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F. H. Harlow, “The Particle-in-Cell Method for Numerical Solution of Problems in Fluid Dynamics,” Proceedings of Symposium in Applied Mathematics, Vol. 15, No. 10, 1963, p. 269.

has been cited by the following article:

• TITLE: The Evolution of the Charge Density Distribution Function for Spherically Symmetric System with Zero Initial Conditions

  AUTHORS: Evgeny E. Perepelkin, Natalia G. Inozemtseva, Alex A. Zhavoronkov

  KEYWORDS: non-uniform charged sphere, Cauchy problem, charge density distribution, particle-in-cell

  JOURNAL NAME: World Journal of Condensed Matter Physics, Vol.4 No.1, February 13, 2014

  ABSTRACT: The evolution of the charge density distribution function is simulated for both the case of a uniformly charged sphere with zero initial conditions and for the case of a non-uniform charged sphere. For the case of a uniformly charged sphere the comparison of a numerical result and an exact analytical demonstrated the agreement between the results. The process of “scattering” of a charged system under the influence of its own electric field has been illustrated on the basis of both the particle-in-cell method and the solution of the Cauchy problem for vector functions of the electric field and vector velocity field of a charged medium.