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Physics Undergraduate

流体力学の最初の最初、ラグランジュ微分のところでつまづいて困っております。 二枚目の?をつけた計算過程はどのような微分なのでしょうか? よろしくお願いします。

の1 流れの運動学 8 1 = (u.V)u U のようにして得られた. 記号▽はナブラ (nabla) とよみ 0 鶏分(1.14) 0 マ= e』 + ey Oy 0z のように定義される演算子 (operator) であるす. ea, ey. Ez はそれぞれ』軸, 軸,2軸の正の向きに向かう単位ベクトル (unit vector) で, これらを基本ベク トル (fundamental unit vector)という。 式(1.12) の両辺を At でわって, At →0 の極限をとると,流体粒子の受け る加速度a(z,t) を求めることができ に Au a(x, t) = lim + (u-V) u(z, t) At→0 At Ot D -u(x,t) Dt となる.ただし D +u.V Ot Dt で,D/Dt をラグランジュ微分 (Lagrangian derivative),あるいは実質微 分(substantial derivative), あるいは物質微分 (material derivative) という。 Du/Dt= Ou/0t+ (u.V)uの右辺第1項は, 流体中のある点aをつぎつぎと 通過する流体粒子の速度の時間的変化の割合を表しており,局所加速度 (local acceleration) とよばれている. また第2項は,点cにある流体粒子がある瞬間 にその前後の流体粒子の速度差のために受ける速度の時間的変化割合で対流加 速度 (convective acceleration) とよばれている。 ラグランジュ微分 D/Dtは, オイラーの方法の意味で »とtの関数として表 された量,すなわち 「場の量」に対してのみ作用させることができる. なぜな ら,その定義式(1.16) の右辺は, 独立変数を αとtとするときの偏微分0/0tと ▽によって構成されているからである. aとtの任意関数 f(z,t) のラグラン ジュ微分は,式(1.15) を導いた過程から理解できるように, 流れに伴う f(x.t) の時間的変化の割合,すなわち, 流体粒子の軌跡に沿っての f(z,t) の時間的変 化の割合を表す。 十演算子▽をスカラー関数f(a)に作用させて得られるVfは, f の勾配 (gradient) とよばれ る。▽をスカラー関数に作用させたときは▽の代わりに grad という記号を使ってもよい。す なわち, ▽f=gradf. 後に述べるように, ▽をベクトルとみなしてベクトル関数に作用させ る(内積をとる)ときは, 記号 gradは使わない、ただし、式(1.13) の▽は grad を使って書 くことができる。

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English Junior High

問 本文の内容から考えて二重四角に共通して入る最も適当な英語一字を書きなさい。 答えmakeなんですがbecomeではだめですか?

4 次の英文は,中学生の大介が, アメリカ人留学生のポール(Paul)と会話している場面のもの です。これを読んで, 問いに答えなさい。 Daisuke: Hi, Paul. Our *graduation ceremony is next week. Paul: Yes, it is. Then we will go to different high schools. Daisuke: Iwill *miss my classmates. but I have a lot of good *memories. Paul: What is your best memory of junior high school? Daisuke: Well, my best memory is our school *chorus contest. Paul: Why? Daisuke: Because we practiced hard as a group and we became good friends. But it wasn't easy. At first, some of our classmates didn't come to the *practice. ① I had the same *feelings. Other members didn't That 2② Paul: I remember that. say *anything. Then, as a leader, you *gave a great speech. *encouraged everyone to sing together. After that, we started to give and listen to ideas to our chorus group better. Finally, our *harmony became Daisuke: Thank you. very beautiful. What is your best memory, Paul? Paul: 3 Mine is the soccer club. Daisuke: I know your soccer team was strong. Paul: Well, our team had the same experience. We were not strong at first, because we didn't listen to each other. Some members didn't come to our practice. So our team *lost our first game. Daisuke: Really? Paul: Yes. After that, we *realized that we had to talk a lot in our team. In the *meeting, we *set our goal, and we decided to give and listen to ideas to our team stronger. Then, our team became better and we could enjoy playing soccer together. Daisuke: We had a wonderful time and learned many things with our classmates and *teammates. That will help us when we are high school students. Paul: That's right. (注) graduation ceremony 卒業式 memory(memories) 思い出 practice 練習 miss いなくて寂しく思う chorus contest 合唱コンテスト anything(否定文で)何も encourage (d)~ to ~を…するよう励ます feelings 感情 give a speech スピーチをする harmony ハーモニー meeting ミーティング teammate(s) lost lose(負ける)の過去形 set one's goal 目標を設定する realize(d) 気づく チームメート

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English Senior High

英語に自信がある人回答づくりお願いします! ※書き込みは気にしないでください。

第2間 次の金会話文を読んで、 股設間に答えなさい。 Miranda: Are you enjoying yourself here in the States, Yuya, now that you've been here for a fow months? Yuya: Yes, I'm having a great time, Ite ( 1 ) how much of it is being in a foreiy Country and how much of it is just being in college, though, Miranda: Iguess I know ( 2 ), There's a lot more freedom iving away from home . don't have my mom and dad badgering me all the time about where P'm telling me to do my homework, either, Yuya: Exactly, olway/my/the /were / parents / same ], Miranda: I suppose that kind of thing has no borders, Do you find yourself ( 3 ).. all? Yuya: Not really, IfI were living alone, I might, But I have roommates and . been ealling or texting my parents once a week, ( 4 )I gues I don't feel tho isolated, Imiss Japanese food a bit but it'snot too bad, How about you'2 Miranda: Not one bit, I'm gl to/ to be / happy / my own/live / able ] life, Even thouoh I guess Iam still adjusting a little, It's tough having to fend for myself for fud I sometimes get so wrapped up in things that I( 5 ), and then I pay for it later Maybe I should have gotten the meal plan after all, Yuya: It's so expensive, though, And you'd still have to go to the dining hall, s01 don't ol solve / your/think/it/problem/would ], Maybe I'll just have to invite you out for lunch like this more often, Miranda: Who am I to say no to that? Yuya: OK, ola/away/ has/ that/and/ half] the best ice eream, 6 ) Do you want to get some dessert? I know a place about a block Miranda: You don't have to twist my arm, lo o A dnids nog o fal 00 fom yod ef'T IAl odhon dd o 3.

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