do You Hear that Beat? Expectation Versus Uncertainty as Influenced by Background Noise
AbstractThe human ability to perceive and synchronize to musical beat has communicative importance beyond the purely musical context. Entrainment to the beat hints at more general deductive and predictive mechanisms. Evidence for beat entrainment and its related mechanisms was found in behavioural as well as neuroimaging studies. However, the mechanisms behind this phenomenon are not yet fully understood, and in particular, it is not known whether beat entrainment relies on lasting, sensory- specific cortical activity. To answer this question, we asked participants to listen to sequences of isochronous and non- isochronous beats. The sequences faded above and below an individual participant's hearing level, into either silence or background noise. Participants were asked to press a button for as long as they heard the sequence, and let go once they no longer hear it. Results show a consistently lengthened button press for isochronous sequences, beyond the actual fade-out period (leptokurtic, slim fit). The release delay to the non-isochronous sequences was instead characterized by uncertainty (platicurtic, broad fit). Background noise appeared to improve the isochronous sequence ending detection, possibly by raising the level of attention to sounds. These results support the view of entrainment mechanism as an internal, self-sustaining circuit. The activity of such a mechanism, driven by temporal regularity, together with the gradual disappearance of the beat, might create an illusory perception of beat continuation
Magnetization reversal of ferromagnetic nanodisc placed above a superconductor
Using numerical simulation we have studied a magnetization distribution and a
process of magnetization reversal in nanoscale magnets placed above a
superconductor plane. In order to consider an influence of superconductor on
magnetization distribution in the nanomagnet we have used London approximation.
We have found that for usual values of London penetration depth the ground
state magnetization is mostly unchanged. But at the same time the fields of
vortex nucleation and annihilation change significantly: the interval where
vortex is stable enlarges on 100-200 Oe for the particle above the
superconductor. Such fields are experimentally observable so there is a
possibility of some practical applications of this effect.Comment: 8 pages, 9 figure
Two Modes of Magnetization Switching in a Simulated Iron Nanopillar in an Obliquely Oriented Field
Finite-temperature micromagnetics simulations are employed to study the
magnetization-switching dynamics driven by a field applied at an angle to the
long axis of an iron nanopillar. A bi-modal distribution in the switching times
is observed, and evidence for two competing modes of magnetization-switching
dynamics is presented. For the conditions studied here, temperature K
and the reversal field 3160 Oe at an angle of 75 to the long axis,
approximately 70% of the switches involve unstable decay (no free-energy
barrier) and 30% involve metastable decay (a free-energy barrier is crossed).
The latter are indistinguishable from switches which are constrained to start
at a metastable free-energy minimum. Competition between unstable and
metastable decay could greatly complicate applications involving magnetization
switches near the coercive field.Comment: 19 pages, 7 figure
Vortex core size in interacting cylindrical nanodot arrays
The effect of dipolar interactions among cylindrical nanodots, with a
vortex-core magnetic configuration, is analyzed by means of analytical
calculations. The cylinders are placed in a N x N square array in two
configurations - core oriented parallel to each other and with antiparallel
alignment between nearest neighbors. Results comprise the variation in the core
radius with the number of interacting dots, the distance between them and dot
height. The dipolar interdot coupling leads to a decrease (increase) of the
core radius for parallel (antiparallel) arrays
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