• Journal of Korean Society of Transportation
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• v.27 no.1
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• pp.169-177
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• 2009

In this paper, the rotated hexagonal lattice model (RHLM) was proposed, which is applied to pedestrian flow, and developed the simulation model for the pedestrian counterflow. RHLM is an upgrade version of the square lattice model(SLM) and hexagonal lattice model(HLM). The simulation was performed at the hexagonal lattice $20{\times}20$ and evaluated by different speed, density and flow conditions. Simulation results are compared with SLM and show that RHLM can replicate the characteristics of pedestrian traffic more effectively and reliably than any other existing models from several perspectives. First, RHLM can explain the shortest-path movement of pedestrians and more realistic avoidance motion. If they cannot move straight direction, they can move shorter distance from previous position to destination. Second, RHLM reflects the characteristics that the pedestrian can move with higher capacity and the speed of pedestrian flow is hard to zero.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.2
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• pp.33-39
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• 2000

Well known is the directed self-avoiding walk model on the square lattice with reflecting and absorbing barriers. We consider two models, namely, a pyramid self-avoiding polygon model and a top and bottom pyramid polygon model, as subcollections of the model. We derive explicit formulas for the number of 2N-step polygons in these models.

• International Journal of Highway Engineering
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• v.12 no.4
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• pp.11-16
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• 2010

Various researches have been performed on the topic of pedestrian traffic flow. At the beginning, the modeling and simulation method for the vehicular traffic flow was simply applied to pedestrian traffic flow. Recently, CA based simulation models are frequently applied to pedestrian flow analysis. Initially, the square Lattice Model is a base model for applying to pedestrians of counterflow and then Hexagonal Lattice Model improves its network as a hexagonal cell for more realistic movement of the avoidance of pedestrian conflicts. However these lattice models express only one directional movement because they express only one directional movement. In this paper, MLPM (the Multi-Layer Pedestrian Model) is suggested to give various origins and destinations for more realistic pedestrian motion in some place.

• Journal of Power System Engineering
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• v.18 no.6
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• pp.207-214
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• 2014

Mass and flow resistance in a square ribbed microchannel have been studied numerically using the Lattice Boltzmann Method. It has been build up on two dimensional nine velocity vectors model with single relaxation time method called the Lattice Bhatnagor-Gross-Krook model. To analyze the roughness effect on the flow resistance namely the friction factor and mass flow has been discussed at the slip flow regime, $0.01{\leq}Kn{\leq}0.10$, where Kn is the Knudsen number. The wall roughness is considered by square microelements with a relative roughness height up to maximum 10% of channel height. The velocity profiles in terms of streamlines near the riblets are demonstrated to be responsible for the roughness effect. It is found that the roughness effect leads to increase the flow resistance with roughness height but it is decreased significantly with increasing the space between two roughness elements as well as the Knudsen number. In addition, the mass flow decreased linearly with increasing both roughness height and gap but significantly changed at the slip flow regime.

• Journal of the Korean Society of Safety
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• v.7 no.2
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• pp.71-79
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• 1992

This paper presents a least-square algorithms of lattice structures and their use for adaptive prediction of time series generated from the dynamic system. As the view point of adaptive prediction, a new method of Identification of dynamic characteristics by means of estimating the parameters of linear auto regressive model is proposed. The fast convergence of adaptive lattice algorithms is seen to be due to the orthogonalization and decoupling properties of the lattice. The superiority of the least-square lattice is verified by computer simulation, then predictor coefficients are computed from the linear sequential time data. For the application to the dynamic characteristic analysis of unknown system, the transfer function of ideal system represented in frquency domain and the estimated one obtained by predicted coefficients are compared. Using the proposed method, the damping ratio and the natural frequency of a dynamic structure subjected to random excitations can be estimated. It is expected that this method will be widely applicable to other technical dynamic problem in which estimation of damping ratio and fundamental vibration modes are required.

• Journal of Advanced Marine Engineering and Technology
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• v.30 no.5
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• pp.580-588
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• 2006

Two-dimensional turbulent flows past a square cylinder and cavity noise are simulated by the finite difference lattice Boltzmann method with subgrid turbulence model. The method, based on the standard Smagorinsky subgrid model and a single-time relaxation lattice Boltzmann method, incorporates the advantages of FDLBM for handling arbitrary boundaries. The results are compared with those by the experiments carried out by Noda & Nakayama and Lyn et al. Numerical results agree with the experimental ones. Besides, 2D computation of the cavity noise generated by flow over a cavity at a Mach number of 0.1 and a Reynolds number based on cavity depth of 5000 is calculated. The computation result is well presented a understanding of the physical phenomenon of tonal noise occurred primarily by well-jet shear layer and vortex shedding and an aeroacoustic feedback loop.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.30 no.5 s.248
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• pp.438-445
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• 2006

We performed the simulation of the unsteady three dimensional flow over a square cylinder in a wind tunnel in moderate Reynolds number range, $100{\sim}2500$ by using LBM. SGS model was applied for the turbulent flow. Frist of all we compared LBM(Lattice Boltzmann Method) solution of Poiseuille flow applied Farout and bounce back boundary conditions with the analytical and FOAM solutions to verify the applicability of the boundary conditions. For LBM simulation the calculation domain was formed by structured grids and prescribed uniform velocity and density inlet and Farout boundary conditions were imposed on the in-out boundaries. Bounceback and wind tunnel boundary conditions were applied to the cylinder walls and the boundaries of calculation domain respectively. The maximum Strouhal number of the vortex shedding is 0.2025 at Re = 750. and the number maintains the constant value of 0.18 when Re>1000. We also predicted that the critical reynolds number of the turbulent flow is in the range of $250{\sim}500$.

• Proceedings of the Korean Nuclear Society Conference
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• 1996.05b
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• pp.379-384
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• 1996

Thermal-hydraulic performance has been analyzed for an advanced reactor core loaded with hexagonal fuel assemblies. Currently available CHF prediction models and data base for triangular lattice bundles have been thoroughly reviewed, and as a result the KfK-3 CHF correlation with limit CHFR of 1.235 has been determined to be most appropriate. The pressure drop model in COBRA-IV-I code has been modified for the analysis of triangular lattice rod bundles. In view of maximizing the thermal margin, the geometry of a hexagonal fuel assembly, such as rod diameter and rod pitch, has been optimized with a fixed fuel assembly cross sectional area The optimum value of the moderator-to-fuel volume ratio is estimated to lie between 0.65 to 1 with 9.5 mm rod diameter. The thermal margin of these hexagonal fuel assemblies in the AP600 core has been evaluated and compared with that of square lattice fuel assemblies such as VANTAGE-5H and KOFA. The analysis result shows that the performances of hexagonal fuel assemblies are more favorable than the square fuel assemblies in the aspect of steady-state overpower margin.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.31 no.7 s.262
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• pp.620-627
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• 2007

In this paper, we adapt a modified internal energy non-equilibrium first-order extrapolation thermal boundary condition to the thermal lattice Boltzmann model (TLBM). This model is the double populations approach to simulate hydrodynamic and thermal fields. The bounce-back boundary condition which is a traditional boundary condition of lattice Boltzmann method has only a first order in numerical accuracy at the boundary and numerical instability. A non-equilibrium first-order extrapolation boundary condition has been verified to be of better numerical stability than the bounce-back boundary condition and this boundary condition is proved to be of second-order accuracy for the flat boundaries. The two-dimensional natural convection flow in a square cavity with Pr=0.71 and various Rayleigh numbers are simulated. The results are found to be in good agreement with those of previous studies.

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1121-1148
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• 2017

Go is an ancient game of great complexity and has a huge following in East Asia. It is also very rich mathematically, and can be played on any graph, although it is usually played on a square lattice. As with any game, one of the most fundamental problems is to determine the number of legal positions, or the probability that a random position is legal. A random Go position is generated using a model previously studied by the author, with each vertex being independently Black, White or Uncoloured with probabilities q, q, 1 - 2q respectively. In this paper we consider the probability of legality for two scenarios. Firstly, for an $N{\times}N$ square lattice graph, we show that, with $q=cN^{-{\alpha}}$ and c and ${\alpha}$ constant, as $N{\rightarrow}{\infty}$ the limiting probability of legality is 0, exp($-2c^5$), and 1 according as ${\alpha}$ < 2/5, ${\alpha}=2/5$ and ${\alpha}$ > 2/5 respectively. On the way, we investigate the behaviour of the number of captured chains (or chromons). Secondly, for a random graph on n vertices with edge probability p generated according to the classical $Gilbert-Erd{\ddot{o}}s-R{\acute{e}}nyi$ model ${\mathcal{G}}$(n; p), we classify the main situations according to their asymptotic almost sure legality or illegality. Our results draw on a variety of probabilistic and enumerative methods including linearity of expectation, second moment method, factorial moments, polyomino enumeration, giant components in random graphs, and typicality of random structures. We conclude with suggestions for further work.