scholarly journals On the Dirichlet form of three-dimensional Brownian motion conditioned to hit the origin

2019 ◽  
Vol 62 (8) ◽  
pp. 1477-1492
Author(s):  
Patrick J. Fitzsimmons ◽  
Liping Li
Keyword(s):  
Brownian Motion ◽  
Dirichlet Form ◽  
Three Dimensional

Magneto convective flow of casson nanofluid due to Stefan blowing in the presence of bio-active mixers

2021 ◽  
pp. 239779142110166
Author(s):  
Venkatesh Puneeth ◽  
Sarpabhushana Manjunatha ◽  
Bijjanal Jayanna Gireesha ◽  
Rama Subba Reddy Gorla
Keyword(s):  
Magnetic Field ◽  
Brownian Motion ◽  
Convective Flow ◽  
Three Dimensional ◽  
Induced Magnetic Field ◽  
Density Profiles ◽  
Casson Nanofluid ◽  
And Brownian Motion ◽  
Similarity Transformations ◽  
The Mathematical Model

The induced magnetic field for three-dimensional bio-convective flow of Casson nanofluid containing gyrotactic microorganisms along a vertical stretching sheet is investigated. The movement of these microorganisms cause bioconvection and they act as bio-active mixers that help in stabilising the nanoparticles in the suspension. The two forces, Thermophoresis and Brownian motion are incorporated in the Mathematical model along with Stefan blowing. The resulting model is transformed to ordinary differential equations using similarity transformations and are solved using [Formula: see text] method. The Velocity, Induced Magnetic field, Temperature, Concentration of Nanoparticles, and Motile density profiles are interpreted graphically. It is observed that the Casson parameter decreases the flow velocity and enhances the temperature, concentration, and motile density profiles and also it is noticed that the blowing enhances the nanofluid profiles whereas, suction diminishes the nanofluid profiles. On the other hand, it is perceived that the rate of heat conduction is enhanced with Thermophoresis and Brownian motion.

scholarly journals Three dimensional distribution of Brownian motion extrema

Stochastics ◽  
2012 ◽  
Vol 85 (5) ◽  
pp. 807-832 ◽  
Author(s):  
Marcos Escobar ◽  
Sebastian Ferrando ◽  
Xianzhang Wen
Keyword(s):  
Brownian Motion ◽  
Three Dimensional ◽  
Dimensional Distribution

scholarly journals Brownian motion and polarized three-dimensional quantum vacuum

2021 ◽  
Vol 67 (4 Jul-Aug) ◽  
Author(s):  
Davide Fiscaletti
Keyword(s):  
Dark Matter ◽  
Brownian Motion ◽  
Energy Density ◽  
Nonlinear Model ◽  
Vacuum Energy ◽  
Three Dimensional ◽  
Vacuum Energy Density ◽  
Quantum Vacuum ◽  
Virtual Particles ◽  
Fundamental Entity

A nonlinear model of Brownian motion is developed in a three-dimensional quantum vacuum defined by a variable quantum vacuum energy density corresponding to processes of creation/annihilation of virtual particles. In this model, the polarization of the quantum vacuum determined by a perturbative fluctuation of the quantum vacuum energy density associated with a fluctuating viscosity, which mimics the action of dark matter, emerges as the fundamental entity which generates the Brownian motion.

scholarly journals On conditional Ornstein–Uhlenbeck processes

1984 ◽  
Vol 16 (04) ◽  
pp. 920-922
Author(s):  
P. Salminen
Keyword(s):  
Brownian Motion ◽  
Three Dimensional ◽  
Bessel Process ◽  
Uhlenbeck Process ◽  
Brownian Motions ◽  
Ornstein Uhlenbeck Process ◽  
The Law ◽  
Similar Description

It is well known that the law of a Brownian motion started from x > 0 and conditioned never to hit 0 is identical with the law of a three-dimensional Bessel process started from x. Here we show that a similar description is valid for all linear Ornstein–Uhlenbeck Brownian motions. Further, using the same techniques, it is seen that we may construct a non-stationary Ornstein–Uhlenbeck process from a stationary one.

scholarly journals Occupation Times, Drawdowns, and Drawups for One-Dimensional Regular Diffusions

2015 ◽  
Vol 47 (1) ◽  
pp. 210-230 ◽  
Author(s):  
Hongzhong Zhang
Keyword(s):  
Brownian Motion ◽  
Diffusion Process ◽  
Time Horizon ◽  
Three Dimensional ◽  
Bessel Processes ◽  
Occupation Times ◽  
Exponential Time ◽  
One Dimensional ◽  
Brownian Motion With Drift ◽  
Running Maximum

The drawdown process of a one-dimensional regular diffusion process X is given by X reflected at its running maximum. The drawup process is given by X reflected at its running minimum. We calculate the probability that a drawdown precedes a drawup in an exponential time-horizon. We then study the law of the occupation times of the drawdown process and the drawup process. These results are applied to address problems in risk analysis and for option pricing of the drawdown process. Finally, we present examples of Brownian motion with drift and three-dimensional Bessel processes, where we prove an identity in law.

Micromachined Linear Brownian Motor: A Nanosystem Exploting Brownian Motion of Nanobeads for Uni-directional Transport

2008 ◽  
Vol 1096 ◽  
Author(s):  
Ersin Altintas ◽  
Edin Sarajlic ◽  
Karl F. Bohringer ◽  
Hiroyuki Fujita
Keyword(s):  
Brownian Motion ◽  
Three Dimensional ◽  
Thermal Fluctuations ◽  
Random Motion ◽  
Microfluidic Channels ◽  
Switching Sequence ◽  
Brownian Motor ◽  
Speed Performance ◽  
Random Fluctuations ◽  
Directional Transport

AbstractNanosystems operating in liquid media may suffer from random thermal fluctuations. Some natural nanosystems, e.g. biomolecular motors, which survive in an environment where the energy required for bio-processes is comparable to thermal energy, exploit these random fluctuations to generate a controllable unidirectional movement. Inspired by the nature, a transportation system of nanobeads achieved by exploiting Brownian motion were proposed and realized. This decreases energy consumption and saves the energy compared to ordinal pure electric or magnetic drive. In this paper we present a linear Brownian motor with a 3-phase electrostatic rectification aimed for unidirectional transport of nanobeads in microfluidic channels. The transport of the beads is performed in 1 μm deep, 2 μm wide PDMS microchannels, which constrain three-dimensional random motion of nanobeads into 1D fluctuation, so-called tamed Brownian motion. We have experimentally traced the rectified motion of nanobeads and observed the shift in the beam distribution as a function of applied voltage. The detailed computational analysis on the importance of switching sequence on the speed performance of motor is performed and compared with the experimental results showing a good agreement.

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