Models & Optimisation and Mathematical Analysis Journal
Volume 9, Numéro 1, Pages 21-25
2021-12-31
Graph Theory And Networks In The Physics Of Microscopic Dispersion Forces In And Between Materials.
Authors : Djafri Youcef .
Abstract
Dispersion forces or as widely known van der Waals forces, play an important role at different scales of the physical world from the visible macroscopic through the nanometric to the microscopic molecular level, and this makes them important in various domains such as biology, physics and chemistry. At the microscopic level in material sciences, these forces present an important factor in the process of modelling materials’ properties and behaviour. Several theories throughout the last decades have been developed; such as the Coupled Dipole Method and similar approaches derived from the fluctuation-dissipation theorem. For more direct derivation and calculation of these interactions and Inspired by and based on the previous works that simplified these interactions at the microscopic level using simple graphical representations such as the work of A.Jones and J.Crain (2013), we propose in this study a novel representation of the phenomena using graph theory and networks, where we will lay the foundations and write the fundamental theorems that will construct such a promising technique. the connection between these theorems and these graphs with the physical aspects of dispersion forces and the pre-existing models are clearly stated, and the different modes of the involved many-body interactions are presented and their energies are derived from and through this mathematical representation.
Keywords
Dispersion forces ; Graph theory ; Many-body interactions ; Networks ; van der Waals forces
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