Результаты поиска по 'variational symmetries':
Найдено статей: 2
  1. Yakovenko G.N.
    Wandering symmetries of the Lagrange's equations
    Computer Research and Modeling, 2010, v. 2, no. 1, pp. 13-17

    The dynamic process can be in equal degree adequately prototyped by a family of Lagrange's systems. Symmetry group ‘wanders’ on this family: systems are transformed from one into another. In this work we show that under determined condition the first integral can be obtained by a simple calculations on some of such groups. The main purpose of the work is to show usefulness of wandering symmetry concept. The considered example: flat motion of a charged particle in magnetic field in presence of viscous friction. With the help of three wandering symmetry first integral is calculated.

    Keywords: the Lagrange's equations, variational symmetries, divergental symmetries, conformal symmetries, wandering symmetries, the first integrals.
    Views (last year): 4.
  2. Nikonov E.G., Nazmitdinov R.G., Glukhovtsev P.I.
    Molecular dynamics studies of equilibrium configurations of equally charged particles in planar systems with circular symmetry
    Computer Research and Modeling, 2022, v. 14, no. 3, pp. 609-618

    The equilibrium configurations of charged electrons, confined in the hard disk potential, are analysed by means of the hybrid numerical algorithm. The algorithm is based on the interpolation formulas, that are obtained from the analysis of the equilibrium configurations, provided by the variational principle developed in the circular model. The solution of the nonlinear equations of the circular model yields the formation of the shell structure which is composed of the series of rings. Each ring contains a certain number of particles, which decreases as one moves from the boundary ring to the central one. The number of rings depends on the total number of electrons. The interpolation formulas provide the initial configurations for the molecular dynamics calculations. This approach makes it possible to significantly increase the speed at which an equilibrium configuration is reached for an arbitrarily chosen number of particles compared to the Metropolis annealing simulation algorithm and other algorithms based on global optimization methods.

    Keywords: Tomson atom, Wigner crystal, molecular dynamics.

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