Brownian motion with killing and reflection and the “hot spots” problem

FIBER BROWNIAN MOTION AND THE “ HOT SPOTS ” PROBLEM Richard

We show that in some planar domains both extrema of the second Neumann eigenfunction lie strictly inside the domain. The main technical innovation is the use of “fiber Brownian motion,” a process which switches between two-dimensional and one-dimensional evolution.

On the Hot Spots of a Catalytic Super-brownian Motion

An inequality for potentials and the “hot–spots” conjecture

Consider a nonnegative continuous potential V on the half disk ID = {z = x + iy : y > 0, |z| < 1} for which r2V (reiθ) is nondecreasing as a function of r for every fixed 0 < θ < π. We prove an inequality for the distribution of the random variable ∫ τID+ 0 V (Bs)ds where Bs is the Brownian motion reflected on the top portion of the boundary and killed on the lower portion and τID+ is its lifet...

Effects of Brownian motion and Thermophoresis on MHD Mixed Convection Stagnation-point Flow of a Nanofluid Toward a Stretching Vertical Sheet in Porous Medium

This article deals with the study of the two-dimensional mixed convection magnetohydrodynamic (MHD) boundary layer of stagnation-point flow over a stretching vertical plate in porous medium filled with a nanofluid. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis in the presence of thermal radiation. The skin-friction coefficient, Nusselt number an...

Mixed convection on radiative unsteady Casson ferrofluid flow due to cone with Brownian motion and thermophoresis: A numerical study

In this study, the Brownian motion and thermophoresis effects on the MHD ferrofluid flow over a cone with thermal radiation were discussed. Kerosene with the magnetic nanoparticles (Fe3O4) was considered. A set of transformed governing nonlinear coupled ordinary differential equations were solved numerically using Runge-Kutta based shooting technique. A simulation was performed by mixing ferrou...