Cage model of polar fluids: Finite cage inertia generalization

Abstract

The itinerant oscillator model describing rotation of a dipole about a fixed axis inside a cage formed by its surrounding polar molecules is revisited in the context of modeling the dielectric relaxation of a polar fluid via the Langevin equation. The dynamical properties of the model are studied by averaging the Langevin equations describing the complex orientational dynamics of two bodies (molecule-cage) over their realizations in phase space so that the problem reduces to solving a system of three index linear differential-recurrence relations for the statistical moments. These are then solved in the frequency domain using matrix continued fractions. The linear dielectric response is then evaluated for extensive ranges of damping, dipole moment ratio, and cage-dipole inertia ratio and along with the usual inertia corrected microwave Debye absorption gives rise to significant far-infrared absorption with a comb-like structure of harmonic peaks. The model may be also regarded as an extension of Budó's [J. Chem. Phys. 17, 686 (1949)] treatment of molecules containing rotating polar groups to include inertial effects.

Comparison of Coupled Nonlinear Oscillator Models for the Transient Response of Power Generating Stations Connected to Low Inertia Systems

“…For comparison, we also analyze the grid and generator dynamics using the alternative cage model [13], [14], where the dynamics of the angles j θ are described by the many body…”

“…model is widely used in chemical physics (for a detailed summary of its applications see [14] and references therein).…”

“…To find the evolution equation for the grid and generator angles in terms of the rotor angle, we follow the method for the Kuramoto-like model. By addition of (19) and (20) we again have (12), thus leading to (14) and (15).…”

“…Here we shall compare two physically acceptable two-body coupled oscillator models, namely, a Kuramoto-like [10]- [12] and a cage model [13], [14]. Both yield insights into the general phase behavior of a generator connected to a power grid with finite inertia such as prevails in Ireland.…”

Active Damping of Power Oscillations Following Frequency Changes in Low Inertia Power Systems

“…The results are shown for the Kuramoto-like model [12], [17]- [20] in Fig. 6(a) and for the cage model [12], [21]- [27] in Fig. 6 (b) (see Appendix A).…”