Average distance

It represents the average distance to the barycentre of the block B3 and reach its maximum when pixels are distanced the barycentre. 

It is known that even condensed films must have surface diffusional mobility Rideal and Tadayon [64] found that stearic acid films transferred from one surface to another by a process that seemed to involve surface diffusion to the occasional points of contact between the solids. Such transfer, of course, is observed in actual friction experiments in that an uncoated rider quickly acquires a layer of boundary lubricant from the surface over which it is passed [46]. However, there is little quantitative information available about actual surface diffusion coefficients. One value that may be relevant is that of Ross and Good [65] for butane on Spheron 6, which, for a monolayer, was about 5 x 10 cm /sec. If the average junction is about 10 cm in size, this would also be about the average distance that a film molecule would have to migrate, and the time required would be about 10 sec. This rate of Junctions passing each other corresponds to a sliding speed of 100 cm/sec so that the usual speeds of 0.01 cm/sec should not be too fast for pressurized film formation. See Ref. 62 for a study of another mechanism for surface mobility, that of evaporative hopping. 

Finally, it is perfectly possible to choose a standard state for the surface phase. De Boer [14] makes a plea for taking that value of such that the average distance apart of the molecules is the same as in the gas phase at STP. This is a hypothetical standard state in that for an ideal two-dimensional gas with this molecular separation would be 0.338 dyn/cm at 0°C. The standard molecular area is then 4.08 x 10 T. The main advantage of this choice is that it simplifies the relationship between translational entropies of the two- and the three-dimensional standard states. 

It is of interest to detennine when the linewidth F( ) associated with the RRKM rate constant lc(E) equals the average distance p( ) between the reactant energy levels. From equation (A3.12.54) F( ) = Dk( ) and from the RRKM rate constant expression equation (A3.12.15) p(Ef = hl% K( )/M( - q). Equating these two... 

The measurement of surface forces calls for a rigid apparatus that exhibits a high force sensitivity as well as distance measurement and control on a subnanometre scale [38]. Most SFAs make use of an optical interference teclmique to measure distances and hence forces between surfaces. Alternative distance measurements have been developed in recent years—predominantly capacitive techniques, which allow for faster and simpler acquisition of an averaged distance [H, 39, 40] or even allow for simultaneous dielectric loss measurements at a confined interface. 

Catalyst particles are usually cylindrical in shape because it is convenient and economical to fonii tliem by extmsion—like spaghetti. Otlier shapes may be dictated by tlie need to minimize tlie resistance to transport of reactants and products in tlie pores tlius, tlie goal may be to have a high ratio of external (peripheral) surface area to particle volume and to minimize the average distance from tlie outside surface to tlie particle centre, witliout having particles tliat are so small tliat tlie pressure drop of reactants flowing tlirough tlie reactor will be excessive. 

Evalii atm g average distances, angles, and torsion angles, pins their deviations, can facilitate understanding of detailed molecular properties and functional characteristics. 

There are two ways in which the volume occupied by a sample can influence the Gibbs free energy of the system. One of these involves the average distance of separation between the molecules and therefore influences G through the energetics of molecular interactions. The second volume effect on G arises from the contribution of free-volume considerations. In Chap. 2 we described the molecular texture of the liquid state in terms of a model which allowed for vacancies or holes. The number and size of the holes influence G through entropy considerations. Each of these volume effects varies differently with changing temperature and each behaves differently on opposite sides of Tg. We shall call free volume that volume which makes the second type of contribution to G. 

The reaction medium plays a very important role in all ionic polymerizations. Likewise, the nature of the ionic partner to the active center-called the counterion or gegenion-has a large effect also. This is true because the nature of the counterion, the polarity of the solvent, and the possibility of specific solvent-ion interactions determines the average distance of separation between the ions in solution. It is not difficult to visualize a whole spectrum of possibilities, from completely separated ions to an ion pair of partially solvated ions to an ion pair of unsolvated ions. The distance between the centers of the ions is different in... 

The mean free path, which is die average distance a molecule navels between collisions, is... 

If the average distance between obstacles is L, the run time between obstacles is... 

Fig. 23-5 Mutual inductivity load M as a function of the average spacing between two individual lines. Average distance, a, with equivalent counter-inductivity for an oblique approach with distances <3, and <32 at the end of the close proximity (<3, < <32)-(a)/= 50 Hz and p = 50 m, (b)/= 16% Hz and p = 30 m.

Referring to Fig. 23-6, through 3)3 are hereby the average distances of the conductor from the ground x, through X3 are the average distances of the conductor from the pylon axis a is the distance of the affected conductor from the pylon axis, and d is the penetration depth in the soil from ... 

Internal dynamics of the macromolecule influences all experimental data that can be measured by NMR. The weighting of the NOE makes the averaging very nonlinear, and the measured distance may appear much shorter than the average distance (see Eig. 9). 

Figure 9 Treating internal dynamics during the refinement process. Due to dynamics and the weighting of the NOE, the measured distance may appear much shorter than the average distance. This can be accounted for by using ensemble refinement techniques. In contrast to standard refinement, an average distance is calculated over an ensemble of C structures (ensemble refinement) or a trajectory (time-averaged refinement). The time-averaged distance is defined with an exponential window over the trajectory. T is the total length over the trajectory, t is the time, and x is a relaxation time characterizing the width of the exponential window.

Figure 4 Comparison of average distances from the bilayer center along the bilayer normal for deuterated methyl and methylene groups distributed throughout the DPPC molecule computed from constant-pressure MD calculations and neutron diffraction measurements on gel and liquid crystalline phase DPPC bilayers.

Scale of segregation A measure of the average distance between clumps of the same component in a mixture. 

Striation thickness Average distance between adjacent interfaces of materials to be mixed by a laminar mechanism. 

Mean free path The average distance travelled by a particle between collisions. In a gas it is inversely proportional to the pressure. 

Figure 13.27 The structures of cationic clusters of Bim"+. The dimensions cited for Bi9 + were obtained from an X-ray study on [(Bi9 +)(Bi )(HfCl6 )3] the corresponding average distances for Bi9 + in BiCli 1 7 i.e. [(Bi9 +)2(BiCl5 )4(Bi2Cl8 )] are 310, 320 and 380pm respectively. The square antiprismatic structure of Big " was established by an X-ray study of Bi8[AlCl4]2. ...

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