The problem of steady Magnetohydrodynamic boundary layer flow of an electrically conducting nanofluid due to an exponentially permeable stretching sheet with heat source/sink in presence of thermal radiation is numerically investigated. The effect of transverse Brownian motion and thermophoresis on heat transfer and nano particle volume fraction considered. The governing partial differential eq...

Ecological theory uses Brownian motion as a default template for describing ecological movement, despite limited mechanistic underpinning. The generality of Brownian motion has recently been challenged by empirical studies that highlight alternative movement patterns of animals, especially when foraging in resource-poor environments. Yet, empirical studies reveal animals moving in a Brownian fa...

In this research various nonlinear fluid models have been introduced and the balloon movement in the porous arteries, including third-order non-Newtonian fluid, is described under the influence of the magnetic field. In order to solve the nonlinear equations governing the desired artery, an analytical method of approximation collocation and least squares are proposed. The effect of various para...

Vicious Brownian motion is a diffusion scaling limit of Fisher's vicious walk model, which is a system of Brownian particles in one dimension such that if two motions meet they kill each other. We consider the vicious Brownian motions conditioned never to collide with each other and call it noncolliding Brownian motion. This conditional diffusion process is equivalent to the eigenvalue process ...

In this paper, we develop Brownian motion and discuss its basic properties. We then turn our attention to the “size” of Brownian motion by defining Hausdorff dimension and its relationship to Brownian motion. This leads to the final result of the paper that for n ≥ 2, both the range and graph of Brownian motion have Hausdorff dimension 2.

We present a decomposition of the sub-fractional Brownian motion into the sum of a fractional Brownian motion plus a stochastic process with absolutely continuous trajectories. The first application we show of this decomposition is the relation between the spaces of integrable functions with respect each one of these three processes. A general result of weak convergence to integrals of L(R) fun...