The Multiscale Hybrid Method with a Localized Constraint. II. Hybrid Equations of Motion Based on Variational Principles


  • M. Bakumenko Taras Shevchenko National University of Kyiv, Aston University
  • V. Bardik Taras Shevchenko National University of Kyiv
  • V. Farafonov V.N. Karazin Kharkiv National University
  • D. Nerukh Aston University



molecular dynamics, multiscale method, control volume function, hydrodynamic equations, equation of motion, Principle of least action, Gauss principle, constraint


A multiscale modelling framework that employs molecular dynamics and hydrodynamics principles has been developed to describe the dynamics of hybrid particles. Based on the principle of least action, the equations of motion for hybrid particles were derived and verified by using the Gauss principle of least constraints testifying to their accuracy and applicability under various system constraints. The proposed scheme has been implemented in a popular open-source molecular dynamics code GROMACS. The simulation for liquid argon under equilibrium conditions in the hydrodynamic limit (s = 1) has demonstrated that the standard deviation of the density exhibits a remarkable agreement with predictions from a pure hydrodynamics model, validating the robustness of the proposed framework.


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How to Cite

Bakumenko, M., Bardik, V., Farafonov, V., & Nerukh, D. (2024). The Multiscale Hybrid Method with a Localized Constraint. II. Hybrid Equations of Motion Based on Variational Principles. Ukrainian Journal of Physics, 69(4), 269.



Physics of liquids and liquid systems, biophysics and medical physics