Rotational Brownian motion the absorption tends toward a maximum and then declines with increasing frequency. The breakdown in Debye's theory in these regimes can be corrected by including inertial effects; allowing the molecules to be non-spherical; including dipole-dipole interactions between molecules; etc. These are computationally very difficult problems and rotational Brownian motion is a topic of much current research interest. Rotational Brownian motion Rotational Brownian motion is the random change in the orientation of a polar molecule due to collisions with other molecules. It is an important element of theories of dielectric materials. The polarization of a dielectric material is a competition between
Fractional Brownian motion Motion are independent, increments for fractional Brownian motion are not. If H > 1/2, then there is positive autocorrelation: if there is an increasing pattern in the previous steps, then it is likely that the current step will be increasing as well. If H < 1/2, the autocorrelation is negative. The process is self-similar, since in terms of probability distributions: This property is due to the fact that the covariance function is homogeneous of order 2H and can be considered as a fractal property. FBm can also be defined as the unique mean-zero Gaussian process, null at the origin, with