Radius of curve

R radius of curved surface (spherical parti- yoo infinite dilution activity coefficient... 

Figure C2.5.6. Thennodynamic functions computed for the sequence whose native state is shown in figure C2.5.7. (a) Specific heat (dotted curve) and derivative of the radius of gyration with respect to temperature dR /dT (broken curve) as a function of temperature. The collapse temperature Tg is detennined from the peak of and found to be 0.83. Tf, is very close to the temperature at which d (R )/d T becomes maximum (0.86). This illustrates...

As would be expected, the enhancement of potential in cylindrical pores turns out to be considerably greater than in dits, as curve (ii) of Fig. 4.9 clearly demonstrates. At R/r = 2 the enhancement is more than 50 per cent, and it is still appreciable when R/r = 3 (R = radius of cylinder). The calculations show that at radii in excess of R = 1086ro, the single minimum (comparable with Fig. 4.8(c)) develops into a ring minimum (i.e. two minima are present in any axial plane, cf. Fig. 4.8(a)). 

Similarly, a sharp edge (razor blade) or a very sharp curve can also provide an intense electric field. For any given electric potential, as the radius of curvature of a tip or edge becomes smaller, the electric field becomes increasingly stronger. 

Fig. 3. Two-dimensional schematic illustrating the distribution of Hquid between the Plateau borders and the films separating three adjacent gas bubbles. The radius of curvature r of the interface at the Plateau border depends on the Hquid content and the competition between surface tension and interfacial forces, (a) Flat films and highly curved borders occur for dry foams with strong interfacial forces, (b) Nearly spherical bubbles occur for wet foams where...

In a synchrotron, electrons are accelerated to near relativistic velocities and constrained magnetically into circular paths. When a charged particle is accelerated, it emits radiation, and when the near-relativistic electrons are forced into curved paths they emit photons over a continuous spectrum. The general shape of the spectrum is shown in Fig. 2.4. For a synchrotron with an energy of several gigaelectronvolts and a radius of some tens of meters, the energy of the emitted photons near the maximum is of the order of 1 keV (i.e., ideal for XPS). As can be seen from the universal curve, plenty of usable intensity exists down into the UV region. With suitable mono-... 

The Plate Constitutive equations can be used for curved plates provided the radius of curvature is large relative to the thickness (typically r/h > 50). They can also be used to analyse laminates made up of materials other than unidirectional fibres, eg layers which are isotropic or made from woven fabrics can be analysed by inserting the relevant properties for the local 1-2 directions. Sandwich panels can also be analysed by using a thickness and appropriate properties for the core material. These types of situation are considered in the following Examples. 

Another important characteristic aspect of systems near the glass transition is the time-temperature superposition principle [23,34,45,46]. This simply means that suitably scaled data should all fall on one common curve independent of temperature, chain length, and time. Such generahzed functions which are, for example, known as generalized spin autocorrelation functions from spin glasses can also be defined from computer simulation of polymers. Typical quantities for instance are the autocorrelation function of the end-to-end distance or radius of gyration Rq of a polymer chain in a suitably normalized manner ... 

FIGURE 2.2 Selectivity curve of Superdex 7S, HR 10/30, as compared to a hypothetical single pore-size support. , experimental data from dextran fractions calculated for a SEC medium having a single pore radius of 60 A. [Reproduced from Hagel (1996), with permission.]... 

FIGURE 2.8 Determination of relative clearance of dextran as a function of solute size. Please note that Stokes radius (left curve) will yield too low a value for the renal clearance barrier. [Reproduced from Hagel et al. (1993), with permission.]... 

Kriimmnng, /. curvature curve, bend, turn, sinuosity crookedness. Kriimmungshalbmesser, m. radius of curvature. Krumm-werden, n. warping, bending, buckling. 

The radius of curvature R of a plane curve at any point P is the distance along the normal (the perpendicular to the tangent to the curve at point P) on the concave side of the curve to the center of curvature (Figure 1-33). If the equation of the curve is y = f(x)... 

Permeability. Permeable zones can be identified with the resistivity measurements made with different radius of investigation. A departure between the curves of deep and shallow investigation is a qualitative indication of permeability. 

While friction increases markedly for sharper curves than this, it also tends to increase up to a certain point for gentler curves. The increases in friction in a bend with a radius of more than 3 pipe diameters result from increased turbulence near the outside edges of the flow. Particles of fluid must travel a longer distance in making the change in direction. When the radius of the bend is less than 2 pipe diameters, the increased pressure loss is due to the abrupt change in the direction of flow, especially for particles near the inside edge of the flow. 

Hence the liquid must be superheated near the surface of the bubble, the extent of the superheat increasing with decrease in the radius of the bubble. On this basis it follows that very small bubbles are difficult to form without excessive superheat. The formation of bubbles is made much easier by the fact that they will form on curved surfaces or on irregularities on the heating surface, so that only a small degree of superheat is normally required. 

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