Connectivity values

However, it should not be concealed that in some cases the Morgan Algorithm has problems. In some structures the numbering show oscillatoiy behavior (for an example, sec Figure 2-44). Moreover, although equivalent atoms obtain the same extended connectivity value, it cannot always be concluded that atoms with the same extended connectivity value are equivalent. 

FIG. 14-82 Approximate installed cost of steel-tower connections. Values apply to 2070-kPa connections. Multiply costs by 0.9 for 1035-kPa (150-lb) connections and by 1.2 for 4140-kPa (600-lb) connections. To convert inches to millimeters, multiply by 25.4 to convert dollars per inch to dollars per centimeter, multiply by 0.394. (Peters and Timmerhaus, Plant Design and Economics for Chemical Engineers, 4th ed.. New Yoik, McGraw-Hill, 1.9.91,)... 

Ashby also constructed sintering maps in which x/a is plotted versus the homologous temperature T/Tm where Tm is the melting point. These maps, which must be drawn for a given initial radius of the sintering particles, use the relevant diffusion and vapour pressure data. Isochrones connect values of x/a which can be achieved in a fixed time of annealing as a function of the homologous temperature. 

The new feature of the Zimm plot is the second extrapolated line, corresponding to c = 0. This line connects values of Kc/R0 measured at different values of 6 and extrapolated to c = 0. Accordingly, it is described by Equation (67) with c = O that is, theory predicts the c = 0 line to have an intercept of l/M and a slope equal to (l6ir2R2g/3X2M). It is expected, then, that the two lines will extrapolate to a common intercept l/M, and that the slope of the c = 0 line will be proportional to/ 2. Summarizing in formulas, we write for the c = 0 line... 

Points on the raffinate line of the triangular diagram are located on lines connecting values of y on the hypotenuse (solids-free) with the origin, at the values of x and corresponding y from the preceding tabulation. 

Assign Stage 1 connectivity values to each atom based on the number of attachments to the atoms. 

Assign Stage 2 connectivity values to each atom by summing the Stage 1 connectivity values for the attached atoms. 

Calculate the number of distinct connectivity values at the Stage i and Stage i+1. 

Otherwise, the final connectivity values are the Stage i values. 

Select the atom with the highest connectivity value and designate that atom as Number 1. 

Since Steps 1-6 provide only a partial order of the atoms, note all other atoms with same connectivity value. 

Atoms connected to Atom 1 are assigned 2, 3, etc. based on decreasing connectivity values. If a choice is arbitrary (where the atoms have the same connectivity value) note the pairs of atoms involved in the arbitrary choice. 

The unnumbered atoms attached to Atom 2 are numbered based on decreasing connectivity values. Again, note pairs of atoms where the choice was arbitrary. 

Figure 9e illustrates the initial numbering and the compact connection table using the Stage 3 connectivity values. The atom with connectivity value of 13 is assigned Number 1. The atoms attached to Atom 1 are numbered 2, 3, and 4 based on decreasing connectivity values. The arbitrary choice between 3 and 4 is noted. 

Turbulent flow NRe >2100 Connect values of /> and by straight line to obtain optimum pipe diameter... 

Approximate installed cost of steel-tower connections. Values apply to 300-lb connections. Multiply costs by 0.9 for 150-lb connections and by 1.2 for 600-lb connections. 

Molecular Connectivity. A class of molecular descriptors derived from the connection table of a structure. For increasing path lengths (1-, 2-, 3-bonds, etc.), the molecular connectivity values are computed as the sum of functions of the connectivity values (number of attachments) of the atoms in the path. Molecular connectivity descriptors can be used to distinguish structures. As such, they can be correlated with physicochemical properties that are functions of structure size, linearity, and degree of branching. 

Figure 2. Electrophoretic mobilities of particles in seven4on (l t) and natural sea water (right). Tie lines connect values for the same kind of particle. Data from Ref. 15.

Comparison of pore connectivity values obtained by different methods ... 

Graph vertices are ordered on the basis of their extended connectivity values obtained after a number of iterations of the Morgan method until constant atom ordering is obtained in two consecutive steps [Morgan, 1965]. The extended connectivity (EC) of a vertex is calculated as the iterative summation of connectivities of all first neighbours as the following ... 

---