24,813 research outputs found
Remarks on the boundary curve of a constant mean curvature topological disc
We discuss some consequences of the existence of the holomorphic quadratic
Hopf differential on a conformally immersed constant mean curvature topological
disc with analytic boundary. In particular, we derive a formula for the mean
curvature as a weighted average of the normal curvature of the boundary curve,
and a condition for the surface to be totally umbilic in terms of the normal
curvature.Comment: 6 pages, 1 figure. Version 2: comments and references adde
Please Lower Small Cell Antenna Heights in 5G
In this paper, we present a new and significant theoretical discovery. If the
absolute height difference between base station (BS) antenna and user equipment
(UE) antenna is larger than zero, then the network capacity performance in
terms of the area spectral efficiency (ASE) will continuously decrease as the
BS density increases for ultra-dense (UD) small cell networks (SCNs). This
performance behavior has a tremendous impact on the deployment of UD SCNs in
the 5th-generation (5G) era. Network operators may invest large amounts of
money in deploying more network infrastructure to only obtain an even worse
network performance. Our study results reveal that it is a must to lower the
SCN BS antenna height to the UE antenna height to fully achieve the capacity
gains of UD SCNs in 5G. However, this requires a revolutionized approach of BS
architecture and deployment, which is explored in this paper too.Comment: Final version in IEEE: http://ieeexplore.ieee.org/document/7842150/.
arXiv admin note: substantial text overlap with arXiv:1608.0669
Single-index copulae
We introduce so-called "single-index copulae". They are semi-parametric
conditional copulae whose parameter is an unknown "link" function of a
univariate index only. We provide estimates of this link function and of the
finite dimensional unknown parameter. The asymptotic properties of the latter
estimates are stated. Thanks to some properties of conditional Kendall's tau,
we illustrate our technical conditions with several usual copula families.Comment: Revised version: correction of Assumption 3 and some minor induced
modification
Quantum point contacts as heat engines
The efficiency of macroscopic heat engines is restricted by the second law of
thermodynamics. They can reach at most the efficiency of a Carnot engine. In
contrast, heat currents in mesoscopic heat engines show fluctuations. Thus,
there is a small probability that a mesoscopic heat engine exceeds Carnot's
maximum value during a short measurement time. We illustrate this effect using
a quantum point contact as a heat engine. When a temperature difference is
applied to a quantum point contact, the system may be utilized as a source of
electrical power under steady state conditions. We first discuss the optimal
working point of such a heat engine that maximizes the generated electrical
power and subsequently calculate the statistics for deviations of the
efficiency from its most likely value. We find that deviations surpassing the
Carnot limit are possible, but unlikely.Comment: 9 pages, 2 figures. Contribution to the Physica E special issue on
"Frontiers in quantum electronic transport" in memory of Markus Buttiker.
Published versio
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