The simulation of a system of particles, located in the plane, with van der Waals interaction described by the Lennard-Jones potential is carried out. The possibility of the existence of a solitary chain of particles, as well as the formation of linear systems of two and three chains, has been established. The spectrum of vibrations of the systems was determined for various configurations and the characteristic frequencies of the vibrations were found. The dispersion law of collective modes is calculated theoretically by the method of equations of motion for small displacements of atoms from their equilibrium position when analyzing the compatibility condition for the arising system of equations. The obtained values of the characteristic frequencies are in rather good agreement with the results obtained in the Fourier analysis of the time dependence of the displacements of particles from their equilibrium positions along and across the system.

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• Сивоконь Віталій Юхимович (фізико-математичні науки)

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