Geodesic
An analysis of the efficiency of higher-order symplectic schemes by the example of a problem of the collision of a nanoparticle with an obstacle
Numerical methods and programming, Tome 25 (2024) no. 2, pp. 214-237.

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The work is devoted to the application of the molecular dynamics (MD) method for numerical simulation of high-velocity interaction of solids. The phenomenon of the copper nanoparticle rebound from the aluminum plate has been simulated numerically. For the Verlet scheme and the new symplectic scheme FR50 obtained recently by the author, the intervals of time steps were found such that at the specification of the time step within these intervals, no drift of the total energy occurs. The total energy drift arises in the case of the FR50 scheme at much larger time steps than in the case of the Verlet method. The need in introducing several similarity criteria by analogy with the continuum mechanics has been shown by analyzing the results of the numerical simulation of problems involving the nanoparticle collision with an obstacle. A rapid and simple computer test has been proposed for the rejection of the EAM potentials before starting to solve the main MD problem.
Keywords: molecular dynamics, Hamilton equations, collision of a nanoparticle with an obstacle, EAM potentials, multi-component systems, symplectic difference schemes. 
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     author = {E. V. Vorozhtsov},
     title = {An analysis of the efficiency of higher-order symplectic schemes by the example of a problem of the collision of a nanoparticle with an obstacle},
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E. V. Vorozhtsov. An analysis of the efficiency of higher-order symplectic schemes by the example of a problem of the collision of a nanoparticle with an obstacle. Numerical methods and programming, Tome 25 (2024) no. 2, pp. 214-237. http://geodesic.mathdoc.fr/item/VMP_2024_25_2_a6/