1,555 research outputs found
Formation of Close-in Super-Earths by Giant Impacts: Effects of Initial Eccentricities and Inclinations of Protoplanets
Recent observations have revealed the eccentricity and inclination
distributions of close-in super-Earths. These distributions have the potential
to constrain their formation processes. In the in-situ formation scenario, the
eccentricities and inclinations of planets are determined by gravitational
scattering and collisions between protoplanets on the giant impact stage. We
investigate the effect of the initial eccentricities and inclinations of
protoplanets on the formation of close-in super-Earths. We perform -body
simulations of protoplanets in gas-free disks, changing the initial
eccentricities and inclinations systematically. We find that while the
eccentricities of protoplanets are well relaxed through their evolution, the
inclinations are not. When the initial inclinations are small, they are not
generally pumped up since scattering is less effective and collisions occur
immediately after orbital crossing. On the other hand, when the initial
inclinations are large, they tend to be kept large since collisional damping is
less effective. Not only the resultant inclinations of planets, but also their
number, eccentricities, angular momentum deficit, and orbital separations are
affected by the initial inclinations of protoplanets.Comment: Accepted for publication in A
Hitting times of Bessel processes, volume of Wiener sausages and zeros of Macdonald functions
We derive formulae for some ratios of the Macdonald functions, which are
simpler and easier to treat than known formulae. The result gives two
applications in probability theory. One is the formula for the L{\'e}vy measure
of the distribution of the first hitting time of a Bessel process and the other
is an explicit form for the expected volume of the Wiener sausage for an even
dimensional Brownian motion. Moreover, the result enables us to write down the
algebraic equations whose roots are the zeros of Macdonald functions.Comment: 42 page
The probability densities of the first hitting times of Bessel processes
We are concerned with the first hitting times of the Bessel processes. We
give explicit expressions for the densities by means of the zeros of the Bessel
functions and show their asymptotic behavior.Comment: 9 page
Hitting times to spheres of Brownian motions with and without drifts
Explicit formulae for the densities of the first hitting times to the sphere
of Brownian motions with drifts are given. We need to consider the joint
distributions of the first hitting times to the sphere and the hitting
positions of the standard Brownian motion and explicit expression for their
Laplace transforms are given, which are different from the known formulae in
the literature and are of independnt interest
A formula for the expected volume of the Wiener sausage with constant drift
We consider the Wiener sausage for a Brownian motion with a constant drift up
to time associated with a closed ball. In the two or more dimensional
cases, we obtain the explicit form of the expected volume of the Wiener
sausage. The result says that it can be represented by the sum of the mean
volumes of the multi-dimensional Wiener sausages without a drift. In addition,
we show that the leading term of the expected volume of the Wiener sausage is
written as for large and an explicit form gives the
constant . The expression is of a complicated form, but it converges to
the known constant as the drift tends to
Asymptotics of the probability distributions of the first hitting times of Bessel processes
The asymptotic behavior of the tail probabilities for the first hitting times
of the Bessel process with arbitrary index is shown without using the explicit
expressions for the distribution function obtained in the authors' previous
works
A Rule-Based Approach For Aligning Japanese-Spanish Sentences From A Comparable Corpora
The performance of a Statistical Machine Translation System (SMT) system is
proportionally directed to the quality and length of the parallel corpus it
uses. However for some pair of languages there is a considerable lack of them.
The long term goal is to construct a Japanese-Spanish parallel corpus to be
used for SMT, whereas, there are a lack of useful Japanese-Spanish parallel
Corpus. To address this problem, In this study we proposed a method for
extracting Japanese-Spanish Parallel Sentences from Wikipedia using POS tagging
and Rule-Based approach. The main focus of this approach is the syntactic
features of both languages. Human evaluation was performed over a sample and
shows promising results, in comparison with the baseline.Comment: International Journal on Natural Language Computing (IJNLC) Vol.1,
No.3, October 201
On the zeros of the Macdonald functions
We are concerned with the zeros of the Macdonald functions or the modified
Bessel functions of the second kind with real index. By using the explicit
expressions for the algebraic equations satisfied by the zeros, we describe the
behavior of the zeros when the index moves. Results by numerical computations
are also presented.Comment: 8 pages, 1 figure, 1 tabl
A Span Selection Model for Semantic Role Labeling
We present a simple and accurate span-based model for semantic role labeling
(SRL). Our model directly takes into account all possible argument spans and
scores them for each label. At decoding time, we greedily select higher scoring
labeled spans. One advantage of our model is to allow us to design and use
span-level features, that are difficult to use in token-based BIO tagging
approaches. Experimental results demonstrate that our ensemble model achieves
the state-of-the-art results, 87.4 F1 and 87.0 F1 on the CoNLL-2005 and 2012
datasets, respectively.Comment: Accepted by EMNLP 201
The Orbital Stability of Planets Trapped in the First-Order Mean-Motion Resonances
Many extrasolar planetary systems containing multiple super-Earths have been
discovered. N-body simulations taking into account standard type-I planetary
migration suggest that protoplanets are captured into mean-motion resonant
orbits near the inner disk edge at which the migration is halted. Previous
N-body simulations suggested that orbital stability of the resonant systems
depends on number of the captured planets. In the unstable case, through close
scattering and merging between planets, non-resonant multiple systems are
finally formed. In this paper, we investigate the critical number of the
resonantly trapped planets beyond which orbital instability occurs after disk
gas depletion. We find that when the total number of planets () is larger
than the critical number (), crossing time that is a timescale of
initiation of the orbital instability is similar to non-resonant cases, while
the orbital instability never occurs within the orbital calculation time
( Kepler time) for . Thus, the transition of crossing
time across the critical number is drastic. When all the planets are trapped in
7:6 resonance of adjacent pairs, . We examine the dependence
of the critical number of 4:3, 6:5 and 8:7 resonance by changing the orbital
separation in mutual Hill radii and planetary mass. The critical number
increases with increasing the orbital separation in mutual Hill radii with
fixed planetary mass and increases with increasing planetary mass with fixed
the orbital separation in mutual Hill radii. We also calculate the case of a
system which is not composed of the same resonance. The sharp transition of the
stability can be responsible for the diversity of multiple super-Earths
(non-resonant or resonant), that is being revealed by mission.Comment: accepted for publication in Icaru
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