Brownian motion and thermal capacity∗
نویسندگان
چکیده
Let W denote d-dimensional Brownian motion. We find an explicit formula for the essential supremum of Hausdorff dimension of W (E)∩F , where E ⊂ (0 ,∞) and F ⊂ R are arbitrary nonrandom compact sets. Our formula is related intimately to the thermal capacity of Watson (1978). We prove also that when d ≥ 2, our formula can be described in terms of the Hausdorff dimension of E × F , where E × F is viewed as a subspace of space time.
منابع مشابه
Preparation of MCM-41 nanofluid and an investigation of Brownian movement of the nanoparticles on the nanofluid conductivity
In this investigation the silicate nano structure of MCM-41 has been used for the production of nanofluid. The particles have negligible heat conductivity and therefore by their dispersion in a base fluid like water, it is possible to study the increase of heat conductivity due to the Brownian motion effects. In this work a suitable apparatus for the measurement of heat conductivity has been bu...
متن کاملInvestigation of Brownian Motion of CuO-Water Nanofluid in a Porous Cavity with Internal Heat Generation by Using of LTNE Model
In this paper, the effect of the Brownian term in natural convection of CuO-Water nanofluid inside a partially filled porous cavity, with internal heat generation has been studied. It is assumed that the viscosity and thermal conductivity of nanofluid consists of a static part and a Brownian part of which is a function of temperature and the volume fraction of nanofluid. Because of internal hea...
متن کاملMixed 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...
متن کاملEffects 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...
متن کاملUnsteady MHD nonlinear radiative squeezing slip-flow of Casson fluid between parallel disks
Effect of nonlinear thermal radiation on the unsteady magnetohydrodynamic slip flow of Casson fluid between parallel disks in the presence of thermophoresis and Brownian motion effects are investigated numerically. A similarity transformation is employed to reduce the governing partial differential equations into ordinary differential equations. Further, Runge-Kutta and Newton’s methods are ado...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011