Coupled physical and magnetodynamic rotational diffusion of a single-domain ferromagnetic nanoparticle suspended in a liquid.

A concise operator form of the Fokker-Planck equation agreeing with that proposed by Weizenecker [Phys. Med. Biol.

Anomalous diffusion of molecules with rotating polar groups: The joint role played by inertia and dipole coupling in microwave and far-infrared absorption.

Budó's generalization [A. Budó, J. Chem.

Generalization to anomalous diffusion of Budó's treatment of polar molecules containing interacting rotating groups.

A fractional Smoluchowski equation for the orientational distribution of dipoles incorporating interactions with continuous time random walk Ansatz for the collision term is obtained. This equation is written via the non-inertial Langevin equations for the evolution of the Eulerian angles and their associated Smoluchowski equation. These equations govern the normal rotational diffusion of an assembly of non-interacting dipolar molecules with similar internal interacting polar groups hindering their rotation owing to their mutual potential energy.

Anomalous diffusion of a dipole interacting with its surroundings.

A fractional Fokker-Planck equation based on the continuous time random walk Ansatz is written via the Langevin equations for the dynamics of a dipole interacting with its surroundings, as represented by a cage of dipolar molecules. This equation is solved in the frequency domain using matrix continued fractions, thus yielding the linear dielectric response for extensive ranges of damping, dipole moment ratio, and cage-dipole inertia ratio, and hence the complex susceptibility. The latter comprises a low frequency band with width depending on the anomalous parameter and a far infrared (THz) band with a comb-like structure of peaks.

Cage model of polar fluids: Finite cage inertia generalization.

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.