38,436 research outputs found
How to project onto extended second order cones
The extended second order cones were introduced by S. Z. N\'emeth and G.
Zhang in [S. Z. N\'emeth and G. Zhang. Extended Lorentz cones and variational
inequalities on cylinders. J. Optim. Theory Appl., 168(3):756-768, 2016] for
solving mixed complementarity problems and variational inequalities on
cylinders. R. Sznajder in [R. Sznajder. The Lyapunov rank of extended second
order cones. Journal of Global Optimization, 66(3):585-593, 2016] determined
the automorphism groups and the Lyapunov or bilinearity ranks of these cones.
S. Z. N\'emeth and G. Zhang in [S.Z. N\'emeth and G. Zhang. Positive operators
of Extended Lorentz cones. arXiv:1608.07455v2, 2016] found both necessary
conditions and sufficient conditions for a linear operator to be a positive
operator of an extended second order cone. This note will give formulas for
projecting onto the extended second order cones. In the most general case the
formula will depend on a piecewise linear equation for one real variable which
will be solved by using numerical methods
On the spherical convexity of quadratic functions
In this paper we study the spherical convexity of quadratic functions on
spherically convex sets. In particular, conditions characterizing the spherical
convexity of quadratic functions on spherical convex sets associated to the
positive orthants and Lorentz cones are given
Strain-Modified RKKY Interaction in Carbon Nanotubes
For low-dimensional metallic structures, such as nanotubes, the exchange
coupling between localized magnetic dopants is predicted to decay slowly with
separation. The long-range character of this interaction plays a significant
role in determining the magnetic order of the system. It has previously been
shown that the interaction range depends on the conformation of the magnetic
dopants in both graphene and nanotubes. Here we examine the RKKY interaction in
carbon nanotubes in the presence of uniaxial strain for a range of different
impurity configurations. We show that strain is capable of amplifying or
attenuating the RKKY interaction, significantly increasing certain interaction
ranges, and acting as a switch: effectively turning on or off the interaction.
We argue that uniaxial strain can be employed to significantly manipulate
magnetic interactions in carbon nanotubes, allowing an interplay between
mechanical and magnetic properties in future spintronic devices. We also
examine the dimensional relationship between graphene and nanotubes with
regards to the decay rate of the RKKY interaction.Comment: 7 pages, 6 figures, submitte
Exponential behavior of the interlayer exchange coupling across non-magnetic metallic superlattices
It is shown that the coupling between magnetic layers separated by
non-magnetic metallic superlattices can decay exponentially as a function of
the spacer thickness , as opposed to the usual decay. This effect
is due to the lack of constructive contributions to the coupling from extended
states across the spacer. The exponential behavior is obtained by properly
choosing the distinct metals and the superlattice unit cell composition.Comment: To appear in Phys. Rev.
Aggregation in a mixture of Brownian and ballistic wandering particles
In this paper, we analyze the scaling properties of a model that has as
limiting cases the diffusion-limited aggregation (DLA) and the ballistic
aggregation (BA) models. This model allows us to control the radial and angular
scaling of the patterns, as well as, their gap distributions. The particles
added to the cluster can follow either ballistic trajectories, with probability
, or random ones, with probability . The patterns were
characterized through several quantities, including those related to the radial
and angular scaling. The fractal dimension as a function of
continuously increases from (DLA dimensionality) for
to (BA dimensionality) for . However, the
lacunarity and the active zone width exhibt a distinct behavior: they are
convex functions of with a maximum at . Through the
analysis of the angular correlation function, we found that the difference
between the radial and angular exponents decreases continuously with increasing
and rapidly vanishes for , in agreement with recent
results concerning the asymptotic scaling of DLA clusters.Comment: 7 pages, 6 figures. accepted for publication on PR
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