Ordination diagrams

The first RDA ordination axis scored an eigenvalue of 0.493, while the first CCA axis 0.003. This contrast indicated that the linear model fitted well, but the unimodal model fitted poorly. Thus, only the RDA ordination diagram was shown in Fig. 4. The diagram visualizes the land degradation gradient. Again, the DEF and the GB soils were shown to be the extremes, while the DDF soil the intermediate. Relationships between the changes in... 

Fig. 4. Redundancy analysis ordination diagram based on the antibiotic resistance MPN data. The diamond ( ), the open square (o) and the triangle (A) indicate BG, DDF and DEF, respectively. The value in the parentheses indicates eigenvalue for the axis. The solid and broken arrows indicate significant environmental gradients at p=0.05 and 0.10, respectively.

Figure 4. Free energy-reaction co-ordinate diagrams for acid-catalysed hydrolysis of simple acetals...

In any general reaction between A and B to give C and D, the reagent A must physically approach the substrate B so that the electrons within each molecule may interact this results in some bonds being broken and re-formed so as to produce the new molecules C and D. This process may be represented on a diagram called a reaction co-ordinate diagram. 

For a two-step reaction, the reaction co-ordinate diagram is as follows. In this case, there is an energy well, i.e. there is a peak either side of it. The species that is caught in the energy well is called an intermediate and may be isolated. The presence of the peaks on either side of the intermediate indicates that energy is required for both the forward or the reverse reaction to proceed from this intermediate species, i.e. there is an activation energy barrier that the intermediate must overcome before it may revert either to the starting materials or proceed to the final products. This is indicative of a real species, which can be isolated. This is in contrast to a transition state, which occupies the cusp of the... 

The rate of a reaction is related to the activation energy barrier that exists between the starting materials and the transition state. On the reaction co-ordinate diagram, this is represented by the difference between the starting materials and the peak of the reaction co-ordinate curve. If the activation barrier is large, how will this affect the rate of the reaction ... 

Transition state The transitory structure that exists at the mid-point in the reaction between the starting materials and the products. This corresponds to the structure that exists at the peak of the reaction co-ordinate diagram, which represents the configuration that has the highest energy along the reaction pathway. This hypothetical species cannot be isolated. 

An ordination diagram has been used by van der Brink et al. (1996) to plot the path of the various treatment groups using the axes generated by the redundancy analysis. This method has the advantage of seeing a number of variables at once and the trajectory of each treatment over the course of the experiment. The plots are still two-dimensional representations, and variability is not pictured. 

Figure 7.4.3 DCCA ordination diagram for the hydromorphological gradient analysis, with the morphological gradient indicated by black (canalised), grey (semi-natural) and open (natural) labels and with the hydrological periods indicated by circles (pre-hydrological restoration) and triangles (post-hydrological restoration)...

Introducing the complex notation enables the impedance relationships to be presented as Argand diagrams in both Cartesian and polar co-ordinates (r,rp). The fomier leads to the Nyquist impedance spectrum, where the real impedance is plotted against the imaginary and the latter to the Bode spectrum, where both the modulus of impedance, r, and the phase angle are plotted as a fiinction of the frequency. In AC impedance tire cell is essentially replaced by a suitable model system in which the properties of the interface and the electrolyte are represented by appropriate electrical analogues and the impedance of the cell is then measured over a wide... 

The first step is the collection of data showing corresponding values of the variables under consideration. From a scatter diagram, a plot of Y (ordinate) versus X (abscissa), it is often possible to visualize a smooth curve approximating the data. For purposes of reference, several types of approximating curves and their equations are listed. All letters other than X and Yrepresent constants. 

Fig. 2. General configurational—coordinate diagrams for (a) broad-band absorbers and emitters, and (b) narrow-band or line emitters. The ordinate represents the total energy of the activator center and the abscissa is a generalized coordinate representing the configuration of ions surrounding the...

Another representation of the stabiUty relations of the siUca minerals is shown in Figure 4. This diagram, developed in the classical studies early in the twentieth century (51), illustrates the relationship of vapor pressure to temperature. It is assumed that vapor pressure increases with temperature and that the form having the lowest vapor pressure is the most stable. The actual values of the vapor pressures are largely unknown. Therefore, the ordinate must be considered only as an indication of relative stabiUties. This diagram does not show all the various forms of tridymite that have been identified. 

The three phase diagrams, or parts of diagrams, shown in Fig. A1.28, all have a eutectic point. Mark the point with an arrow and list the eutectic temperature and composition in wt% (the co-ordinates of the point). 

For any particular system, a graph can be constructed using the concentration of the solute in the liquid phase (Ca) and the concentration or partial pressure of the solute in the gas phase (Pa) as the abscissa and ordinate, respectively. A line indicating the equilibrium concentrations of the solute in the gas and solvent drawn on this graph, results in an equilibrium diagram. 

Thus far we have drawn reaction coordinate diagrams with potential energy as the ordinate. However, the free energy is a much more accessible quantity (actually... 

Figure 8.19 F.llingham diagram for the free energy of formation of metallic oxides. (After F. D. Richardson and J. H. F. Jeffes, J. Iron Steel Inst. 160, 261 (1948).) The oxygen dissociation pressure of a given M - MO system at a given temperature is obtained by joining on the lop left hand to the appropriate point on the M-MO frec-energy line, and extrapolating to the scale on the right hand ordinate for POi (atm).

Locate this value on the diagram and connect it to the feed point, xp. Extend this line to intersect the bottoms condition ordinate (extended), xb- In this case, it is impos-... 

The first step in data analysis is the selection of the best filling probability function, often beginning with a graphical analysis of the frequency histogram. Moment ratios and moment-ratio diagrams (with p as abscissa and as ordinate) are useful since probability functions of known distributions have characteristic values of p, and p. ... 

Where a large collection of data exists then it may be effectively condensed in the form of diagrams. A popular method is the use of iso-corrosion rates plotted on co-ordinates of temperature and concentration for one material and one chemical. Because of the large amount of data on the common acids there are many examples of this type of diagram, e.g. the work of Berg who has chosen metals and alloys that are readily available. He has excluded many metals and alloys on the grounds that they are either Non-resistant or can be substituted by cheaper materials. ... 

In Figs. 31 and 32 the ordinates give the equivalent conductivity of HC1, each point being the result of a series of measurements extrapolated to infinite dilution.1 For comparison with similar diagrams given in a later... 

Fig. 5. Tentative mixed potential model for the sodium-potassium pump in biological membranes the vertical lines symbolyze the surface of the ATP-ase and at the same time the ordinate of the virtual current-voltage curves on either side resulting in different Evans-diagrams. The scale of the absolute potential difference between the ATP-ase and the solution phase is indicated in the upper left comer of the figure. On each side of the enzyme a mixed potential (= circle) between Na+, K+ and also other ions (i.e. Ca2+ ) is established, resulting in a transmembrane potential of around — 60 mV. This number is not essential it is also possible that this value is established by a passive diffusion of mainly K+-ions out of the cell at a different location. This would mean that the electric field across the cell-membranes is not uniformly distributed.

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