Broken line

Figure 2 Flow diagram of the DHT with N=8, P=3. Broken lines represent transfer factors -1 while full lines represent unity transfer factor. The crossover boxes perform the sign reversal called for by the shift theorem which also requires the sine and cosine factors Sn, Cn.

Figure A3.6.9. Viscosity dependence of photoisomerization rate constants of tran.s -stilbene (open circles) and E,E-diphenylbutadiene (fiill circles) in n-butanol. The broken line indicates a -dependence of k [96],...

Figure B2.5.11. Schematic set-up of laser-flash photolysis for detecting reaction products with uncertainty-limited energy and time resolution. The excitation CO2 laser pulse LP (broken line) enters the cell from the left, the tunable cw laser beam CW-L (frill line) from the right. A filter cell FZ protects the detector D, which detennines the time-dependent absorbance, from scattered CO2 laser light. The pyroelectric detector PY measures the energy of the CO2 laser pulse and the photon drag detector PD its temporal profile. A complete description can be found in [109].

Figure 1. Numerical test of the reciprocal relations in Eqs. (9) anti (10) for Cg shown in Eq. (29), The values computeti directly from Eq. (29) are plotted upward and the values from the integral downward (by broken lines) for K/(ii= 16. The two curves are clearly identical, (a) ln C (/) against (//period). The modulus is an even function of /, (b) argC (f) against (//period). The phase is odd in /.

The broken lines indicate hydrogen bonds. The full lines are to show the structure, they do not simply represent single covalent bonds. 

Fig. 1. Superposition of three crystal structures of cAMP-dependent protein kinase that show the protein in a closed conformation (straight line), in an intermediate conformation (dashed line), and in an open conformation (broken line). The structures were superimposed on the large lobe. In three locations, arrows identify corresponding amino acid positions in the small lobe.

Fig. 6. Free energies of hydration calculated, for a series of polar and non-polar solute molecules by extrapolating using (3) from a 1.6 ns trajectory of a softcore cavity in water plotted against values obtained using Thermodynamic Integration. The solid line indicates an ideal one-to-one correspondence. The broken line is a line of best fit through the calculated points.

Figure 3-19. Reaction center of the dataset of 120 reactions (reacting bonds are indicated by broken lines), and some reaction instances of this dataset.

Figure 7-9. Variation of the potential energy of the bonded interaction of two atoms with the distance between them. The solid line comes close to the experimental situation by using a Morse function the broken line represents the approximation by a harmonic potential.

Figure 7-10. Two examples of torsional potentials plotted using Eq, (24) with the parameters rt = 2, V = 5.0, y = Fi (solid line), and n = 3. = 3.0, y = 0 (broken line). All other V, ...

Only one-dimensional diffusion is considered and Che particles are represented in section by squares, as shown in the diagram. -The authors then consider three routes by which a molecule may move between the planes ab and cd, indicated by broken lines. These are ... 

Fig. 230 Adsorption of nitrogen at 77 K on a silica powder a) adsorption isotherms b) /-plot. Broken line, uncompacted powder continuous line, power compacted at 2-00 x 10 N m (130 ton in ). (—>—) adsorption (—<-) desorption. / is the ratio of the amount adsorbed on the powder to the amount adsorbed on the compact at the same relative...

Figure 1.4 Histogram showing the number of molecules Nj having the molecular weight Mj for classes indexed i. The broken line shows how the distribution would be described by a continuous function.

At the beginning of this section we enumerated four ways in which actual polymer molecules deviate from the model for perfectly flexible chains. The three sources of deviation which we have discussed so far all lead to the prediction of larger coil dimensions than would be the case for perfect flexibility. The fourth source of discrepancy, solvent interaction, can have either an expansion or a contraction effect on the coil dimensions. To see how this comes about, we consider enclosing the spherical domain occupied by the polymer molecule by a hypothetical boundary as indicated by the broken line in Fig. 1.9. Only a portion of this domain is actually occupied by chain segments, and the remaining sites are occupied by solvent molecules which we have assumed to be totally indifferent as far as coil dimensions are concerned. The region enclosed by this hypothetical boundary may be viewed as a solution, an we next consider the tendency of solvent molecules to cross in or out of the domain of the polymer molecule. 

Figure 2.7 Potential energy as a function of location along the reaction coordinate. The solid line describes an undisturbed liquid the broken line applies to liquids subjected to shearing force.

All the entries above the broken line in Table 2.3 are disubstituted, and those below, with the exception of poly (dimethyl siloxane), are mono-substituted. Those in the former category consistently have larger values of f than the latter. 

The upswing in compliance from the rubbery plateau marks the onset of viscous flow. In this final stage the slope of the lines (the broken lines in Fig. 3.12) is unity, which means that the compliance increases linearly with time. 

An obvious difficulty here is deciding the location of the broken line portions of the peaks in the region of overlap. Some features of the infrared absorption spectrum may also be analyzed by the same procedure to yield values for 6. 

Figure 4.15 Geometrical representation of the temperature variation of the actual volume (solid line) and the occupied volume (broken line). The shaded difference indicates the free volume which decreases to a critical value at T .

Figure 5.1 The reaction of A and B groups at the ends of two different chains. Note that rotations around only a few bonds will bring A and B into the same cage of neighboring groups, indicated by the broken line enclosure.

Figure 5.4 Comparison of catalyzed (solid lines) and uncatalyzed (broken lines) polymerizations using results calculated in Example 5.2. Here 1 - p (left-hand ordinate) and n (right-hand ordinate) are plotted versus time.

It is convenient to begin by backtracking to a discussion of AS for an athermal mixture. We shall consider a dilute solution containing N2 solute molecules, each of which has an excluded volume u. The excluded volume of a particle is that volume for which the center of mass of a second particle is excluded from entering. Although we assume no specific geometry for the molecules at this time, Fig. 8.10 shows how the excluded volume is defined for two spheres of radius a. The two spheres are in surface contact when their centers are separated by a distance 2a. The excluded volume for the pair has the volume (4/3)7r(2a), or eight times the volume of one sphere. This volume is indicated by the broken line in Fig. 8.10. Since this volume is associated with the interaction of two spheres, the excluded volume per sphere is... 

Figure 8.12 Schematic illustration showing with the solid line how the probability of placement varies with the distance of separation between the centers of the coils. The broken line is the equivalent result for hard spheres.

The accompanying sketch qualitatively describes the phase diagram for the system nylon-6,6, water, phenol for T > 70°C.f In this figure the broken lines are the lines whose terminals indicate the concentrations of the three components in the two equilibrium phases. Consult a physical chemistry textbook for the information as to how such concentrations are read. In the two-phase region, both phases contain nylon, but the water-rich phase contains the nylon at a lower concentration. On this phase diagram or a facsimile, draw arrows which trace the following procedure ... 

Figure 9.5a shows a portion of a cylindrical capillary of radius R and length 1. We measure the general distance from the center axis of the liquid in the capillary in terms of the variable r and consider specifically the cylindrical shell of thickness dr designated by the broken line in Fig. 9.5a. In general, gravitational, pressure, and viscous forces act on such a volume element, with the viscous forces depending on the velocity gradient in the liquid. Our first task, then, is to examine how the velocity of flow in a cylindrical shell such as this varies with the radius of the shell.

These are plotted in Fig. 10.6, which shows the net intensity envelope in the xy plane as a solid line and represents the horizontally and vertically polarized contributions to the resultant by the broken lines. Since 0 is symmetrical with respect to the x axis, the three-dimensional scattering pattern is generated by rotating the solid contour around the x axis. 

Figure 10.6 Two-dimensional representation of i and i (broken lines) and their resultant ifotai (solid line) for scattering by a molecule situated at the origin and illuminated by unpolarized light along the x axis. The intensity in any direction is proportional to the length of the radius vector at that angle. (Reprinted from Ref, 2, p. 168.)...

Fig. 19. Correction factor for axial dispersion as a function of NTU. SoHd lines are rigorous calculations broken lines, approximate formulas according to hterature (61). (a) Numbers on lines represent Pe values Pe = 20 /Lj = 0.8. (b) For design calculations. Numbers on lines represent Pep u ...

The position predicted for short-Hved lawrencium is indicated by a broken line. 

Fig. 12. The relationship between the mean oceanic residence time, T, yr, and the seawater—cmstal rock partition ratio,, of the elements adapted from Ref. 29. , Pretransition metals I, transition metals , B-metals , nonmetals. Open symbols indicate T-values estimated from sedimentation rates. The sohd line indicates the linear regression fit, and the dashed curves show the Working-Hotelling confidence band at the 0.1% significance level. The horizontal broken line indicates the time required for one stirring revolution of the ocean, T. ...

Fig. 4. pM vs pH for A Cu(II), and B Mn (IT) EDTA chelates. For each family of curves, the lowest curve represents 1% the second, 10% and the top curve, 100% of free ligand species ia excess of the amount needed to form the metal chelate. Broken lines represent soHd—solution equiUbria for... 

Fig. 5. pM vs pH for M = Ca(II), L = EDTA, in the presence of excess oxalate. Sohd lines A, B, C represent 100%, 10%, and 1% excess EDTA, respectively. Broken lines indicate sohd—solution equihbria of calcium oxalate in the presence of dissolved oxalate. 

FIG. 10-26 Pump coverage chart based on normal ranges of operation of commercially available types. Solid lines use left ordinate, bead scale. Broken lines use right ordinate, pressure scale. To conveii gallons per minute to cubic meters per hour, multiply by 0.2271 to conveii feet to meters, multiply by 0.3048 and to conveii poiinds-force per square inch to Idlopascals, multiply by 6.895. 

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