Search results
Results from the WOW.Com Content Network
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.,
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 [] = / /.
This is a special case of the thin rectangular plate with axis of ... the value r is called the radius of gyration. Solid cylinder of radius ... formula is for the ...
This formula was derived in 1744 by the Swiss mathematician Leonhard Euler. [2] ... is the radius of gyration, is the second moment of area (area moment of inertia ...
Since the gyration tensor is a symmetric 3x3 matrix, ... The squared radius of gyration is the sum of the principal moments: = ...
where is the radius of gyration of the polymer, is the number of bond segments (equal to the degree of polymerization) of the chain and is the Flory exponent. For good solvent, ν ≈ 3 / 5 {\displaystyle \nu \approx 3/5} ; for poor solvent, ν = 1 / 3 {\displaystyle \nu =1/3} .
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 ...
In structural engineering, Johnson's parabolic formula is an empirically based equation for calculating the critical buckling stress of a column. The formula is based on experimental results by J. B. Johnson from around 1900 as an alternative to Euler's critical load formula under low slenderness ratio (the ratio of radius of gyration to ...