• 한국대기환경학회지
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• 제21권2호
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• pp.145-153
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• 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
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• 한국가시화정보학회 2004년도 Proceedings of 2004 Korea-Japan Joint Seminar on Particle Image Velocimetry
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• pp.91-110
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• 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.

• 대한수학회보
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• 제57권3호
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• pp.547-568
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• 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.

• 대한수학회지
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• 제45권3호
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• pp.683-693
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• 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.

• 대한수학회지
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• 제47권6호
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• pp.1137-1146
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• 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.

• 한국대기환경학회:학술대회논문집
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• 한국대기환경학회 2003년도 춘계학술대회 논문집
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• pp.355-356
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• 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
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• 제7권1호
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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 Mechanical Science and Technology
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• 제17권4호
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• pp.545-561
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• 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.

• 대한수학회논문집
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• 제11권2호
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• pp.471-480
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• 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.

• 멤브레인
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• 제12권4호
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• pp.207-215
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• 2002

한정된 미세공간에서의 제한확산(hindered diffusion)은 멤브레인 기공(pore)에서 입자들의 운동에 의해 결정되는 여과 메카니즘을 매우 미세한 수준에서 이해하는데 중요한 현상이다. 구형(spherical) 콜로이드 입자에 비해 보다 복잡한 형태(conformation)인 고분자사슬 구조를 갖는 다가전해질(polyelectrolyte)의 제한확산 거동에는 다양한 인자들이 관련되어 있기 때문에, 이론 접근은 물론 실험적 접근도 한층 어려운 것이 사실이다. 본 연구에서는, 슬릿형 미세기공에 한정되어 있는 단일한 다가전해질(single polyelectrolyte)에 coarse-grained bead spring model과 먼거리(long-range) 정전상호작용(electrostatic interaction)인 Debye-Huckel potential을 적용하여 분자시뮬레이션 기법인 브라운 동력학 모사를 수행하였다. 기공과 다가전해질 사슬(Polyelectrolyte chain)의 주어진 크기에서, 용액의 전해질 이온농도가 감소함에 따른 사슬의 신장(extension)효과는 제한확산계수를 감소시켰고, 기공 벽면의 하전성은 제한확산계수를 더욱 감소시켰다. 이는, 다가전해질 사슬(polyelectrolyte chain)의 입체적 장애(steric hindrance)와 함께 정전반발력이 미세기공에서의 확산이동을 억제함을 의미한다.