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
Brownian meander Brownian meander In the mathematical theory of probability, Brownian meander formula_1 is a continuous non-homogeneous Markov process defined as follows: Let formula_2 be a standard one-dimensional Brownian motion, and formula_3, i.e. the last time before "t" = 1 when formula_4 visits formula_5. Then the Brownian meander is defined by the following: In words, let formula_7 be the last time before 1 that a standard Brownian motion visits formula_5. (formula_9 almost surely.) We snip off and discard the trajectory of Brownian motion before formula_7, and scale the remaining part so that it spans a time interval of length 1. The scaling