74 research outputs found
Many touchings force many crossings
Given n continuous open curves in the plane, we say that a pair is touching if they have finitely many interior points in common and at these points the first curve does not get from one side of the second curve to its other side. Otherwise, if the two curves intersect, they are said to form a crossing pair. Let t and c denote the number of touching pairs and crossing pairs, respectively. We prove that c >= 1/0(5) t(2)/n(2), provided that t >= 10n. Apart from the values of the constants, this result is best possible. (C) 2018 Elsevier Inc. All rights reserved
Many touchings force many crossings
Given n continuous open curves in the plane, we say that a pair is touching if they have only one interior point in common and at this point the first curve does not get from one side of the second curve to its other side. Otherwise, if the two curves intersect, they are said to form a crossing pair. Let t and c denote the number of touching pairs and crossing pairs, respectively. We prove that c ≥ 1/105 t2/n2, provided that t ≥ 10n Apart from the values of the constants, this result is best possible. © Springer International Publishing AG 2018
Dual strings and magnetohydrodynamics
We investigate whether dual strings could be solutions of the
magnetohydrodynamics equations in the limit of infinite conductivity. We find
that the induction equation is satisfied, and we discuss the Navier-Stokes
equation (without viscosity) with the Lorentz force included. We argue that the
dual string equations (with a non-universal maximum velocity) should describe
the large scale motion of narrow magnetic flux tubes, because of a large
reparametrization (gauge) invariance of the magnetic and electric string
fields. It is shown that the energy-momentum tensor for the dual string can be
reinterpreted as an energy-momentum tensor for magnetohydrodynamics, provided
certain conditions are satisfied. We also give a brief discussion of the case
when magnetic monopoles are included, and indicate how this can lead to a
non-relativistic "electrohydrodynamics" picture of confinement.Comment: 10 pages. LaTex. A minor correction has been mad
Symmetry and topology in antiferromagnetic spintronics
Antiferromagnetic spintronics focuses on investigating and using
antiferromagnets as active elements in spintronics structures. Last decade
advances in relativistic spintronics led to the discovery of the staggered,
current-induced field in antiferromagnets. The corresponding N\'{e}el
spin-orbit torque allowed for efficient electrical switching of
antiferromagnetic moments and, in combination with electrical readout, for the
demonstration of experimental antiferromagnetic memory devices. In parallel,
the anomalous Hall effect was predicted and subsequently observed in
antiferromagnets. A new field of spintronics based on antiferromagnets has
emerged. We will focus here on the introduction into the most significant
discoveries which shaped the field together with a more recent spin-off
focusing on combining antiferromagnetic spintronics with topological effects,
such as antiferromagnetic topological semimetals and insulators, and the
interplay of antiferromagnetism, topology, and superconductivity in
heterostructures.Comment: Book chapte
Non-local signatures of the chiral magnetic effect in Dirac semimetal BiSb
The field of topological materials science has recently been focussing on
three-dimensional Dirac semimetals, which exhibit robust Dirac phases in the
bulk. However, the absence of characteristic surface states in accidental Dirac
semimetals (DSM) makes it difficult to experimentally verify claims about the
topological nature using commonly used surface-sensitive techniques. The chiral
magnetic effect (CME), which originates from the Weyl nodes, causes an
-dependent chiral charge polarization, which
manifests itself as negative magnetoresistance. We exploit the extended
lifetime of the chirally polarized charge and study the CME through both local
and non-local measurements in Hall bar structures fabricated from single
crystalline flakes of the DSM BiSb. From the non-local
measurement results we find a chiral charge relaxation time which is over one
order of magnitude larger than the Drude transport lifetime, underlining the
topological nature of BiSb.Comment: 6 pages, 6 figures + 7 pages of supplemental materia
- …