Elastic properties of two-dimensional soft discs of various diameters at zero temperature

Elastic properties of two classes of two-dimensional models, consisting of soft particles of various sizes have been determined numerically and compared: (1) polydisperse discs (with Gaussian probability distribution of diameters) and (2) binary discs (with probability density distribution of diameters composed of two Dirac delta functions of equal amplitudes). Simple analytical formulae approximating the numerical results are found. It is shown that the elastic properties of both systems are very close to each other if the first two moments (i.e. the mean value and the standard deviation) of the probability density distribution in the systems are equal.