6,786 research outputs found
Evolution of Massive Black Hole Binaries
We present the result of large-scale N-body simulations of the
stellar-dynamical evolution of a massive black-hole binary at the center of a
spherical galaxy. We focus on the dependence of the hardening rate on the
relaxation timescale of the parent galaxy. A simple theoretical argument
predicts that a binary black hole creates the ``loss cone'' around it. Once the
loss cone is formed, the hardening rate is determined by the rate at which
field stars diffuse into the loss cone. Therefore the hardening timescale
becomes proportional to the relaxation timescale. Recent N-body simulations,
however, have failed to confirm this theory and various explanations have been
proposed. By performing simulations with sufficiently large N (up to )
for sufficiently long time, we found that the hardening rate does depend on N.
Our result is consistent with the simple theoretical prediction that the
hardening timescale is proportional to the relaxation timescale. This
dependence implies that most massive black hole binaries are unlikely to merge
within the Hubble time through interaction with field stars and gravitational
wave radiation alone.Comment: Reviced version accepted for publication in ApJ. Scheduled to appear
in the February 10, 2004 issu
Non-Poissonian level spacing statistics of classically integrable quantum systems based on the Berry-Robnik approach
Along the line of thoughts of Berry and Robnik\cite{[1]}, we investigated the
gap distribution function of systems with infinitely many independent
components, and discussed the level-spacing distribution of classically
integrable quantum systems. The level spacing distribution is classified into
three cases: Case 1: Poissonian if , Case 2: Poissonian
for large , but possibly not for small if , and
Case 3: sub-Poissonian if . Thus, even when the energy
levels of individual components are statistically independent, non-Poisson
level spacing distributions are possible.Comment: 5 pages, 0 figur
Long-Range Spectral Statistics of Classically Integrable Systems --Investigation along the Line of the Berry-Robnik Approach--
Extending the argument of Ref.\citen{[4]} to the long-range spectral
statistics of classically integrable quantum systems, we examine the level
number variance, spectral rigidity and two-level cluster function. These
observables are obtained by applying the approach of Berry and Robnik\cite{[0]}
and the mathematical framework of Pandey \cite{[2]} to systems with infinitely
many components, and they are parameterized by a single function ,
where corresponds to Poisson statistics, and
indicates deviations from Poisson statistics. This implies that even when the
spectral components are statistically independent, non-Poissonian spectral
statistics are possible.Comment: 13 pages, 4 figure
Long-Term Evolution of Massive Black Hole Binaries. II. Binary Evolution in Low-Density Galaxies
We use direct-summation N-body integrations to follow the evolution of binary
black holes at the centers of galaxy models with large, constant-density cores.
Particle numbers as large as 400K are considered. The results are compared with
the predictions of loss-cone theory, under the assumption that the supply of
stars to the binary is limited by the rate at which they can be scattered into
the binary's influence sphere by gravitational encounters. The agreement
between theory and simulation is quite good; in particular, we are able to
quantitatively explain the observed dependence of binary hardening rate on N.
We do not verify the recent claim of Chatterjee, Hernquist & Loeb (2003) that
the hardening rate of the binary stabilizes when N exceeds a particular value,
or that Brownian wandering of the binary has a significant effect on its
evolution. When scaled to real galaxies, our results suggest that massive black
hole binaries in gas-poor nuclei would be unlikely to reach gravitational-wave
coalescence in a Hubble time.Comment: 13 pages, 8 figure
Time-Symmetrized Kustaanheimo-Stiefel Regularization
In this paper we describe a new algorithm for the long-term numerical
integration of the two-body problem, in which two particles interact under a
Newtonian gravitational potential. Although analytical solutions exist in the
unperturbed and weakly perturbed cases, numerical integration is necessary in
situations where the perturbation is relatively strong. Kustaanheimo--Stiefel
(KS) regularization is widely used to remove the singularity in the equations
of motion, making it possible to integrate orbits having very high
eccentricity. However, even with KS regularization, long-term integration is
difficult, simply because the required accuracy is usually very high. We
present a new time-integration algorithm which has no secular error in either
the binding energy or the eccentricity, while allowing variable stepsize. The
basic approach is to take a time-symmetric algorithm, then apply an implicit
criterion for the stepsize to ensure strict time reversibility. We describe the
algorithm in detail and present the results of numerical tests involving
long-term integration of binaries and hierarchical triples. In all cases
studied, we found no systematic error in either the energy or the angular
momentum. We also found that its calculation cost does not become higher than
those of existing algorithms. By contrast, the stabilization technique, which
has been widely used in the field of collisional stellar dynamics, conserves
energy very well but does not conserve angular momentum.Comment: figures are available at http://grape.c.u-tokyo.ac.jp/~funato/; To
appear in Astronomical Journal (July, 1996
Cluster Mass Estimate and a Cusp of the Mass Density Distribution in Clusters of Galaxies
We study density cusps in the center of clusters of galaxies to reconcile
X-ray mass estimates with gravitational lensing masses. For various mass
density models with cusps we compute X-ray surface brightness distribution, and
fit them to observations to measure the range of parameters in the density
models. The Einstein radii estimated from these density models are compared
with Einstein radii derived from the observed arcs for Abell 2163, Abell 2218,
and RX J1347.5-1145. The X-ray masses and lensing masses corresponding to these
Einstein radii are also compared. While steeper cusps give smaller ratios of
lensing mass to X-ray mass, the X-ray surface brightnesses estimated from
flatter cusps are better fits to the observations. For Abell 2163 and Abell
2218, although the isothermal sphere with a finite core cannot produce giant
arc images, a density model with a central cusp can produce a finite Einstein
radius, which is smaller than the observed radii. We find that a total mass
density profile which declines as produces the largest radius
in models which are consistent with the X-ray surface brightness profile. As
the result, the extremely large ratio of the lensing mass to the X-ray mass is
improved from 2.2 to 1.4 for Abell 2163, and from 3 to 2.4 for Abell 2218. For
RX J1347.5-1145, which is a cooling flow cluster, we cannot reduce the mass
discrepancy.Comment: 23 pages, 10 figures, Latex, uses aasms4.sty, accepted for
publication in ApJ, Part
A general framework for online audio source separation
We consider the problem of online audio source separation. Existing
algorithms adopt either a sliding block approach or a stochastic gradient
approach, which is faster but less accurate. Also, they rely either on spatial
cues or on spectral cues and cannot separate certain mixtures. In this paper,
we design a general online audio source separation framework that combines both
approaches and both types of cues. The model parameters are estimated in the
Maximum Likelihood (ML) sense using a Generalised Expectation Maximisation
(GEM) algorithm with multiplicative updates. The separation performance is
evaluated as a function of the block size and the step size and compared to
that of an offline algorithm.Comment: International conference on Latente Variable Analysis and Signal
Separation (2012
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Reactive oxygen species induced by water containing nano-bubbles and its role in the improvement of barley seed germination
This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.The study of reactive oxygen species (ROS) generation caused by nano-bubbles (NBs) is of great importance for its application in both physiological activity promotion aspect and sterilization aspect. In this paper, Aminophenyl Fluorescein (APF) was used as a fluorescent reagent for the detection of ROS generation by NBs. The NBs scattering could cause the decrease of fluorescence intensity. Meanwhile, the quenching effect of oxygen could also cause the decrease of fluorescence intensity. Although the above two factors masked the fluorescence intensity generation by ROS, the fluorescence intensity of the water containing NBs still increased with NBs generation time, which proved that oxygen NBs could generate ROS. Moreover, the endogenous ROS in the barley seed cells were measured in the seed that germinated in the water containing NBs and the distilled water respectively. According to the results of seed staining experiments, both the microscope images and the absorbance at 560nm proved that the seeds dipped in the water containing NBs could generate more ROS compared to those in the distilled water. These findings greatly increase the NBs potential use both in agricultural field and environmental field
The dynamics of spiral arms in pure stellar disks
It has been believed that spirals in pure stellar disks, especially the ones
spontaneously formed, decay in several galactic rotations due to the increase
of stellar velocity dispersions. Therefore, some cooling mechanism, for example
dissipational effects of the interstellar medium, was assumed to be necessary
to keep the spiral arms. Here we show that stellar disks can maintain spiral
features for several tens of rotations without the help of cooling, using a
series of high-resolution three-dimensional -body simulations of pure
stellar disks. We found that if the number of particles is sufficiently large,
e.g., , multi-arm spirals developed in an isolated disk can
survive for more than 10 Gyrs. We confirmed that there is a self-regulating
mechanism that maintains the amplitude of the spiral arms. Spiral arms increase
Toomre's of the disk, and the heating rate correlates with the squared
amplitude of the spirals. Since the amplitude itself is limited by the value of
, this makes the dynamical heating less effective in the later phase of
evolution. A simple analytical argument suggests that the heating is caused by
gravitational scattering of stars by spiral arms, and that the self-regulating
mechanism in pure-stellar disks can effectively maintain spiral arms on a
cosmological timescale. In the case of a smaller number of particles, e.g.,
, spiral arms grow faster in the beginning of the simulation
(while is small) and they cause a rapid increase of . As a result, the
spiral arms become faint in several Gyrs.Comment: 18 pages, 19 figures, accepted for Ap
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