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reflection of X rays from the crystal. In the ordered state X-ray reflection will reveal that there are two sets of atomic planes with spacing d, whereas in the state of disorder there is only one set of atomic planes with spacing d/2. It is observed experimentally that the specific heat Cp approaches infinity as the temperature approaches the critical temperature from both sides. A model for a binary alloy follows. Let there be two kinds of atoms, called 1 and 2, of which there are N I and N z, respectively. Let their positions be confined to the lattice sites of a given lattice, with y nearest neighbors to each lattice site. At each lattice site there shall be one and only one atom. Thus the total number of sites is N = N I + N z. There are three types of nearest-neighbor pairs: (11), (22), and (12). The pair (12) is not distinguished from the pair (21). Let a configuration of the system be such that the number of pairs of each type present is, respectively, NIl> N zz , N 12 . Neglecting the kinetic energy of the atoms and all but nearest-neighbor interactions, we take the energy of the system to be EA(Nn , N zz , N 12 ) = INn + zNn + 12N12 (14.20)
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where the subscript A stands for "alloy." Obviously E A is in general degenerate. Moreover, the numbers N n , N zz , N 12 are not independent of one another. By analogy with (14.7) we have the relations yNI
The cryptographically significant components of the Enigma cipher are the stecker, the three rotors, and the reflector. The Enigma key consists of the configuration of the cipher used to encrypt and decrypt a particular message. The variable settings that comprise the key are the following: 1. The choice of rotors.
You cannot include sales tax on your purchase order, but when the invoice arrives, you can indicate on the Enter Bills screen what portion of the invoice s total was sales tax. You learn more about this in the section Entering Bills later in this chapter.
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2. The position of a movable ring on each of the two rightmost rotors. This ring allows the outer part of the rotor (labeled with the 26 letters) to rotate with respect to the inner part of the ring (where the actual permutation is wired).2 Rotating this ring shifts the permutation and
Hence the energy depends only on one variable, N ll : EA(Nn )
+ ty zN]
Set up miscellaneous Items and Items describing categories of goods and services to keep your Items list manageable and to avoid frequently having to create new Items on the y. You can enter the applicable price on your purchase order each time you use these miscellaneous or general category Items.
cause the middle rotor to step again. The middle rotor thereby steps twice in succession, violating the odometer effect. Note that this same ratcheting mechanism causes the right rotor to step whenever the middle rotor steps, but since the right rotor already steps for each letter typed, there is no noticeable effect on the right rotor. 'This is analogous to rotating the position of a car tire relative to the rim.
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where the term in brackets is a constant. A correspondence between the binary alloy and the lattice gas may be established by identifying N I with N a , which in turn is identified with N + of the Ising model. Comparison of (14.23) and the exponent in (14.19) immediately leads to the correspondence summarized in the accompanying table:
As mentioned above, each rotor implements a permutation of the 26 letters of the alphabet. The movable rings can be set t,o any of the 26 positions corresponding to the letters. Each rotor is initially set to one of the 26 positions on the rotor, which are labeled with A through Z. The stecker is similar to an old-fashioned telephone switchboard, with 26 holes, each labeled with a letter of the alphabet. The stecker can have from 0 to 13 cables, where each cable connects a pair of letters. The reflector implements a permutation of the 26 letters, with the restriction that no letter can be permuted to itself, since this would cause a short circuit. Consequently, the reflector is equivalent to a stecker with 13 cables. Since there are three rotors, each containing a permutation of the 26 lettcrs, there are 26! . 26! . 26! M 2265
N1 N - N 1 = Nz 1 + z - 2 12
You might want to add some extra elds to your purchase order template. For example, if you have multiple employees issuing POs, you may want to add a eld for the employee initials. QuickBooks allows you to add or omit a number of elds from your standard purchase order form. You can use one of the other elds in the Customize Template dialog box shown in Figure 17-2.
(Helmholtz free energy)
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