in this paper the effect of using various models for conductivity and viscosity considering brownian motion of nanoparticles is investigated. this study is numerically conducted inside a cavity full of water-al2o3 nanofluid at the case of mixed convection heat transfer. the effect of some parameters such as the nanoparticle volume fraction, rayleigh, richardson and reynolds numbers has been exa...

The fractal dimension estimate for two-variable fractional Brownian motion using the maximum likelihood estimate (MLE) is developed. We formulate a model to describe the two-variable fractional Brownian motion, then derive the likelihood function for that model and estimate the fractal dimension by maximizing the likelihood function. We then compare the MLE with the box-dimension estimation met...

1 Historical notes • 1765 Jan Ingenhousz observations of carbon dust in alcohol. • 1828 Robert Brown observed that ”pollen grains suspended in water per­ form a continual swarming motion”. • 1900 Bachelier’s work ”The theory of speculation” on using Brownian motion to model stock prices. • 1905 Einstein and Smoluchovski. Physical interpretation of Brownian motion. • 1920’s Wiener concise mathem...