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POINT LATTICES AND THE UNIT CELL Let’s consider the three-dimensional arrangement of points in Fig.15.This arrangement is called a point lattice. If we take any point in the point lattice it has exactly the same number and arrangement of neighbors(i.e.,identical surroundings) as any other point in the lattice. This condition should be fairly obvious considering our description of long-range order in Sec. 2.1 We can also see from Fig. 15 that it is possible to divide the point lattice into much smaller untils such that when these units are stacked in three dimensions they reproduce the point lattice. This small repeating unit is known as the unit cell of the lattice and is shown in Fig.16 A unit cell may be described by the interrelationship between the lengths(a,b,c) of its sides and the interaxial angles (α,β,γ)between them. (α is the angle between the b and c, axes,β is the angle between the a and c axes, and γ is the angle between the a and b axes.)The actual values of a,b,and c, and α,β and γ are not important, but their interrelation is. The lengths are measured from one corner of the cell, which is taken as the origin. These lengths and angles are called the lattice parameters of the unit cell, or sometimes the lattice constants of the cell. But the latter term is not really appropriate because they are not necessarily constants; for example, they can vary with changes in temperature and pressure and with alloying. [Note: We use a,b and c to indicate the axes of the unit cell; a,b and c for the lattice parameters, and a,b and c for the vectors lying along the unit-cell axes.]

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点格子と単位格子 Fig.15.This取り決めの点の3次元配列が1ポイントの格子と呼ばれていると考えましょう。我々が点格子で点をとるならば、それは格子の他のどの点とも同じ正確に隣人（i.e.,identical環境）の数と配列を持ちます。条項2.1のWeの長期の命令の我々の説明が図からわかることもできると考えて、この状態はかなり明らかでなければなりません。点格子を非常により小さな非ゴマに分けることができる15、これらの単位が3つの局面で積み重なるとき、彼らは点格子を再現します。この小さな繰り返し単位は格子の単位格子として知られていて、図16 Aに、単位格子がその側の長さ（a,b,c）と彼らの間のインター軸の角度（α、β、γ）の間で相互関係によって記述されるかもしれないことを明らかにされます。（αはbとc（軸）の間の角度です。そして、βは角度です、そして、c軸、そして、γは角度です、そして、b軸。）ドキュメンタリーはa,b,andのcを評価します、そして、α、βとγは重要でありません、しかし、彼らの相互関係はそうです。長さは独房の1つの隅から計られます。そして、それは起源としてされます。これらの長さと角度は、単位格子の格子定数または時々細胞の格子の定数と呼ばれています。しかし、彼らが必ずしも定数であるというわけではないので、後の語は本当に適切でありません;たとえば、温度と圧力の変化で、そして、合金になることで、彼らは異なることができます。［注：我々は、単位格子の軸を示すために、a,bとcを使います;格子定数とa,bと単位-細胞軸に沿って存在しているベクトルのためのcのためのa,bとc。］

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  • 和訳をお願いします

    POINT LATTICES AND THE UNIT CELL Let’s consider the three-dimensional arrangement of points in Fig.15.This arrangement is called a point lattice. If we take any point in the point lattice it has exactly the same number and arrangement of neighbors(i.e.,identical surroundings) as any other point in the lattice. This condition should be fairly obvious considering our description of long-range order in Sec. 2.1 We can also see from Fig. 15 that it is possible to divide the point lattice into much smaller untils such that when these units are stacked in three dimensions they reproduce the point lattice. This small repeating unit is known as the unit cell of the lattice and is shown in Fig.16 A unit cell may be described by the interrelationship between the lengths(a,b,c) of its sides and the interaxial angles (α,β,γ)between them. (α is the angle between the b and c, axes,β is the angle between the a and c axes, and γ is the angle between the a and b axes.)The actual values of a,b,and c, and α,β and γ are not important, but their interrelation is. The lengths are measured from one corner of the cell, which is taken as the origin. These lengths and angles are called the lattice parameters of the unit cell, or sometimes the lattice constants of the cell. But the latter term is not really appropriate because they are not necessarily constants; for example, they can vary with changes in temperature and pressure and with alloying. [Note: We use a,b and c to indicate the axes of the unit cell; a,b and c for the lattice parameters, and a,b and c for the vectors lying along the unit-cell axes.]

  • 和訳をお願いします。

    To readily calculate some of the physical characteristics of crystals, such as atomic density and density of three electrons, we must know the number of lattice points per cell. You may think that such a determination is quite trivial, but it is surprising how many people have difficulty with it! The number of lattice points per cell, N, is given by the equation N= Ni+ Ni/2+ Nc/8 Where Ni is the number of lattice points in the interior of the cell (these points “belong” only to one cells), Nf is the number of lattice points on faces (these are shared by two cells), and Nc is the number of lattice points on corners (these are shared by eight cells). For the three cubic unit cells the number of lattice points per cell is Primitive cubic (cubic P) 1 Body-centered cubic (cubic I) 2 Face-centered cubic(cubic F) 4 All primitive cells have one lattice point per cell. All nonprimitive cells have more than one lattice point per cell.

  • 英文の和訳をお願いしたいのですが・・・

    Lattice type and systematic absences In indexing the powder patterns it has been assumed that all the possible reflections are observed, that is, scattering from each of the different lattice planes is sufficiently intense to contribute to the diffraction profile. This is normally so for a primitive lattice, but for body centred and face centred lattices restrictions occur on the values that h, k and I may take if the reflections are to have any intensity. This results in certain reflections not being observed in the powder diffraction pattern and these are known as systematic absences. The origin of these absences can be illustrated with regard to Fig.2.3. という文章です。できれば翻訳サイト丸々ってのは控えてほしいです。

  • この文章の和訳をお願いします。

    　　Now, Figs. 3(a) and (b) indicate that there seems to be several discontinuous spikes in the range of |bi| between 1.8 and 2.6, which hereafter is called the discontinuous band. 　　In order to see the detailed features of the scattering in this region, we have calculated the particle orbits in a fine division of bi. The results, which are illustrated in Figs. 3(a) and (b), show that in almost all of the region ⊿b continues smoothly with respect to bi but there remain the fine discontinuous bands near bi=1.92 and bi=2.38. Again we have tried to magnify the range of bi between 1.915 and 1.925 and found that there are still finer discontinuities near bi=1.919(see Figs. 4(a) and (b)).

  • この文章の和訳をお願いします。

    3.2. Case of e=1.0 and i=0.5 In the three-dimensional case, the orbit is characterized by three parameters b, τ_s, and ω_s (in this section, we will omit the subscript “s” describing a starting point of orbital calculations). Recalling that b_max<3.7 from Eq. (16) and b_min>1.3 from Eq. (18) in the present case, we first examine orbits with b in the range between 1.3 and 3.7: Phase space (b, τ, ω) is divided into about 22000 meshes, i.e., 24 in b (1.3~3.7), 60 in τ (-π~π), and 15 ω (0~π). These orbital calculations show that there is no collision orbit where b<1.5 and b>3.2: b_max and b_min are set at 3.2 and 1.5, respectively, rather than 3.7 and 1.3. In parallel with the argument in the previous subsection, we consider the minimum separation r_min between the protoplanet and the planetesimal. In Fig.7, contours of r_min in the first encounter are illustrated in the τ-ω diagram for the three cases of b=2.3 (Fig. 7a), 2.8 (b), and 3.1 (c). Each figure is compiled from the orbital calculations of 5000 orbits, i.e., the τ-ω plane is divided into 100 (in τ)×50 (in ω). We concentrate first on Fig. 7a. In the coarsely dotted region where r_min>1, particles cannot enter the Hill sphere of the protoplanet. Such regions are beyond our interest. In the other regions where particles can enter the Hill sphere, r_min varies with τ and ω in a complicated manner. In particular, near the points (τ, ω)=(-0.24π,0.42π) and (-0.26π, 0.06π), r_min varies drastically in a small area in the τ-ω diagram. These may be chaotic zones. But in almost all regions, r_min varies continuously with τ and ω, and in this sense the orbits are regular. The finely dotted regions show those in which r_min becomes smaller than 0.03 (the radius of the two-body).Such orbits will be called close-encounter orbits in the chaotic zones is very small compared with that in the regular zones. This is the same conclusion as reached earlier. 長文ですが、どうかよろしくお願いします。

  • これの和訳を教えてください。

    It should be noticed that the collision probability is, of course, a function of the radius of the planet, which depends on the distance between the Sun and the planet in the system of units adopted here ( see Eq.(2・12)). Hence, using the results of our orbital calculations, we can evaluate Pc(bi~) individually for the various regions from the Sun. Now, the differential cross section (or, more exactly, cross length in our two-dimensional case), dσc(bi~), is defined such that the number of particles which collide with the planet per unit time is given by Fdσc(bi~). Here, F is a flux( per unit time and per unit length) of particles which come near the planet with an impact parameter, bi~. よろしくお願いします。

  • 解釈と和訳の質問です

    a vocabulary which is in the nature of things restricted この部分のwhich以下はどういうことを言っているのでしょうか。 [　]内を、できるだけ翻訳色の抜けた日本語にしていただけないでしょうか。 The difference in point of language between the early romancers and Murasaki is astonishing. They are almost childish in comparison with her sophistication. She moves without faltering through long, intricate sentences, and is the mistress not the slave of a most complex grammatical apparatus. She extracts the fullest value from a vocabulary which is in the nature of things restricted, and [the Chinese words that she uses are not pedantic intruders but seem to be at home in their surroundings.]

  • この文章の和訳をよろしくお願いします。

    Fig. 3a and b. An example of recurrent non-collision orbits. The orbit with b=2.4784, e=0, and i=0 is illustrated. To see the orbital behavior near the protoplanet, the central region is enlarged in b; the circle shows the sphere of the two-body approximation and the small one the protoplanet. Fig. 4a and b. Same as Fig. 3 but b=2.341, e=0, and i=0. This is an example of recurrent collision orbits. Fig.5. Minimum separation distance r_min between the protoplanet and a planetesimal in the case of (e, i)=(0, 0). By solid curves, r_min in the first encounter is illustrated as a function of b. The level of protoplanetary radius is shown by a thin dashed line. The collision band in the second encounter orbits around b=2.34 is also shown by dashed curves. Fig. 6. Minimum distance r_min in the chaotic zone near b=1.93 for the case of (e, i)=(0, 0); it changes violently with b. Fig. 7a-c. Contours of minimum separation distance r_min in the first encounter for the case of (e, i)=(1.0, 0.5); b=2.3(a), 2.8(b), and 3.1 (c). Contours are drawn in terms of log_10 (r_min) and the contour interval is 0.5. Regions where r_min>1 are marked by coarse dots. Particles in these regions cannot enter the Hill sphere of the protoplanet. Fine dots denotes regions where r_min is smaller than the radius r_cr of the sphere of the two-body approximation (r_cr=0.03; log_10(r_cr)=-1.52). Fig. 3a and b.　および　Fig. 4a and b.　↓ http://www.fastpic.jp/images.php?file=3994206860.jpg Fig.5.　および Fig. 7a-c. 　↓ http://www.fastpic.jp/images.php?file=2041732569.jpg Fig. 6. ↓ http://www.fastpic.jp/images.php?file=2217998690.jpg お手数ですが、よろしくお願いします。

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    With this information. we can see that the human body maintains a very delicate balance between cell creation and cell destruction, when this balance is disrupted the result can be a potentially fatal health condition, cancer is a disease in which too little apoptosis occurs, as cancerous cells often are corrupted in ways that make them resistant to the natural death process and can continue multiplying until destructive tumors are created. On the other hand, in a body that suffers from too much apoptosis, degenerative diseases such as Parkinson's and Alzheimer's can arise. With the process of apoptosis playing such a vital role in human health, it is no surprise that researchers are continuously studying it. If we can learn how to artificially control the apoptosis of cells in our bodies, it could lead to treatments for many life-threatening illnesses.

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    Now, the orbital elements (e, i, b, τ, ω) appearing in Eq. (14) are those at infinity. However, we cannot carry out an orbital calculation from infinity. In practice, we start to compute orbits from a sufficiently large but finite distance. Hence, we have to find the relation between orbital elements at infinity and those at a starting point. For b, it is readily done by Eq. (17); denoting quantities at a starting point of orbital calculations by subscripts “s”, we obtain b_s=(b^2-8/r_s)^(1/2), ・・・・・・・・(19) where we assumed e_s^2=e^2 and i_s^2=i^2 in the same manner as earlier. Hénon and Petit (1986) obtained a more accurate and complicated expression of b_s in the two-dimensional case. However, since we are now interested only in the averaged collisional rate but not detailed behavior of orbital motion, it is sufficient to use the simple relation (19). よろしくお願いします。

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