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It is often useful to give the gyrofrequency a sign with the definition = or express it in units of hertz with =. For electrons, this frequency can be reduced to , = (/).. In cgs-units the gyroradius = | | and the corresponding gyrofrequency = | | include a factor , that is the velocity of light, because the magnetic field is expressed in units [] = / /.
Radius of gyration (in polymer science)(, unit: nm or SI unit: m): For a macromolecule composed of mass elements, of masses , =1,2,…,, located at fixed distances from the centre of mass, the radius of gyration is the square-root of the mass average of over all mass elements, i.e.,
For this case the radius of gyration is approximated using Flory's mean field approach which yields a scaling for the radius of gyration of: R g ∼ N ν {\displaystyle R_{g}\sim N^{\nu }} , where R g {\displaystyle R_{g}} is the radius of gyration of the polymer, N {\displaystyle N} is the number of bond segments (equal to the degree of ...
A quantity frequently used in polymer physics is the radius of gyration: = It is worth noting that the above average end-to-end distance, which in the case of this simple model is also the typical amplitude of the system's fluctuations, becomes negligible compared to the total unfolded length of the polymer N l {\displaystyle N\,l} at the ...
It is defined [8] as = where s b is the mean square radius of gyration of the branched macromolecule in a given solvent, and s l is the mean square radius of gyration of an otherwise identical linear macromolecule in the same solvent at the same temperature. A value greater than 1 indicates an increased radius of gyration due to branching.
A Guinier plot made with X-ray scattering in the small-angle regime. The slopes of these linear curves correspond to the radius of gyration of the polymers in the solution, while different curves correspond to different concentrations. and by utilising the definition of the radius of gyration:
It is defined as / where is the effective length of the column and is the least radius of gyration, the latter defined by = / where is the area of the cross-section of the column and is the second moment of area of the cross-section. The effective length is calculated from the actual length of the member considering the rotational and relative ...
The mobility of non-spherical aerosol particles can be described by the hydrodynamic radius. In the continuum limit, where the mean free path of the particle is negligible compared to a characteristic length scale of the particle, the hydrodynamic radius is defined as the radius that gives the same magnitude of the frictional force, as that of a sphere with that radius, i.e.