Brownian motion of sol particles Brownian motion of sol particles Colloidal particles in a sol are continuously bombarded by the molecules of the dispersion medium on all sides. The impacts are however not equal in every direction. As a result, the sol particles show random or zig-zag movements. This random or zig-zag motion of the colloidal particles in a sol is called Brownian motion or Brownian movement. The phenomenon of Brownian motion was observed by Robert Brown in the form of random zig-zag motion of pollen grains suspended in water. This kind of movement is found in all colloidal systems. Such random motion is visible
Brownian surface Brownian motion, Brownian surfaces are named after 19th-century biologist Robert Brown. Efficient generation of fractional Brownian surfaces poses significant challenges. Since the Brownian surface represents a Gaussian process with a nonstationary covariance function, one can use the Cholesky decomposition method. A more efficient method is Stein's method, which generates an auxiliary stationary Gaussian process using the circulant embedding approach and then adjusts this auxiliary process to obtain the desired nonstationary Gaussian process. The figure below shows three typical realizations of fractional Brownian surfaces for different values of the roughness or Hurst parameter. The Hurst parameter is always between zero and