87 research outputs found
First-order logic of uniform attachment random graphs with a given degree
In this paper, we prove the first-order convergence law for the uniform
attachment random graph with almost all vertices having the same degree. In the
considered model, vertices and edges are introduced recursively: at time
we start with a complete graph on vertices. At step the vertex
is introduced together with edges joining the new vertex with
vertices chosen uniformly from those vertices of , whom degree is
less then . To prove the law, we describe the dynamics of the logical
equivalence class of the random graph using Markov chains. The convergence law
follows from the existence of a limit distribution of the considered Markov
chain
The Fluid Mechanics of Liquid Democracy
Liquid democracy is the principle of making collective decisions by letting
agents transitively delegate their votes. Despite its significant appeal, it
has become apparent that a weakness of liquid democracy is that a small subset
of agents may gain massive influence. To address this, we propose to change the
current practice by allowing agents to specify multiple delegation options
instead of just one. Much like in nature, where --- fluid mechanics teaches us
--- liquid maintains an equal level in connected vessels, so do we seek to
control the flow of votes in a way that balances influence as much as possible.
Specifically, we analyze the problem of choosing delegations to approximately
minimize the maximum number of votes entrusted to any agent, by drawing
connections to the literature on confluent flow. We also introduce a random
graph model for liquid democracy, and use it to demonstrate the benefits of our
approach both theoretically and empirically.Comment: Simulation code is available at https://github.com/pgoelz/flui
X-ray Diagnostics of Thermal Conditions of the Hot Plasmas in the Centaurus Cluster
X-ray data of the Centaurus cluster, obtained with {\it XMM-Newton} for 45
ksec, were analyzed. Deprojected EPIC spectra from concentric thin shell
regions were reproduced equally well by a single-phase plasma emission model,
or by a two-phase model developed by {\it ASCA}, both incorporating cool
(1.7--2.0 keV) and hot ( keV) plasma temperatures. However, EPIC
spectra with higher statistics, accumulated over 3-dimentional thick shell
regions, were reproduced better by the two-phase model than by the singe-phase
one. Therefore, hot and cool plasma phases are inferred to co-exist in the
cluster core region within kpc. The iron and silicon abundances of
the plasma were reconfirmed to increase significantly towards the center, while
that of oxygen was consistent with being radially constant. The implied
non-solar abundance ratios explains away the previously reported excess X-ray
absorption from the central region. Although an additional cool (
keV) emission was detected within kpc of the center, the RGS data
gave tight upper limits on any emission with a tempeartures below
keV. These results are compiled into a magnetosphere model, which interprets
the cool phase as confined within closed magnetic loops anchored to the cD
galaxy. When combined with so-called Rosner-Tucker-Vaiana mechanism which
applies to solar coronae, this model can potentially explain basic properties
of the cool phase, including its temperature and thermal stability.Comment: 53 pages, 11 figures, accepted for publication in Astrophysical
Journa
Dynamic Evolution Model of Isothermal Voids and Shocks
We explore self-similar hydrodynamic evolution of central voids embedded in
an isothermal gas of spherical symmetry under the self-gravity. More
specifically, we study voids expanding at constant radial speeds in an
isothermal gas and construct all types of possible void solutions without or
with shocks in surrounding envelopes. We examine properties of void boundaries
and outer envelopes. Voids without shocks are all bounded by overdense shells
and either inflows or outflows in the outer envelope may occur. These
solutions, referred to as type void solutions, are further
divided into subtypes and
according to their characteristic behaviours across the sonic critical line
(SCL). Void solutions with shocks in envelopes are referred to as type
voids and can have both dense and quasi-smooth edges.
Asymptotically, outflows, breezes, inflows, accretions and static outer
envelopes may all surround such type voids. Both cases of
constant and varying temperatures across isothermal shock fronts are analyzed;
they are referred to as types and
void shock solutions. We apply the `phase net matching procedure' to construct
various self-similar void solutions. We also present analysis on void
generation mechanisms and describe several astrophysical applications. By
including self-gravity, gas pressure and shocks, our isothermal self-similar
void (ISSV) model is adaptable to various astrophysical systems such as
planetary nebulae, hot bubbles and superbubbles in the interstellar medium as
well as supernova remnants.Comment: 24 pages, 13 figuers, accepted by ApS
New measurement of via neutron capture on hydrogen at Daya Bay
This article reports an improved independent measurement of neutrino mixing
angle at the Daya Bay Reactor Neutrino Experiment. Electron
antineutrinos were identified by inverse -decays with the emitted
neutron captured by hydrogen, yielding a data-set with principally distinct
uncertainties from that with neutrons captured by gadolinium. With the final
two of eight antineutrino detectors installed, this study used 621 days of data
including the previously reported 217-day data set with six detectors. The
dominant statistical uncertainty was reduced by 49%. Intensive studies of the
cosmogenic muon-induced Li and fast neutron backgrounds and the
neutron-capture energy selection efficiency, resulted in a reduction of the
systematic uncertainty by 26%. The deficit in the detected number of
antineutrinos at the far detectors relative to the expected number based on the
near detectors yielded in the
three-neutrino-oscillation framework. The combination of this result with the
gadolinium-capture result is also reported.Comment: 26 pages, 23 figure
Evolution of the Reactor Antineutrino Flux and Spectrum at Daya Bay
The Daya Bay experiment has observed correlations between reactor core fuel
evolution and changes in the reactor antineutrino flux and energy spectrum.
Four antineutrino detectors in two experimental halls were used to identify 2.2
million inverse beta decays (IBDs) over 1230 days spanning multiple fuel cycles
for each of six 2.9 GW reactor cores at the Daya Bay and Ling
Ao nuclear power plants. Using detector data spanning effective Pu
fission fractions, , from 0.25 to 0.35, Daya Bay measures an average
IBD yield, , of
cm/fission and a fuel-dependent variation in the IBD yield,
, of cm/fission.
This observation rejects the hypothesis of a constant antineutrino flux as a
function of the Pu fission fraction at 10 standard deviations. The
variation in IBD yield was found to be energy-dependent, rejecting the
hypothesis of a constant antineutrino energy spectrum at 5.1 standard
deviations. While measurements of the evolution in the IBD spectrum show
general agreement with predictions from recent reactor models, the measured
evolution in total IBD yield disagrees with recent predictions at 3.1.
This discrepancy indicates that an overall deficit in measured flux with
respect to predictions does not result from equal fractional deficits from the
primary fission isotopes U, Pu, U, and Pu.
Based on measured IBD yield variations, yields of and cm/fission have been determined for the two
dominant fission parent isotopes U and Pu. A 7.8% discrepancy
between the observed and predicted U yield suggests that this isotope
may be the primary contributor to the reactor antineutrino anomaly.Comment: 7 pages, 5 figure
Improved Measurement of the Reactor Antineutrino Flux and Spectrum at Daya Bay
A new measurement of the reactor antineutrino flux and energy spectrum by the
Daya Bay reactor neutrino experiment is reported. The antineutrinos were
generated by six 2.9~GW nuclear reactors and detected by eight
antineutrino detectors deployed in two near (560~m and 600~m flux-weighted
baselines) and one far (1640~m flux-weighted baseline) underground experimental
halls. With 621 days of data, more than 1.2 million inverse beta decay (IBD)
candidates were detected. The IBD yield in the eight detectors was measured,
and the ratio of measured to predicted flux was found to be
() for the Huber+Mueller (ILL+Vogel) model. A 2.9~
deviation was found in the measured IBD positron energy spectrum compared to
the predictions. In particular, an excess of events in the region of 4-6~MeV
was found in the measured spectrum, with a local significance of 4.4~.
A reactor antineutrino spectrum weighted by the IBD cross section is extracted
for model-independent predictions.Comment: version published in Chinese Physics
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