感謝の意を表す 教授や博士の助言に感謝
- この文章は、教授や博士からの有益な助言と絶え間ない励ましに感謝の意を表しています。
- 計算は、主に京都大学データ処理センターのFACOM M-200で行われました。
- この研究は、文部科学省科学研究費補助金（課題番号: 511409, 56110009, 57103006）の支援を受けています。また、本論文の発表は、大阪工業大学中央研究所の援助を受けています。
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Acknowledgements The author wishes to thank Professor C.Hayashi and Dr.K. Nakazawa for their useful advice and continuous encouragement. The numerical calculations were mainly performed by FACOM M-200 at Data Processing Center of Kyoto University. This work was supported by the Grant-in-Aid for Scientific Research of the Ministry of Education, Science and Culture (Nos. 511409, 56110009 and 57103006). The publication of this paper is indebted to the aid of Central Research Laboratory of Osaka Institute of Technology. よろしくお願いします。
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謝辞 本論文の作成に当たり、C.Hayashi教授ならびにK. Nakazawa博士の適切な助言と絶え間ない励ましに感謝の意を表したい。数値計算は、主に京都大学大型計算機センター（※1）のFACOM M-200で行った。本研究は、文部科学省基盤研究費（Nos. 511409, 56110009及び 57103006)の助成を受けたものである（※2）。本論文の刊行にあたっては大阪工業大学中央研究所の多大な協力を頂戴している。 ※1：固有名詞なので下記から名称を引用いたしました。 https://ipsj.ixsq.nii.ac.jp/ej/index.php?active_action=repository_view_main_item_detail&item_id=35765&item_no=1&page_id=13&block_id=8 ※2：国費を使っての研究発表においてはその旨を謝辞で表示することが義務づけられておりますので下記表記ルールに従って訳しました。 http://www.mext.go.jp/a_menu/shinkou/hojyo/faq/1322968.htm
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- marbleshit
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謝辞 著者はC.林教授とK.中沢博士の有益なアドバイスと絶間ない励ましに対し感謝を述べたい。数値計算は、主に京都大学のデータ処理センターのFACOM M-200を使用した。この業績は、文部科学省の助成金の補助を受けている(511409、56110009と57103006)。またこの論文刊行に際しては、大阪工業大学の中央研究所の恩義に浴することとなった。
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謝辞 著者は、有益なアドバイスと不断の激励をいただきました林教授並びに中沢博士に感謝いたします。 計算は、主として京都大学データ処理センターの FACOM M-200 で行いました。 本研究は文部科学省の学術研究助成金 (Nos. 511409, 56110009 and 57103006) の支持を受けました。本研究の公刊に際しましては大阪工業大学中央研究所の援助をいただいております。
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3. Results of the orbital calculations In this paper, we describe our numerical results only for the special cases e_i~=0 and e_i~=4 in order to find the characteristic features of the two-body encounters of Keplerian particles. 3.1. For the case e_i~=0 In this case the orbital element, δ_i, loses its meaning because the particle orbits have no periheria and , hence, we can actually assign the initial condition by one parameter, b_i~. The orbital calculations are performed for about 3800 cases with various values of b_i~ from －10 to 10. よろしくお願いします。
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3. Examples of orbital calculations To find efficient numerical procedures for obtaining <P(e ,i)>, we have made detailed orbital calculations for two typical cases, (e, i)=(0, 0) and (1, 0.5). The former is the simplest case with a single parameter b, and corresponds to that studied by Giuli (1968), Nishida (1983) and Petit and Hénon (1986). In the latter, the orbit changes with three parameters b, τ, and ω in a complicated manner. From this example, we can see the characteristic features of orbits in the three-dimensional case. In the present examples, it is supposed that a protoplanet with a mean mass density 3gcm^-3, orbits in the Earth’s region. Furthermore, we adopt 1% as the limiting accuracy criterion for use of the two-body approximation. These give 0.005 and 0.03 for the radius of the protoplanet and that of the two-body sphere, respectively (see Eqs. (12) and (13)). よろしくお願いします。
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In the present paper, we first describe initial conditions for orbital calculations in the framework of Hill’s equations (Sect.2). In Sect.3, orbital calculations are made for particular sets of e and i, i.e., (e,i)=(0,0) and (1,0.5). Based on these calculations and previous works: Papers I and II, Nishida (1983), Hénon and Petit (1986), and Petit and Hénon (1986), we develop an efficient numerical procedure obtaining <P(e, i)> (Sect. 4).According to this procedure, we systemically integrate the orbits of relative motion, to find collision orbits. Furthermore, compiling results of these orbital calculations, we find <P(e, i)> for various sets of e and i and compare them with those in the two-body approximation <P(e, i)>_2B (Sects. 5 to 7). The results will be compared with those of Nishida (1983) and Wetherill and Cox (1985) who also studied the collisional rate taking account of the effect of solar gravity (but their studies were restricted, as mentioned later).
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Furthermore, ρ is the density of the planet and is taken to be 4.45g/cm^3 according to Lewis. The values of r_p/h are tabulated in Table I for various regions from the Sun. It is to be noticed that the planetary radius decreases as the increase in the distance from the Sun in the system of units adopted here. Orbital calculations are performed by means of the 4th order Runge-Kutter-Gill method with an accuracy of double precision. よろしくお願いします。
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Table 3. Numbers of two-dimensional collision orbits (i=0) found by our orbital calculations. Only four cases of e are tabulated as examples. The numbers of collision orbits decrease with the decrease in the planetary radius r_p. Fig.11. The two-dimensional enhancement factor R(e,0) as a function of e for r_p=0.005, 0.001, and 0.0002. The enhancement factor depends rather weakly on r_p. Fig.12. The collisional flux F(e,E) defined by Eq. (32) as a function of the Jacobi energy E for e=0, 0.5, 1.0, and 2.0. ↓Table 3. http://www.fastpic.jp/images.php?file=0416143752.jpg ↓Fig.11. http://www.fastpic.jp/images.php?file=9556242912.jpg ↓Fig.12. http://www.fastpic.jp/images.php?file=1594984078.jpg よろしくお願いします。
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2. Initial conditions for orbital integration To obtain <P(e, i)>, we must numerically compute a number of orbits of planetesimals with various values of b, τ, and ω for each set of (e, i) and then examine whether they collide with the protoplanet or not. In this section, we consider the ranges of b, τ, and ω to be assigned in orbital calculations, and give initial conditions for orbital integration. One can see in Eq. (6) that Hill’s equations are invariant under the transformation of z→-z and that of x→-x and y→-y; on the other hand, a solution to Hill’s equations is described by Eq. (7). From the above two characteristics, it follows that it is sufficient to examine only cases where 0≦ω≦π and b≧0. Furthermore, we are not interested in orbits with a very small b or a very large b; an orbit with a very small b bends greatly and returns backward like a horse shoe ( Petit and Hénon, 1986; Nishida, 1983 ), while that with a very large b passes by without any appreciable change in its orbital element. どうかよろしくお願いします。
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The article mentions that it took 17 years from the beginning of the investigation to the publication of the 11 papers on Ardi in 2009. During that time only one paper was published by the team members, in 1994. It is interesting that the team did not publish papers on the research for 15 years, for we live in the era of “publish or perish” – in other words, professors understand that they need to publish academic articles in order to keep their jobs, or at least to be able to advance their careers. True, 47 of the 70 investigators on the team were listed as authors on the 11 papers. Also, the publication of the papers all at once essentially guaranteed that the papers were given a lot of attention. Still, it is encouraging that the universities and other institutions that funded the research continued to support the team members despite the lack of papers. After all, “publish or perish” is largely due to the need for universities to be recognized as places where a lot of research is being done. High levels of publication lead to high evaluations, which helps attract students and funding to a particular university. The presence of good students and large research budgets help the school maintain its excellence. So the term “publish or perish” may not be quite as cynical as it first sounds.
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2. Methods The record of carbon-14 content for the Medieval Maximum Period was obtained using a ~ 2000-year-old Japanese cedar tree (Cryptomeria japonica) taken at the Yakushima Island in Japan (30.18 N, 130.30 E). For the measurements of carbon-14 content in annual rings with absolute date, dendro-chronology has been applied. The dated rings were separated carefully and washed using (1) HCl solution (70 °C), (2) NaOH solution (70 °C) and (3) NaClO2/HCl solution (75 °C) to extract cellulose from every tree-ring sample. The cellulose samples were combusted and converted to graphite on Fe powder by hydrogen reduction. The graphite samples were introduced to the Accelerator Mass Spectrometer (AMS) to measure the 14C/12C and 13C/12C ratios. We have used HVEE AMS at Nagoya University in Japan ( Nakamura et al., 2000), which achieves accuracy of 0.3%. The Δ14C was calculated according to the method by Stuiver and Polach (1977). よろしくお願いします。
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The corresponding velocity components are given by x_s'=esin(t_0-τ_s) y_s'=‐(3/2)b_s+2ecos(t_0-τ_s), (22) z_s'=icos(t_0-ω_s). In the above, we set t_0=-(2y_0/(3b)) without any loss of generality, for later convenience, which is equivalent to the choice of φ=0 in Eq. (7). In Eq. (21), y_0 is set to be max (40, 20e, 20i). The choice of y_0 is not essential to the evaluation of <P(e, i)> as long as y_0 is larger than this value since Eq. (19) is valid for such a large y_0. In Table 2, the evaluated values of <P(e,i)> are tabulated for various y_0 in the cases of (e, i) = (0,0) and (4,0): when y_0≧max(40, 20e, 20i), <P(e, i)> is almost independent of y_0 within an accuracy of 0.1% for the case of (e, i)=(0, 0) and 5% for (e, i)=(4, 0). よろしくお願いします。
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Fig.10. The collision probability P_c(b_i~) for e_i~=4 at the region near the present Earth’s orbit. ↓Fig.10. http://www.fastpic.jp/images.php?file=3466353586.jpg Fig.11. The coefficient C_K obtained from our orbital calculations for both cases e_i~=0 and 4. Each mark indicates the value of C_K at the position of each present planet. Solidlines show C_K∝R^－(1/2). ↓Fig.11. http://www.fastpic.jp/images.php?file=4992926857.jpg Table I. The ratio, γ, of the collisional rate of Keplerian particles to that of free space particles for the various regions from the Sun. The coefficient C_K, defined by Eq. (4・6), and the planetary radius, γ_p, in units of h are also tabulated. ↓Table I. http://www.fastpic.jp/images.php?file=9315075324.jpg For e_i~=0, the orbital element, δ_i, loses its meaning as mentioned in §3.1 and only impact parameter b_i~ determines whether a particle collides with the planet or not; i.e., the collision probability P_c(b_i~) is unity or zero. 長文になりますが、どうかよろしくお願いします。
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