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 $N$-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

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 $t$ 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 $\kappa t(1+o[1])$ for large $t$ and an explicit form gives the constant $\kappa$. The expression is of a complicated form, but it converges to the known constant as the drift tends to $0$

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

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 ($N$) is larger than the critical number ($N_{\rm crit}$), 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 ($10^8$ Kepler time) for $N\leq N_{\rm crit}$. 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, $N_{\rm crit} = 4$. 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 $Kepler$ mission.Comment: accepted for publication in Icaru