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
Reflected Brownian motion "roughly speaking, "Z" is pushed in direction "R" whenever the boundary surface formula_5 is hit, where "R" is the "j"th column of the matrix "R"." Stability conditions are known for RBMs in 1, 2, and 3 dimensions. "The problem of recurrence classification for SRBMs in four and higher dimensions remains open." In the special case where "R" is an M-matrix then necessary and sufficient conditions for stability are The marginal distribution (transient distribution) of a one-dimensional Brownian motion starting at 0 restricted to positive values (a single reflecting barrier at 0) with drift "μ " and variance "σ" is for