98,083 research outputs found
Spin-Orbit Misalignment of Merging Black-Hole Binaries with Tertiary Companions
We study the effect of external companion on the orbital and spin evolution
of merging black-hole (BH) binaries. An sufficiently close by and inclined
companion can excite Lidov-Kozai (LK) eccentricity oscillations in the binary,
thereby shortening its merger time. During such LK-enhanced orbital decay, the
spin axis of the BH generally exhibits chaotic evolution, leading to a wide
range (-) of final spin-orbit misalignment angle from an
initially aligned configuration. For systems that do not experience
eccentricity excitation, only modest () spin-orbit
misalignment can be produced, and we derive an analytic expression for the
final misalignment using the principle of adiabatic invariance. The spin-orbit
misalignment directly impacts the gravitational waveform, and can be used to
constrain the formation scenarios of BH binaries and dynamical influences of
external companions.Comment: Published in ApJ
Blocks of group algebras are derived simple
A derived version of Maschke's theorem for finite groups is proved: the
derived categories, bounded or unbounded, of all blocks of the group algebra of
a finite group are simple, in the sense that they admit no nontrivial
recollements. This result is independent of the characteristic of the base
field.Comment: 8 page
Cache-enabled Heterogeneous Cellular Networks: Comparison and Tradeoffs
Caching popular contents at base stations (BSs) is a promising way to unleash
the potential of cellular heterogeneous networks (HetNets), where backhaul has
become a bottleneck. In this paper, we compare a cache-enabled HetNet where a
tier of multi-antenna macro BSs is overlaid by a tier of helper nodes having
caches but no backhaul with a conventional HetNet where the macro BSs tier is
overlaid by a tier of pico BSs with limited-capacity backhaul. We resort
stochastic geometry theory to derive the area spectral efficiencies (ASEs) of
these two kinds of HetNets and obtain the closed-form expressions under a
special case. We use numerical results to show that the helper density is only
1/4 of the pico BS density to achieve the same target ASE, and the helper
density can be further reduced by increasing cache capacity. With given total
cache capacity within an area, there exists an optimal helper node density that
maximizes the ASE.Comment: Accepted by IEEE International Conference on Communications (ICC)
2016. This version includes detailed proofs of the proposition
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