Figure 21 Schematic illustrating the one-dimensional array of layers considered in the mixed potential model of nuclear fuel corrosion in a failed (flooded) nuclear waste container. |

Fig. 44.22. Three commonly used Kohonen network structures, (a) One-dimensional array (b) two-dimensional rectangular network (each unit, apart from the borderline units has 8 neighbours) and (c) two-dimensional hexagonal network (each unit, apart from the borderline units, has 6 neighbours). (Reprinted with permission from Ref. [70]). |

Figure 3.6. Calculation of the Madelung constant for a one-dimensional array of cations and anions, before and after aliovalent ion exchange. |

Figure 8.20 Condition for constructive interference for a one-dimensional array of scattering centers (top). Constructive interference occurs along the cones that reflect the rotational symmetry of the one-dimensional arrangement (middle). For a two-dimensional crystal, constructive interference is obtained along lines (bottom). |

We have considered scalar, vector, and matrix molecular properties. A scalar is a zero-dimensional array a vector is a one-dimensional array a matrix is a two-dimensional array. In general, an 5-dimensional array is called a tensor of rank (or order) s a tensor of order s has ns components, where n is the number of dimensions of the coordinate system (usually 3). Thus the dipole moment is a first-order tensor with 31 = 3 components the polarizability is a second-order tensor with 32 = 9 components. The molecular first hyperpolarizability (which we will not define) is a third-order tensor. [Pg.348]

The process is as follows the term number m is first input, then two one-dimensional arrays will be created as a = Array[t, m, u = Array[l, m[. a circle sentence Do[c = [[ ]] /. 1 + c, i,m ] with introducing the parameter 2 is used to produce the expression [Pg.297]

Longitudinal Elastic Waves on a 1-D Line of Equidistant Equal Atoms. Consider next the longitudinal motion of a one-dimensional array of E equal atoms of mass M (Fig. 5.7). These atoms at rest are equidistant—that is, spaced a (meters) apart—and can interact via Hooke s law with force constant kH (N m ), but only with their nearest neighbors. Let u be the longitudinal displacement of atom n from its equilibrium position. The net Hooke s law force on atom n, due to the displacements un, un v and un +, is [Pg.310]

The degree of association through —H- -Au bonds can vary depending on the complex analyzed and, thus, we can find one-dimensional arrays, such as in the [Pg.315]

It was known from experiment that all the spectral lines of an element could be represented as the differences of a relatively small number or terms. If these terms are arranged in a one-dimensional array 7 = Ti,T2,..., the atomic frequencies form a two-dimensinal array of elements u nm) = Tn—Tm, [Pg.86]

Fig. 3. Alignment of amide dipoles in polyamide crystals (a) for a two-dimensional array of an odd nylon, nylon-7, (b) for a one-dimensional array of an odd—odd nylon, nylon-5,7 (c) for one-dimensional arrays of polyamides containing even segments an even nylon, nylon-6 an even—even nylon, nylon-6,6 |

Fig. 8. Concentration B in reaction mechanism for diffusion coefficient of X much less than that of Y, necessary to achieve instability in a system in which the autocatalytic mechanism occurs on a one-dimensional array of local sites, versus logarithm of site density a (solid line). Dashed and dotted lines are for the isolated and continuum site limit, respectively. |

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