D-dimensional solid body

D-dimensional solid body embedded in a D-dimensional space As was previously pointed out, p(r) is the common volume of the solid body and of its replica obtained by the translation of vector r. For small values of r, compared to the radii of curvature of the surface of the solid body, we have (see Fig. E.1)... 

Thus, the correlation function corresponding to a D-dimensional solid body with a random orientation in a D-dimensional space, is given for small r by the... 

Now let us put the D-dimensional solid body in a d-dimensional space (with d > D) with a random orientation. The corresponding function p(r) is related to pD(r) by the equality... 

When the structure under consideration is a well-defined solid-body of volume v in a d-dimensional space, we set A(r) = 1 if r corresponds to a point... 

In particular, it will be shown that a solid D-dimensional body with a random orientation in a d-dimensional space (d > D) has a form function whose asymptotic behaviour is not at all the same when d > D and when d = D. 

Now we can see that (E.22) is very analogous to (E.20) the form function of a random chain of dimension D, embedded in a d-dimensional space, has the same asymptotic dependence on to q, as a solid body of dimension D, oriented at random in a d-dimensional space (with d > D). 

Figure 29-2 (A) Secondary structure model for the 1542-residue E. coli 16S rRNA based on comparative sequence analysis.733 Dots indicate G U or A G pairs dashes indicate G C or A U pairs. Strongly implied tertiary interactions are shown by solid green lines. Helix numbering according to Brimacombe. Courtesy of Robin Gutell. (B) Simplified schematic drawing of type often used. (C) Positions of the A, P, and E sites on the 30S ribosomal subunit from Carter et al7° (D) Stereoscopic view of the three-dimensional fold of the 16S RNA from Thermus thermophilus as revealed by X-ray structural analysis at 0.3 nm resolution. Features labeled are the head (H), beak (Be), neck (N), platform (P), shoulder (Sh), spur (Sp), and body (Bo). (E-H) Selected parts of the 16S RNA. In (E) and (F) the helices are numbered as in (A). (F) and (H) are stereoscopic views. The decoding site...

Consider sleady two-dimensional heat transfer in a long solid bar of (a) square and (b) rectangular cross sections as shown in ihe figure. The measured lemperatuces at selecied points of the outer surfaces are as shown. The thermal conductivity of the body is k = 20 W/m °C, and there is no heat generation. Using the finite difference method with a mesh size of d-v = Ay = 1.0 cm, determine the tempeialures at the indicated points in the medium. 

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