• Journal of the Korean Data and Information Science Society
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• v.7 no.1
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• pp.69-78
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• 1996

Consider a natural model for stochastic flow systems is Brownian motion, which is Brownian motion on the positive real line with constant drift and constant diffusion coefficient, modified by an impenetrable reflecting barrier at $x_{0}$. In this paper, we investigate the joint distribution functions and study on the distribution of the first-passage time. Also we find out the distribution of ${\mu}-RBMPx_{0}$.

• Journal of the Korean Statistical Society
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• v.34 no.4
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• pp.281-295
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• 2005

We investigate the rate of convergence of the distribution of the maximum likelihood estimator (MLE) of an unknown parameter in the drift coefficient of a stochastic process described by a linear stochastic differential equation driven by a fractional Brownian motion (fBm). As a special case, we obtain the rate of convergence for the case of the fractional Ornstein- Uhlenbeck type process studied recently by Kleptsyna and Le Breton (2002).

• Computers and Concrete
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• v.30 no.2
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• pp.143-150
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• 2022

In this paper, the non-linear mathematical problem is solved via numerical scheme by utilizing shooting method. Brownian diffusion and thermophoresis along mass and heat transfer are accounted for. Non-linear expression is reduced via non-dimensional variables. The simplified ordinary differential equations are tackled by shooting technique. Behavior of distinct influential parameters is investigated graphically and analyzed for temperature and concentration profile. Our finding indicates that temperature profile is enhanced for the thermophoresis, Brownian motion coefficient, Prandtl number, Eckert number and temperature slip parameter. Comparison of numerical technique with the extant literature is made and an acceptable agreement is attained. Graphs are plotted to examine the influence of these parameters.

• Computers and Concrete
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• v.29 no.3
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• pp.201-207
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• 2022

The evaluation of velocity profile for large values of buoyancy parameter and Bioconvected Rayleigh number is examined. The non-linear problem has been tackled numerically by shooting technique. Nanofluid temperature and nanoparticle concentration slightly elevates for increasing values of thermophoresis coefficient. Thickness of thermal boundary layer is significantly increased with thermophoresis coefficient whereas thickness of concentration boundary layer is more slightly enhanced. The response of temperature and nanoparticles concentration is observed due to change in Brownian motion parameter. As Brownian motion parameter increased temperature distribution is slightly enhanced. The reverse behavior is observed in case of nanoparticles concentration. Comparison of numerical technique with the extant literature is made and an acceptable agreement is attained.

• Mass Spectrometry Letters
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• v.6 no.4
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• pp.91-98
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• 2015

The Brownian motion or Wiener process, as the physical model of the stochastic procedure, is observed as an indexed collection random variables. Stochastic procedure are quite influential on the confinement potential fluctuation in the quadrupole ion trap (QIT). Such effect is investigated for a high fractional mass resolution Δm/m spectrometry. A stochastic procedure like the Wiener or Brownian processes are potentially used in quadrupole ion traps (QIT). Issue examined are the stability diagrams for noise coefficient, η=0.07;0.14;0.28 as well as ion trajectories in real time for noise coefficient, η=0.14. The simulated results have been obtained with a high precision for the resolution of trapped ions. Furthermore, in the lower mass range, the impulse voltage including the stochastic potential can be considered quite suitable for the quadrupole ion trap with a higher mass resolution.

• Journal of applied mathematics & informatics
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• v.28 no.5_6
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• pp.1305-1314
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• 2010

In this paper, we deal with a class of one-dimensional reflected backward stochastic differential equations driven by a Brownian motion and the martingales of Teugels associated with an independent L$\acute{e}$vy process having a stochastic Lipschitz coefficient. We derive the existence and uniqueness of solutions for these equations via Snell envelope and the fixed point theorem.

• Advances in nano research
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• v.10 no.4
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• pp.349-357
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• 2021

In present study, the numerical investigations are carried out for effects of suction and blowing on boundary layer slip flow of casson nano fluid along permeable stretching cylinder in an exponential manner. The modeled PDEs are changed into nonlinear ODEs through appropriate nonlinear transformations. Change in physical quantities like friction coefficient, Nusselt and Sherwood numbers with variation of the aforementioned parameters are also examined and their numerical values are listed in the form of tables. Effects of Reynold number, suction parameter, Prandtl number, Lewis number, Brownian motion parameter and thermophoresis parameter are seen graphically with temperature profile.

• Advances in concrete construction
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• v.14 no.2
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• pp.103-113
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• 2022

On the basis of fabrication, the utilization of nano material in numerous industrial and technological system, obtained the utmost significance in current decade. Therefore, the current investigation presents a theoretical disposition regarding the flow of electric conducting Williamson nanoliquid over a stretchable surface in the presence of the motile microorganism. The impact of thermal radiation and magnetic parameter are incorporated in the energy equation. The concentration field is modified by adding the influence of chemical reaction. Moreover, the splendid features of nanofluid are displayed by utilizing the thermophoresis and Brownian motion aspects. Compatible similarity transformation is imposed on the equations governing the problem to derive the dimensionless ordinary differential equations. The Homotopy analysis method has been implemented to find the analytic solution of the obtained differential equations. The implications of specific parameters on profiles of velocity, temperature, concentration and motile microorganism density are investigated graphically. Moreover, coefficient of skin friction, Nusselt number, Sherwood number and density of motile number are clarified in tabular forms. It is revealed that thermal radiation, thermophoresis and Brownian motion parameters are very effective for improvement of heat transfer. The reported investigation can be used in improving the heat transfer appliances and systems of solar energy.

• Membrane Journal
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• v.12 no.4
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• pp.207-215
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• 2002

The hindered diffusion in confined spaces is an important phenomenon to understand in a micro-scale the filtration mechanism determined by the particle motion in membrane pores. Compared to the case of spherical colloids, both the theoretical investigations and the experiments on the hindered diffusion of polyelectrolytes is actually more difficult, due to lots of relevant parameters resulting from the complicated conformational properties of the polyelectrolyte chain. We have successfully performed the Brownian dynamics simulations upon a single polyeiectrolyte confined in a slit-like pore, where a coarse-grained bead-spring model incorporated with Debye-Huckel interaction is properly adopted. For the given sizes of both the polyelectrolyte and the pore width, the hindered diffusion coefficient decreases as the solution ionic concentration decreases. It is evident that a charge effect of the pore wall enhances the hindered diffusion of polyelectrolyte. Simulation results allow us to make sense of the diffusive transport through the micro-pore, which is restricted by the influences of the steric hindrance of polyelectrolytes as well as the electrostatic repulsion between the polyelectrolytes and pore wall.

• Journal of Magnetics
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• v.21 no.3
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• pp.476-489
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• 2016

In the present study, squeezing flow of micropolar nanofluid between parallel infinite disks in the presence of magnetic field perpendicular to plane of the disks is taken into account. The constitutive equations that govern the flow configuration are converted into nonlinear ordinary differential with the help of suitable similarity transforms. HAM package BVPh2.0 has been employed to solve the nonlinear system of ordinary differential equations. Effects of different emerging parameters like micropolar parameter K, squeezed Reynolds number R, Hartmann number M, Brownian motion parameter Nb, thermophoresis parameter Nt, Lewis number Le for dimensionless velocities, temperature distribution and concentration profile are also discussed graphically. In the presence of strong and weak interaction (i.e. n = 0 and n = 0.5), numerical values of skin friction coefficient, wall stress coefficient, local Nusselt number and local Sherwood number are presented in tabulated form. To check the validity and reliability of the developed algorithm BVPh2.0 a numerical investigation is also a part of this study.