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Figure 8 shows r_min in the second encounter for b=2.8. In this case, there are four zones of close-encounter orbit in the τ-ω diagram. Comparing Fig.8 with Fig. 7b, the total area occupied by the recurrent close-encounter orbits (the dotted regions in Fig. 8) is smaller than that in the first encounter but not small enough to be neglected.
Collision orbits belong necessarily to close-encounter orbits. Consequently, to find collision orbits, we subdivided the τ-ω phase space of close-encounter orbits (i.e., the finely dotted regions in Fig.7) more densely (mesh width being as small as 0.002π in τ) and pursued orbits for each set of τ and ω. Furthermore, as the phase volume of τ and ω occupied by collision orbits, we evaluated a “differential” collisional rate <p(e, i, b)> given by
<p(e, i, b)>=(1/(2π)^2)∫p_col (e, i, b, τ, ω)dτdω. (24)
Here, we calculated <p(e, i, b)> separately for 1-, 2-, and more recurrent orbits. The results are shown in Fig. 9, from which we can see that 2-recurrent collision orbits exist for relatively large b, and n-current (n≧3) ones exist only for b≒b_max. That is, the recurrent collision orbits appear only in cases of relatively low energy. From Eq. (10), we have
<P(e, i)>=∫【-∞→∞】(3/2)|b|<p(e, i, b)>db. (25)
Using evaluated values of <p(e, i, b)> for various b, we finally obtain <P(e, i)>=0.114 for (e, i)=(1.0, 0.5); the contribution of 2-recurrent orbits is 5%, and that of 3- and more-recurrent orbits is less than 1%. For this case (e=1.0 and i=0.5), we observed 874 collision orbits. The statistical error in evaluating <P(e, i)> is therefore presumed to be of the order of 4%. Since the contribution of 3- and more-recurrent orbits is within the statistical fluctuation, it can be neglected.
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お礼
強調は。。。笑う そうね。。。この文章だけを見ると変よね! lol..:o) その頁全体はこちら (5番目の段落はまだ和訳してない) 1. “Law and order exist for the purpose of establishing justice.” This fundamental principle isn't widely followed in Japan, however think about it for a moment. “Law and order exist for the purpose of establishing justice.” 2. “Justice” (fairness) is the goal, and we use “law and order” (rules and enforcement) to maintain it. This fundamental principle is used by judges in every society to a different degree. The more a society follows the fundamental principle, the more socially advanced (civilized) the country is considered. And the more a society devotes to “order” rather than justice, the more barbaric the country is considered. 3. “Barbaric” is used to describe the country, because if a society devotes more to “order” than to justice (fairness) it means that the society is serving a dictator's interest. 4. So how does Japan rank? At “A screening of the film I Just Didn’t Do It, held for invited members of the Committee against Torture. Viewing the film were about 60 people including three committee members, UN employees, and NGO personnel. The film is a story about a young man who is falsely accused of groping, held in long-term confinement, and put on trial. It received a considerable response, with statements such as, 'Is this true? And Japan is an advanced nation?'” 5. This response begs the question, since Japan no longer has an acting dictator (Absolutism of the Emperor), why is Japan still devoted more to “order” than to fairness?