Radial plots

Figure 157 Radial plots of outer emission intensity from a microcavity (a) and microcavity-free (b) structures from Fig. 141 at different emission wavelengths as indicated in the figure. After Ref. 550. Copyright 1993 American Institute of Physics.

Figure 1. Radial plots of the s and p terms of a Li shape consistent effective potential. (Data are from ref. 68.)...

Figure 3-E Radiation Survey Techniques. Radial Plot (left) and Grid Plot (right) 3-33...

Fig. 13. Radial plot of azimuthal dependence of photoemission intensity from a Si l 11 2 X 1 surface (after Traum et al. [159]). Surface state emission intensity from a clean surface is shown by the open circles (in the energy window — 1.7 eV to F). The filled triangles show, on a 10 X reduced scale, the remainder of the photoemission intensity.

Galbraith RF (1984) On statistical estimation in fission track dating. Math Geol 16 653-669 Galbraith RF (1990) The radial plot graphical assessment of spread in ages. Nucl Tracks Radiat Meas 17 207-214... 

Figure 6 Diffuse basis functions are more spatially extended than their valence counterparts. The dashed curve represents the radial plot of the normalized diffuse Is Gaussian basis function for H from the aug-cc-pVDZ basis set while the solid curve is for the corresponding contracted valence Is basis function.

FIGURE 12.18 Radial plots of the molecular orbitals and their probabilities ... 

Figure 7.11a shows the radial functions R r) for the H atom Is, 2s and 2p orbital functions defined in Appendix 9. The Is orbital is a simple exponential decay with distance from the nucleus r (Equation (7.11)). The 2s function looks similar at small r values but passes through zero and becomes negative at just over 1 A. This, and any other point on the radial plot, actually represents a whole set of points at that radius defining a sphere centred on the nucleus. A zero in a wavefiinction is referred to as a node this is the radial node in the 2s function. 

Figure 3. (a) Origin of powder patterns, and (b) radial plot of intensity. 

Figure 24 Radial plots of the SOMOs for the two weakly-bound anions from Figure 22, illustrating the / -> c algorithm of Ref. 228. The dotted regions would be encapsulated by a 10% isoprobability contour and the hashed regions by a 50% isoprobability contour. Adapted with permission from Ref. 228 copyright 2008 American Chemical Society.

In the simplest case, for a pressure drawdown survey, the radial inflow equation indicates that the bottom hole flowing pressure is proportional to the logarithm of time. From the straight line plot ot pressure against the log (time), the reservoir permeability can be determined, and subsequently the total skin of the well. For a build-up survey, a similar plot (the so-called Horner plot) may be used to determine the same parameters, whose values act as an independent quality check on those derived from the drawdown survey. 

Figure A2.4.4. Plot of the radial distribution difference fiinction Ag(r) against distance r (pm) for a 1.46 M solution of NiCl in D O. From [5].

Another example of the difficulty is offered in figure B3.1.5. Flere we display on the ordinate, for helium s (Is ) state, the probability of finding an electron whose distance from the Fie nucleus is 0.13 A (tlie peak of the Is orbital s density) and whose angular coordinate relative to that of the other electron is plotted on the abscissa. The Fie nucleus is at the origin and the second electron also has a radial coordinate of 0.13 A. As the relative angular coordinate varies away from 0°, the electrons move apart near 0°, the electrons approach one another. Since both electrons have opposite spin in this state, their mutual Coulomb repulsion alone acts to keep them apart. 

Plot the radial portions of the 4s, 4p, 4d, and 4f hydrogen like atomie wavefunetions. 

Draw a plot of the radial probability density (e.g., r2[Rjjj(r)]2 with R referring to the radial portion of the STO) versus r for eaeh of the orthonormal Ei s orbitals found in Exereise 1. 

Therefore a plot of the radial probability for a given orthogonalized atomie orbital, n, will 3 3... 

The magnitude and "shape" of sueh a mean-field potential is shown below for the Beryllium atom. In this figure, the nueleus is at the origin, and one eleetron is plaeed at a distanee from the nueleus equal to the maximum of the Is orbital s radial probability density (near 0.13 A). The radial eoordinate of the seeond is plotted as the abseissa this seeond eleetron is arbitrarily eonstrained to lie on the line eonneeting the nueleus and the first eleetron (along this direetion, the inter-eleetronie interaetions are largest). On the ordinate, there are two quantities plotted (i) the Self-Consistent Field (SCF) mean-field... 

Plot RI against p (or r), as shown in Figure 1.7(b). Since R dr is the probability of finding the electron between r and r + dr this plot represents the radial probability distribution of the electron. 

Figure 1.7 Plots of (a) the radial wave function (b) the radial probability distribution function and (c) the radial charge density function 4nr Rl( against p...

The resulting eontours of the stream lines, a elose-up of a veetor plot near the top eover plate and the profile of radial veloeity at the inner edge of the eatalyst bed (Profile C, Figure 10-15) all show us that these last-named proposed ehanges would have many benefits. The main ones are ... 

FIG. 32 Radial density distribution function G(r) plotted vs r in the xy-plane for five choices of e [23]. 

Normalized radial functions for a hydrogenlike atom are given in Table A 1.1 and plotted graphically in Fig. A 1.1 for the first ten combinations of n and /. It will be seen that the radial functions for Is, 2p, 3d, and 4f orbitals have no nodes and are everywhere of... 

The phase relationship of each point of imbalance is the third factor that must be known. Balancing instruments isolate each point of imbalance and determine their phase relationship. Plotting each point of imbalance on a polar plot does this. In simple terms, a polar plot is a circular display of the shaft end. Each point of imbalance is located on the polar plot as a specific radial, ranging from 0 to 360°. 

From microscopic measurements of the rates of nucleation and of growth of particles of barium metal product, Wischin [201] observed that the number of nuclei present increased as the third power (—2.5—3.5) of time and that the isothermal rate of radial growth of visible nuclei was constant. During the early stages of reaction, the acceleratory region of the a—time plot obeyed the power law [eqn. (2)] with 6 temperature coefficients of these processes were used by Wischin [201]... 

This plot shows the radial distribution function of the 3s and 3p orbitals of a hydrogen atom. Identify each curve and explain how you made your decision. 

Figure 4 [29] shows the (s) versus profiles for potato amylose and the amylose/amylopectin mixture from wheat starch corresponding to the concentration versus radial displacement data of Fig. 3. The s data used in the concentration dependence plot of Fig. 3 for wheat amylopectin comes from (s) vs. s analysis data of Fig. 2b and similar. The concentrations shown in the abscissa in Fig. 4 have been obtained from the total starch loading concentration normalised by the weight fraction of the amylopectin component estimated from the (s) vs. s profiles.

Fig. 4 Sedimentation velocity g (s) profiles for starch polysaccharides using DCDT+. The profiles correspond to the radial displacement plots of Fig. 2. a Potato amylose, sample concentration 8 mg/ml in 90% in dimethyl sulphoxide. Rotor speed was 50 000 rpm at a temperature of 20 °C. b Wheat starch (containing amylose, left peak and the faster moving amylopectin, right peak), (total) sample concentration 8 mg/ml in 90% dimethyl sulphoxide. Rotor speed was 35 000 rpm at a temperature of 20 °C. From [29]...

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