• Journal of the Korean Mathematical Society
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• v.61 no.2
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• pp.377-393
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• 2024

In this paper, we study the positive solutions to a discrete harmonic function for a random walk satisfying finite range and ellipticity conditions, killed at the boundary of an unbounded cylinder in ℤ^d. We first prove the existence and uniqueness of positive solutions, and then establish that all the positive solutions are generated by two special solutions, which are exponential growth at one end and exponential decay at the other. Our method is based on maximum principle and a Harnack type inequality.

• Journal of Korean Society of Forest Science
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• v.100 no.4
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• pp.664-671
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• 2011

Random Walk Model can predict the sediment areas of debris flow but it must be extracted three parameters fitted topographical environment. This study developed the method to extract the optimal values of three parameters - Once flowing volume, Stopping slope and Gravity weight - for Random Walk Model. And the extracted parameters were validated by aerial photographs of the debris flowed area. To extract the optimal parameters was randomly performed, limiting the range values of three parameters and developing an accuracy decision method that is called the rate of concordance. The set of the optimal parameters was decided on highest the rate of concordance and a consistency. As a result, the optimal parameters in Bonghwa county were showed that the once flowing volume is $1.0m^3$, the stopping slope is $4.2^{\circ}$ and the gravity weight is 2 when the rate of concordance is -0.2. The validating result of the optimal parameters showed closely that the rate of concordance is average -0.2.

• 한국가시화정보학회:학술대회논문집
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• 2002.11a
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• pp.59-62
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• 2002

A study of three-dimensional unsteady incompressible flow past elliptic disk with aspect ratio 3 is presented. Numerical visualization using the vortex filament method was performed at Reynolds number of 20,000 on the basis of the minor diameter, the random walk method was used to calculate viscous diffusion effect. We suggest 3 stages about the wake development according to its structures, stability and motions and described the characteristics of each stages. The structure of the elliptic wake is more complicate and unstable than the wake behind a circular disk.

• Journal of the Korean Society of Combustion
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• v.8 no.3
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• pp.15-23
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• 2003

Partial quenching structure of turbulent diffusion flames in a turbulent mixing layer is investigated by the method of flame hole dynamics in order to develop a prediction model for turbulent flame lift off. The essence of flame hole dynamics is derivation of the random walk mapping, from the flame-edge theory, which governs expansion or contraction of flame holes initially created by local quenching events. The numerical simulation for flame hole dynamics is carried out in two stages. First, a direct numerical simulation is performed for constant-density fuel-air channel mixing layer to obtain the turbulent flow and mixing fields, from which a time series of two dimensional scalar dissipation rate array is extracted at a fixed virtual flame surface horizontally extending from the end of split plate to the downstream. Then, the Lagrangian simulation of the flame hole random walk mapping projected to the scalar dissipation rate array yields temporally evolving turbulent extinction process and its statistics on partial quenching characteristics. The statistical results exhibit that the chance of partial quenching is strongly influenced by the crossover scalar dissipation rate while almost unaffected by the iteration number of the mapping that can be regarded as a flame-edge speed.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.17 no.6
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• pp.65-76
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• 2007

The P2P file sharing system sends the results to users by searching the files in the shared folders. In the process of it, the problem is that the transferred information includes the pathname and file information and it can be revealed who searches which files. In related to this problem, anonymous file sharing P2P protocol has been an active research area where a number of works have been produced. However, the previous studies still have a few of weakness. Therefore, We propose two anonymous P2P file sharing protocols based on the decentralized and unstructured Random Walk. The first scheme uses the dynamic onion routing where the requester can receive the wanted file without knowing other peers' IDs. The second scheme uses the IP multicast method which lowers the computational overhead. Both of them are more suited for the dynamic P2P system.

• 한국전산유체공학회:학술대회논문집
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• 1995.10a
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• pp.246-252
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• 1995

The transient incompressible flow behind the bluffbody is numerically simulated using the random vortex method(RVM). Based on the vorticity formulation of the unsteady Navier-Stokes equations, the Lagrangian approach with the random walk technique is employed to account for the transport processes of the vortex elements. The random walk procedure for the diffusion process has been validated against the exact solutions. The present simulation focuses on the transition flow regime where the recirculation zone behind the bluffbody becomes highly unsteady and large-scale vortex eddies are shed from the bluffbody wake. The unsteady flow structures and the mixing characteristics behind the bluffbody are discussed in details.

• Journal of the Korean GEO-environmental Society
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• v.4 no.3
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• pp.79-88
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• 2003

This paper presents a numerical study of the spatial behavior of a linear absorbing solute in a heterogeneous porous medium. The spatially correlated log-normal hydraulic conductivity field is generated in a given two-dimensional domain by using the geostatistical method (Turning Bands algorithm). The velocity vector field is calculated by applying the two-dimensional saturated groundwater flow equation to the Galerkin finite element method. The simulation of solute transport is carried out by using the random walk particle tracking model with CD(constant displacement) scheme in which the time interval is automatically adjusted. In this study, the spatial behavior of a solute is analyzed by the longitudinal center-of-mass displacement, longitudinal spatial spread moment and longitudinal plume skewness.

• 한국연소학회:학술대회논문집
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• 2004.06a
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• pp.102-111
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• 2004

Partial quenching structure of turbulent diffusion flames in a turbulent mixing layer is investigated by the method of flame hole dynamics to develope a prediction model for the turbulent lift off. The present study is specifically aimed to remedy the problem of the stiff transition of the conditioned partial burning probability across the crossover condition by adopting level-set method which describes propagating or retreating flame front with specified propagation speed. In light of the level-set simulations with two model problems for the propagation speed, the stabilizing conditions for a turbulent lifted flame are suggested. The flame hole dynamics combined with level-set method yields a temporally evolving turbulent extinction process and its partial quenching characteristics is compared with the results of the previous model employing the flame-hole random walk mapping. The probability to encounter reacting' state, conditioned with scalar dissipation rate, demonstrated that the conditional probability has a rather gradual transition across the crossover scalar dissipation rate in contrast to the stiff transition of resulted from the flame-hole random walk mapping and could be attributed to the finite response of the flame edge propagation.

• The Korean Journal of Applied Statistics
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• v.24 no.1
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• pp.35-43
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• 2011

In this paper, we introduce a unit root test via discrete cosine transform in the AR(1) process. We first investigate the statistical properties of DCT coefficients under the stationary AR(1) process and the random walk process in order to verify the validity of the proposed method. A bootstrapping approach is proposed to induce the distribution of the test statistic under the unit root. We performed simulation studies for comparing the powers of the Dickey-Fuller test and the proposed test.

• Proceedings of the Korea Society of Information Technology Applications Conference
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• 2007.05a
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• pp.47-54
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• 2007

In this study, we consider the movement-based registration (MBR), location-based registration (LBR) and distance-based registration (DBR) schemes. Analytical models based on a 2-dimensional random walk in a hexagonal cell configuration are considered to analyze and compare the performances of these three schemes. We focus on the derivation of the registration costs of LBR and DBR using an analytical method and then show that DBR always outperforms both MBR and LBR. Numerical results are provided to demonstrate the validity of our models under various circumstances.