Graphical representation surface

Figure2-116. Graphical representations of molecular surfaces of phenylalanine a) dots b) mesh or chicken-wire c) solid d) semi-transparent,...

SP (Graphical Representation and Analysis of Surface Properties) A Nicholls, Columbia University, New York, USA. 

Particulate systems composed of identical particles are extremely rare. It is therefore usefiil to represent a polydispersion of particles as sets of successive size intervals, containing information on the number of particle, length, surface area, or mass. The entire size range, which can span up to several orders of magnitude, can be covered with a relatively small number of intervals. This data set is usually tabulated and transformed into a graphical representation. 

A graphical representation of the potential energy surface or reaction coordinate. The transition state occurs at the saddle point. ( Adapted from Ref. 18.)... 

The raw output of a molecular structure calculation is a list of the coefficients of the atomic orbitals in each LCAO (linear combination of atomic orbitals) molecular orbital and the energies of the orbitals. The software commonly calculates dipole moments too. Various graphical representations are used to simplify the interpretation of the coefficients. Thus, a typical graphical representation of a molecular orbital uses stylized shapes (spheres for s-orbitals, for instance) to represent the basis set and then scales their size to indicate the value of the coefficient in the LCAO. Different signs of the wavefunctions are typically represented by different colors. The total electron density at any point (the sum of the squares of the occupied wavefunctions evaluated at that point) is commonly represented by an isodensity surface, a surface of constant total electron density. 

Figure 18. A graphical representation of Eq. (63). The surface corresponds to Jz = 0, with conical points that correspond to C and D in Table I. Taken from Ref. [4] with permission.

Figure 4.2 Graphical representation of the supetcell structure, with a single (3 x 3) unit cell indicated by dashed lines that is repeated along lattice vectors a, b, and c, as indicated, (a) and (b) are vapor phase and aqueous phase models of the reaction environment, respectively, for an adsorbed CH2OH intermediate with a surface coverage of...

Gradient analysis (Parczewski [1981], Singer and Danzer [1984], Parczewski et al [1986], Parczewski and Danzer [1993]) which is based on two-dimensional regression models and adds pictorial information to statistical decisions. Figure 3.12 shows such a graphical representation of an element distribution on a surface. 

The first graphical representation using MATLAB software is that of a two-dimensional contour surface plot of the data from Table 75-1 [2], This Figure 75-3 plot can represent multiple levels of j-axis data (absorbance) by the use of contours and color schemes. The MATLAB commands for generating this image are given in Table 75-2 where A represents the raster data matrix shown in Table 75-1. 

As AD is made smaller, a histogram becomes a frequency distribution curve (Fig. 4.1) that may be used to characterize droplet size distribution if samples are sufficiently large. In addition to the frequency plot, a cumulative distribution plot has also been used to represent droplet size distribution. In this graphical representation (Fig. 4.2), a percentage of the total number, total surface area, total volume, or total mass of droplets below a given size is plotted vs. droplet size. Therefore, it is essentially a plot of the integral of the frequency curve. 

Table 9.1 and Fig. 9.11 also depict vaporization temperatures of the metals in each product composition and give a graphical representation of Glassman s criterion. When Vvo (or Td, as the case dictates) of the refractory compound formed is greater than the vaporization temperature, Tb, of the metal reactant, small metal particles will vaporize during combustion and bum in the vapor phase. When the contra condition holds, much slower surface reactions will... 

Graphical representation of the saddle point (here marked with an X) for the transfer of atom B as the substance A-B reacts with another species, C. Potential energy is plotted in the vertical direction. Note also that the surface resembles a horse saddle, with the horn of the saddle closest to the observer. As drawn here, the dissociation to form three discrete species (A + B J- C) requires much more energy than that needed to surmount the path that includes the saddle point. A two-dimensional "slice" through a saddle point diagram is typically called a reaction-coordinate diagram or potential-energy profile. 

Response surface plot a graphical representation of the response surface as a contour map of the dependent variable on a coordinate scale of two of the independent variables. 

Figure 15.9 Graphical representation of the calculation of the near-surface specific light absorption rate, k°, for para-nitro-acetophe-none (PNAP) for a clear-sky midday, midsummer at 40°N latitude. The shaded area corresponds to the total rate. Note that the y axes are on logarithmic scales.

Figure 2.1 Graphical representation of isotherms (a), isochores (b), isobars (c), and the 3D PVT surface (d) for an ideal gas.

A potential surface is a graphical representation of the energy of the system as a function of its geometry. For a lucid account on potential energy surfaces, transition states, methods for calculating reaction paths, etc., see Chapter 2 in ref. 7. 

Figure 1. Temperature/pH response surface at 0.033 m rhamnose and 0.167 m proline. Graphical representation of the quantity (ppm) of 6-methyl-2,3-dihydro-(lH)-pyrrolizine.

Figure 10.9 A simplified graphic representation of EPDM chains at the carbon black surface [62], Monomer units with low mobility in the interface and mobile chain units outside of interface are represented by solid and open points, respectively. The rotational and translational mobilities of a few chain units next to the adsorption layer along the chain (dashed points) are hindered somewhat more than those of the chain units in the matrix. The chain fragments with low mobility in the interface provide adsorption network junctions for the rubber matrix. At the bottom of the figure, the spatial profile of the correlation time Tc of the chain motion is schematically represented as a function of the distance, r, from the carbon black surface. The xc is the average time of a single reorientation of a chain unit...

Figure 2.8 illustrates the SAS concept as well as the method used for its determination. SASs are essentially computed by generating a three-dimensional, graphical representation of the dendrimer and computationally rolling probes (p) of various radii (r) over the surface. Intuitively, as well as physically, the larger the probe radius the less chance for contact the probe has within the internal void region of the dendrimer. For probes with a small radius, and in particular at the limit r = 0 A, the total internal surface area can be determined. Typically, the solvent accessible surface area ( Msas) is plotted versus probe radius or diameter. Thus, a measure of dendritic porosity can be derived. 

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