Nonlinear dynamics and energy transfer for two rotating dipoles in an external field: A complete dimensional analysis

• Published in: Communications in nonlinear science & numerical simulation 2020-03, Vol.82, p.105049, Article 105049
• Main Authors: González-Férez, Rosario, Iñarrea, Manuel, Salas, J. Pablo, Schmelcher, Peter
• Format: Article
• Language: English
• Subjects: Dimensional analysis; Dipole interactions; Dynamic structural analysis; Electric field strength; Electric fields; Energy transfer; Equipartition theorem; Fluid dynamics; Free energy; Heat transfer; Initial conditions; Kinetic energy; Kinetics; Mathematical analysis; Nonlinear dynamics; Nonlinear systems; Rotors
• ISSN: 1007-5704; 1878-7274
• DOI: 10.1016/j.cnsns.2019.105049

•Theoretically investigation of two interacting classical rigid dipoles in the presence of a homogenous electric field.•The classical dynamics of the two dipoles is explored in terms of the energy transfer mechanisms between them and their orientations along the electric field axis.•In the field-free case, the system falls to either an energy equipartition regime or a non-equipartition one, and the dynamics is regular.•In the presence of the field, the classical dynamics strongly depend on the electric field strength and on the initial conditions.•For weak external fields, the dynamics is dominated by the dipole-dipole interaction and the energy transfer dynamics resembles the field-free dynamics.•By increasing the electric field, the interaction with this field dominates the classical dynamics and the orientation of the two dipoles along the electric field direction increases.•Even for large electric field strengths the system shows a highly chaotic behavior. We investigate the structure and the nonlinear dynamics of two rigid polar rotors coupled through the dipole-dipole interaction in an external homogeneous electric field. In the field-free stable head-tail configuration, an excess energy is provided to one of the dipoles, and we explore the resulting complete dimensional classical dynamics. This dynamics is characterized in terms of the kinetic energy transfer between the dipoles, their orientation along the electric field, as well as their chaotic behavior. The field-free energy transfer mechanism shows an abrupt transition between equipartition and non-equipartition regimes, which is independent of the initial direction of rotation due to the existence of an infinite set of equivalent manifolds. The field-dressed dynamics is highly complex and strongly depends on the electric field strength and on the initial conditions. In the strong field regime, the energy equipartition and chaotic behavior dominate the dynamics.