• Journal of Korean Society for Atmospheric Environment
• /
• v.21 no.2
• /
• pp.145-153
• /
• 2005

An electret fiber with a dipole charge distribution was used to capture charged ultrafine particles in this study. Brownian diffusion and Coulombic force are the dominant collection mechanisms in the electret filtration of charged ultrafine particles. The interaction between Brownian diffusion and Coulombic force for the deposition of ultrafine particles onto a dipolarly charged fiber is studied by solving the convective diffusion equation including Coulombic force as an external force, and the numerical results are compared with the experimental data. As a result, it is shown that there is a negative interaction between Brownian diffusion and Coulombic force, i.e., Coulombic capture efficiency is reduced with decreasing Pe. These results suggest that Brownian diffusion and Coulombic capture efficiency, $\eta$$_{CD}$ is not a simple sum of Brownian diffusion efficiency, $\eta$$_{D}$ and Coulombic capture efficiency, $\eta$$_{C}$.

• 한국가시화정보학회:학술대회논문집
• /
• 2004.12a
• /
• pp.91-110
• /
• 2004

A comprehensive three-dimensional nano-particle tracking technique in micro- and nano-scale spatial resolution using the Total Internal Reflection Fluorescence Microscope (TIRFM) is discussed. Evanescent waves from the total internal reflection of a 488nm argon-ion laser are used to measure the hindered Brownian diffusion within few hundred nanometers of a glass-water interface. 200-nm fluorescence-coated polystyrene spheres are used as tracers to achieve three-dimensional tracking within the near-wall penetration depth. A novel ratiometric imaging technique coupled with a neural network model is used to tag and track the tracer particles. This technique allows for the determination of the relative depth wise locations of the particles. This analysis, to our knowledge is the first such three-dimensional ratiometric nano-particle tracking velocimetry technique to be applied for measuring Brownian diffusion close to the wall.

• Bulletin of the Korean Mathematical Society
• /
• v.57 no.3
• /
• pp.547-568
• /
• 2020

In this paper, we introduce the linear self-attracting diffusion driven by a weighted fractional Brownian motion with weighting exponent a > -1 and Hurst index |b| < a + 1, 0 < b < 1, which is analogous to the linear fractional self-attracting diffusion. For the 1-dimensional process we study its convergence and the corresponding weighted local time. As a related problem, we also obtain the renormalized intersection local time exists in L² if max{a₁ + b₁, a₂ + b₂} < 0.

• Journal of the Korean Mathematical Society
• /
• v.45 no.3
• /
• pp.683-693
• /
• 2008

In this paper, we study the asymptotic behavior of the residual empirical process from diffusion processes. For this task, adopting the discrete sampling scheme as in Florens-Zmirou [9], we calculate the residuals and construct the residual empirical process. It is shown that the residual empirical process converges weakly to a Brownian bridge.

• Journal of the Korean Mathematical Society
• /
• v.47 no.6
• /
• pp.1137-1146
• /
• 2010

In this paper, we study the divergence based goodness of fit test for partially observed sample from diffusion processes. In order to derive the limiting distribution of the test, we study the asymptotic behavior of the residual empirical process based on the observed sample. It is shown that the residual empirical process converges weakly to a Brownian bridge and the associated phi-divergence test has a chi-square limiting null distribution.

• Proceedings of the Korea Air Pollution Research Association Conference
• /
• 2003.05b
• /
• pp.355-356
• /
• 2003

Coagulation is a process whereby particles collide with one another due to their relative motion, and adhere to form large particles. Coagulation caused by the random Brownian motion of particles is called Brownian coagulation. Many properties, such as light scattering, electrostatic charges, toxicity, as well as physical processes, including diffusion, condensation and thermophoresis depend strongly on their size distribution. Therefore, Brownian coagulation is substantially important in atmospheric science, combustion technology, inhalation toxicology and nuclear safety analysis. (omitted)

• Journal of the Korean Data and Information Science Society
• /
• v.7 no.1
• /
• pp.69-78
• /
• 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 Mechanical Science and Technology
• /
• v.17 no.4
• /
• pp.545-561
• /
• 2003

We use the first-passage-time formulation by Torquato, Kim and Cule ［J. Appl. Phys., Vol. 85, pp. 1560∼1571 (1999) ］, which makes use of the first-passage region in association with the diffusion tracer's Brownian movement, and develop a new efficient Brownian motion simulation method to compute the effective conductivity of digitized composite media. By using the new method, one can remarkably enhance the speed of the Brownian walkers sampling the medium and thus reduce the computation time. In the new method, we specifically choose the first-passage regions such that they coincide with two, four, or eight digitizing units according to the dimensionality of the composite medium and the local configurations around the Brownian walkers. We first obtain explicit solutions for the relevant first-passage-time equations in two-and three-dimensions. We then apply the new method to solve the illustrative benchmark problem of estimating the effective conductivities of the checkerboard-shaped composite media. for both periodic and random configurations. Simulation results show that the new method can reduce the computation time about by an order of magnitude.

• Communications of the Korean Mathematical Society
• /
• v.11 no.2
• /
• pp.471-480
• /
• 1996

Consider a strong Markov process $X^0$ that has continuous sample paths in the closed cone $\bar{G}$ in $R^d(d \geq 3)$ such that the process behaves like a ordinary Brownian motion in the interior of the cone, reflects instantaneously from the boundary of the cone and is absorbed at the vertex of the cone. It is shown that $X^0(t)$ has a representation $R(t) \ominus (t)$ where $R(t) \in [0, \infty)$ and $\ominus(t) \in S^{d-1}$, the surface of the unit ball.

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