Radius calculation

Fig. 5. Band gap as a function of nanotube radius calculated using empirical tight-binding Hamiltonian. Solid line gives estimate using Taylor expansion of graphene sheet results in eqn. (7).

Fig. 7. Strain energy per carbon (total energy minus total energy extrapolated for the graphite sheet) as a function of nanotube radius calculated for unoptimized nanotube structures (open squares) and optimized nanotube structures (solid circles). Solid line depicts inverse square relationship drawn through point at smallest radius.

M +(g)-(-e" this is 7297kJ mol for Li but drops to 2255kJmol for Cs. The largest possible lattice energy to compensate for this would be obtained with the smallest halogen F and (making plausible assumptions on lattice structure and ionic radius) calculations indicate that CsF2 could indeed be formed exothermically from its elements ... 

Table 3.1 N parameter and boundary radius calculated for several a values.

In equation (2) Rq is the equivalent capillary radius calculated from the bed hydraulic radius (l7), Rp is the particle radius, and the exponential, fxinction contains, in addition the Boltzman constant and temperature, the total energy of interaction between the particle and capillary wall force fields. The particle streamline velocity Vp(r) contains a correction for the wall effect (l8). A similar expression for results with the exception that for the marker the van der Waals attraction and Born repulsion terms as well as the wall effect are considered to be negligible (3 ). 

Figure 14 The predicted uptake of phosphorus by maize over a 22 day period. The Barber-Cushman model (F, ), u.ses an average root radius calculated at the end of the simulation period, while the F, model uses a population of roots of different radius. Identical parameter values were used by both simulation models with the exception of root radius.

PC = partition coefficient values from Adson et at. (1995). Molecular density p 1.0 g/mL. Diffusion coefficient and molecular radius calculated by Eqs. (41) and (42). 

Fig. 17.4 Steady state velocity of freely falling microdroplets as function of droplet radius calculated from the balance between gravitation and Stokes drag...

Table 1. Total mass of the neutron star model versus its radius calculated by Oppenheimer and Volkoff (1939).

According to gel-filtration experiments conducted by P. Wills and J. Dijk (personal communication), proteins L17, L25, L28, L29, and L30 are compact LI, L4, L5, L6, L13, L16, L19, and L24 are moderately elongated and L2, L3, L9, Lll, L15, L23, L27, L32, and L33 are quite extended. A discrepancy between these results and those mentioned earlier is protein L9 which appears to be globular from hydrodynamic measurements (Giri et al., 1979), but the Stokes radius calculated from gel-filtration experiments was found to be quite large, suggesting an elongated particle. 

Fig. 1.16 Typical intrusion and extrusion schematic curves for porous beads (A) and the log differential pore volume versus pore radius calculated from the intrusion branch (B).

Geiaxo is the radius calculated from NMRD curves. 

We have carried out calculations for transitions for which empirical energy data were available [3,5,6,7], The core polarizabilities have been take from Fraga et al. [13], Since there is no analytical way of obtaining the cutoff radius r, we have chosen a value equal to the core mean radius, calculated in accord with an expression given by Chichkov Shevelko[14],... 

These same arguments are now applied to the alkali-metal hydrides. The following Table shows the nearest-neighbour distances 24) and the anion-radius calculated on the assumption of anion-cation and anion-anion contact if one consistently assumes anion-anion contact in the... 

Table 9.2 shows some of these values for POPC liposomes of various radius, calculated assuming monolamellarity. 

Numerical methods have been used to study propagation of a bent laminar flame in a tube with varying radius. Calculations showed that stabilization of the... 

Application of the Stokes-Einstein equation requires a value for the solute radius. A simple approach is to assume the molecule to be spherical and to calculate the solute radius from the molar volume of the chemical groups making up the molecule. Using values for the solute radius calculated this way along with measured and known diffusion coefficients of solutes in water, Edward [26]... 

Note that the parameter a for the gold unit cell canceled and that the result holds for any cubic close-packed structure. The metallic radius calculated above, r = a/23/2 = 143.9 pm, is different from both an ionic radius and a covalent... 

Polyhedron" Circum radius Calculated hole (in A) for d = 1.4 A b Comparison with some covalent radii (A)... 

Figure 4. Normalized concentration profiles of reactant A versus the pellet radius, calculated from eq 49 for different values of the Thiele modulus (isothermal, first order, irreversible reaction in a sphere).

Real Border radius Calculated expansion ratio ... 

All alternative procedure is to calculate the radius of a sphere equivalent to the protein molecule from hydrodynamic measurements. The value of R obtained in this way is always larger than that calculated by Eq. (15), even for the native protein conformation, the reason being that protein molecules are in fact never perfectly spherical. The resulting values of w are roughly 20 % less than those obtained with a radius calculated by Eq. (15). 

The hydrogen atom has a radius on the order of 0.05 nm. Assuming that we know the position of an electron to an accuracy of 1% of the hydrogen radius, calculate the uncertainty in the velocity of the electron, using the Heisenberg uncertainty principle. Then compare this value with the uncertainty in the velocity of a ball of mass 0.2 kg and radius 0.05 m whose position is known to an accuracy of 1% of its radius. 

The total interfacial surface area can be simply related to the dispersed phase volume in terms of the microemulsion droplet radius. Calculated radii for the systems studied are shown in Table 1. As expected, the droplets increasingly grow in size as the volume of dispersed phase increases. Thus, the observed decrease in X is merely a consequence of the decreasing surface-to-volume ratio needing a correspondingly smaller fraction of the MMA to create new interface. The droplet sizes predicted are consistent with the observed transparency of our systems which requires droplet sizes of under 100 A in radius. Thus, the simple swollen micelle serves as an adequate structural model for this microemulsion system. 

A location not Class 3 or 4 that has an identified site within a potential impact circle of an impact radius calculated from a specified equation in the regulation. 

The mean hydrodynamic radius, calculated from Dgpp, is given by ... 

The magnitude of the JT effect itself, as expressed by the JT radius, is in the expected range. Holuj and Wilson (35) found a value of 0.019 nm for a trigonal distortion of Cu(OD) . With our assumed force constant of 70 Nm, the JT radius calculated from Strome and Klier s data is 0.016 nm (7). 

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