• 대한수학회지
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• 제36권1호
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• pp.139-157
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• 1999

Consider a supercritical Bellman-Harris process evolving from one particle. We superimpose on this process the additional structure of movement. A particle whose parent was at x at its time of birth moves until it dies according to a given Markov process X starting at x. The motions of different particles are assumed independent. In this paper we show that when the movement process X is standard Brownian the proportion of particles with position $\leq${{{{ SQRT { t} }}}} b and age$\leq$a tends with probability 1 to A(a)$\Phi$(b) where A(.) and $\Phi$(.) are the stable age distribution and standard normal distribution, respectively. We also extend this result to the case when the movement process is a Levy process.

• 응용통계연구
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• 제19권3호
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• pp.579-585
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• 2006

본 연구에서는 보험 상품의 잉여금 변화가 브라운 운동을 따르는 파산 모형에 대하여 연구하였다. 만약 잉여금이 재투자를 위한 목표 잉여금을 닿으면 보험회사는 다른 금융 상품에 재투자하는 것으로 가정하였다. 잉여금 과정에 마팅게일 방법을 적용하여 잉여금이 V > 0 또는 0에 도달할 때까지의 시간 T를 초기 잉여금 x(0 < x < V)의 함수로 표시하였으며, 미분방정식을 이용하여 기간 동안의 총 잉여금과 평균 잉여금을 계산하였다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제26권2호
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• pp.108-120
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• 2022

We considered qualitative behaviour of the generalization of Einstein's model of Brownian motion when the key parameter of the time interval of free jump degenerates. Fluids will be characterised by number of particles per unit volume (density of fluid) at point of observation. Degeneration of the phenomenon manifests in two scenarios: a) flow of the fluid, which is highly dispersing like a non-dense gas and b) flow of fluid far away from the source of flow, when the velocity of the flow is incomparably smaller than the gradient of the density. First, we will show that both types of flows can be modeled using the Einstein paradigm. We will investigate the question: What features will particle flow exhibit if the time interval of the free jump is inverse proportional to the density and its gradient ? We will show that in this scenario, the flow exhibits localization property, namely: if at some moment of time t₀ in the region, the gradient of the density or density itself is equal to zero, then for some T during time interval [t₀, t₀ + T] there is no flow in the region. This directly links to Barenblatt's finite speed of propagation property for the degenerate equation. The method of the proof is very different from Barenblatt's method and based on the application of Ladyzhenskaya - De Giorgi iterative scheme and Vespri - Tedeev technique. From PDE point of view it assumed that solution exists in appropriate Sobolev type of space.

• 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.

• 상하수도학회지
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• 제9권3호
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• pp.65-77
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• 1995

The kinetics of flocculation of heterodisperse suspension like those in water treatment plants and natural water system are usually described by the Smoluchowski equation, which incorporates collision frequency functions for particle collisions by Brownian motion, fluid shear, and differential sedimentation. These collisionfrequeney functions have been based on a rectilinear view of collisions, i.e., one that ignores short-range forces and changes in fluid motion as particles approach one another. In this research, a curvilinear approach, i.e., one that accounts for hydrodynamic forces and particle interaction in the collision of two different size particles is developed. Collision efficiency factors of each mechanism can be calculated by trajectory analysis (fluid shear and differential sedimentation) or the solution of diffusion equation (Brownian motion). The results are presented as a set of corrections to the rectilinear collision frequency functions for each mechanism.

• 한국데이터정보과학회:학술대회논문집
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• 한국데이터정보과학회 2005년도 추계학술대회
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• pp.207-207
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• 2005

• Communications for Statistical Applications and Methods
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• 제9권3호
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• pp.649-663
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• 2002

We consider an unlimited fluid queueing model which has Fractional Brownian motion(FBM) as an input and a single server of constant service rate. By using the result of Duffield and O'Connell(6), we investigate the asymptotic tail-distribution of the stationary work-load. When there are multiple homogeneous FBM inputs, the workload distribution is similar to that of the queue with one FBM input; whereas for the heterogeneous sources the asymptotic work-load distributions is dominated by the source with the largest Hurst parameter.

• 대한수학회지
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• 제38권2호
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• pp.275-281
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• 2001

The trajectory of a classical dynamics is determined by the least action principle. As soon as we come to quantum dynamics, we have to consider all possible trajectories which are proposed to be a sum of the classical trajectory and Brownian fluctuation. Thus, the action involves the square of the derivative B(t) (white noise) of a Brownian motion B(t). The square is a typical example of a generalized white noise functional. The Feynman propagator should therefore be an average of a certain generalized white noise functional. This idea can be applied to a large class of dynamics with various kinds of Lagrangians.

• 대한화학회지
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• 제51권3호
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• pp.227-231
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• 2007

윌렘스키-픽스만(Wilehemski-Fixmann)의 사슬고분자 내 화학반응동력학 이론을 반응 그룹들 간의 배제효과를 고려하여 개선하였다. 가우스 체인 양극단 반응 모델의 반응 동력학에 대한 해석적인 표현을 얻어 이를 브라운 동력학 모의 실험결과와 비교하였다. 비교결과 본 이론의 예측이 기존 이론들의 예측 보다 모의실험 결과와 더 잘 일치하였다.

• Journal of Korean Society for Atmospheric Environment
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• 제15권E호
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• pp.65-71
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• 1999

The log-normal size distribution theories developed recently for aerosol coagulation are reviewed. The analytical solutiosn to Brownian coagulation developed recently for various particle size regimes are reviewed. In order to describe the evolution of the size distribution of a coagulating aerosol over the entire size range, the analytical solutions developed individually for the free-molecule regime, the transition regime, the nearcontinuum regime, and the continuum regime have been combined. The work described here represents the first analytical solution to the aerosol coagulation problem covering the entire particle size range.