• Journal of Mechanical Science and Technology
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• v.17 no.4
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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.

• Communications for Statistical Applications and Methods
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• v.28 no.3
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• pp.251-265
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• 2021

This paper discusses the pricing of autocallable structured product with knock-in (KI) feature using the exit probability with the Brownian Bridge technique. The explicit pricing formula of autocallable ELS derived in the existing paper handles the part including the minimum of the Brownian motion using the inclusion-exclusion principle. This has the disadvantage that the pricing formula is complicate because of the probability with minimum value and the computational volume increases dramatically as the number of autocall chances increases. To solve this problem, we applied an efficient and robust simulation method called the Brownian Bridge technique, which provides the probability of touching the predetermined barrier when the initial and terminal values of the process following the Brownian motion in a certain interval are specified. We rewrite the existing pricing formula and provide a brief theoretical background and computational algorithm for the technique. We also provide several numerical examples computed in three different ways: explicit pricing formula, the Crude Monte Carlo simulation method and the Brownian Bridge technique.

• Proceedings of the KSME Conference
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• 2008.11a
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• pp.1922-1927
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• 2008

In the present study, deposition of discrete and small particles, which diameter is less than $1{\mu}m$, on a filter element was simulated by stochastic method. Trajectory of each particle was numerically solved by Langevin equation and Brownian random motion was treated by Brownian dynamics. Lattice Boltzmann method (LBM) was used to solve flow field around the filter collector and deposit layer. Interaction between flow field and deposit layer was obtained from a converged solution from an inner-loop calculation. Simulation method is properly validated and collection efficiency due to different filtration parameters are examined and discussed. Morphology of deposit layer and its evolution was visualized in terms of the particle size. The particle loaded effect on collection efficiency was also discussed.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.2
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• pp.189-198
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• 2004

We consider the problem of whether the three-dimensional checkerboard has the connectivity. For this purpose, we first consider the problem of determining the effective conductivity of a checkerboard-shaped composite material by the Brownian motion simulation method. Specifically, we use the efficient first-passage-time technique. Simulation results show that the effective conductivity of the three-dimensional checkerboard increases faster than the two-dimensional counterpart as the contrast between the phase conductivities increases. This implies that the three-dimensional checkerboard's connectivity is stronger than the two-dimensional checkerboard's and thus each phase material of the three-dimensional checkerboard is more likely to be connected than not to be connected.

• Journal of the Korean Chemical Society
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• v.51 no.3
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• pp.227-231
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• 2007

We improve Wilehemski-Fixmann theory for intrachain reaction dynamics of a polymer chain by taking into account excluded volume effects between reactive groups in the polymerchain. An approximate analytic expression for the intra-chain reaction dynamics is obtained for Gaussian chain model and compared to Brownian dynamics simulation results. The results of the present theory are in a better agreement to Brownian dynamics simulation results than those calculated by previously reported theories.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.20 no.4
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• pp.277-293
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• 2016

We develop an efficient numerical method for pricing the Derivative Linked Securities (DLS). The payoff structure of the hybrid DLS consists with a standard 2-Star step-down type ELS and the range accrual product which depends on the number of days in the coupon period that the index stay within the pre-determined range. We assume that the 2-dimensional Geometric Brownian Motion (GBM) as the model of two equities and a no-arbitrage interest model (One-factor Hull and White interest rate model) as a model for the interest rate. In this study, we employ the Monte Carlo simulation method with the Compute Unified Device Architecture (CUDA) parallel computing as the General Purpose computing on Graphic Processing Unit (GPGPU) technology for fast and efficient numerical valuation of DLS. Comparing the Monte Carlo method with single CPU computation or MPI implementation, the result of Monte Carlo simulation with CUDA parallel computing produces higher performance.

• Proceedings of the KSME Conference
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• 2001.06d
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• pp.605-611
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• 2001

A numerical technique for simulating the aggregation of charged particles was presented with a Brownian dynamic simulation in the free molecular regime. The Langevin equation was used for tracking each particle making up an aggregate. A periodic boundary condition was used for calculation of the aggregation process in each cell with 500 primary particles of 16 nm in diameter. We considered the thermal force and the electrostatic force for the calculation of the particle motion. The morphological shape of aggregates was described in terms of the fractal dimension. The fractal dimension for the uncharged aggregate was $D_{f}=1.761$. The fractal dimension changed slightly for the various amounts of bipolar charge. However, in case of unipolar charge, the fractal dimension decreased from 1.641 to 1.537 with the increase of the average number of charges on the particles from 0.2 to 0.3 in initial states.

• Bulletin of the Korean Chemical Society
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• v.21 no.9
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• pp.875-881
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• 2000

We study the rheological properties of concentrated polymer solution and the melt under simple shear and elon-gational flow using Brownian dynamicssimulation. In order to describe the anisotropic molecular motion, we modifiedthe Giesekus' mobility tensor by incorporating the finitely extensible non-linear elastic (FENE) spring force into dumbbell model. To elucidate the nature of this model, our simulation results are compared with the data of FENE-P ("P"standsfor the Perterin) dumbbell model and experiments. While in steady state both original FENE and FENE-P models exhibit a similar viscosity response,the growthof viscosity becomes dissimilar as the anisotropy decreases and the flowrate increases. The steady state viscosity obtained from the simulation well describes the experiments including the shear-thinning behavior in shear flow and viscosity-thinning behavior in elongational flow. But the growth of viscosity oforiginal FENE dumbbell model cannot describe the experimental results in both flow fields.

• Communications for Statistical Applications and Methods
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• v.14 no.2
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• pp.413-429
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• 2007

Equity-linked securities (ELS) provide their customers with the return linked to the underlying equity (or equities). Equity-linked products in Korea have recently gained popularity due to relatively low interest rates. This paper discusses an equity-linked security whose principal is not guaranteed. The payoff of the ELS depends on the returns of two underlying assets. This paper presents numerical prices of the proposed product by using Monte-Carlo simulation method. It assumes that the log-returns of two stocks follow either Brownian motion or variance gamma process. Finally, the comparison of the two approaches is discussed.

• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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• pp.21-22
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• 2003

We perform two kinds of computer simulations on polydisperse hard-sphere systems; a molecular-dynamics simulation on atomic systems and a Brownian-dynamics simulation on colloidal suspensions. Analyses of the mean square displacement, the radial distribution function, and the pressure suggest that there exist three phase regions, a liquid phase region, a metastable phase region, and a crystal phase region, where the freezing and melting points are shifted to the values higher than in monodisperse case. It is also shown that the long-time behavior of colloidal suspensions is exactly the same as that of atomic systems.