Rotational Brownian motion (astronomy) Rotational Brownian motion (astronomy) In astronomy, rotational Brownian motion is the random walk in orientation of a binary star's orbital plane, induced by gravitational perturbations from passing stars. Consider a binary that consists of two massive objects (stars, black holes etc.) and that is embedded in a stellar system containing a large number of stars. Let formula_1 and formula_2 be the masses of the two components of the binary whose total mass is formula_3. A field star that approaches the binary with impact parameter formula_4 and velocity formula_5 passes a distance formula_6 from the binary, where formula_7 the latter expression
Fractional Brownian motion Hypergeometric functions are part of the GNU scientific library. Fractional Brownian motion In probability theory, fractional Brownian motion (fBm), also called a fractal Brownian motion, is a generalization of Brownian motion. Unlike classical Brownian motion, the increments of fBm need not be independent. fBm is a continuous-time Gaussian process "B"("t") on [0, "T"], which starts at zero, has expectation zero for all "t" in [0, "T"], and has the following covariance function: where "H" is a real number in (0, 1), called the Hurst index or Hurst parameter associated with the fractional Brownian motion. The Hurst exponent describes the raggedness