• Nuclear Engineering and Technology
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• v.24 no.3
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• pp.319-328
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• 1992

The Galerkin formulation of the finite element method is applied to the integral law of the first-order form of the one-group neutron transport equation in one-dimensional spherical geometry. Piecewise linear or quadratic Lagrange polynomials are utilized in the integral law for the angular flux to establish a set of linear algebraic equations. Numerical analyses are performed for the scalar flux distribution in a heterogeneous sphere as well as for the criticality problem in a uniform sphere. For the criticality problems in the uniform sphere, the results of the finite element method, with the use of continuous finite elements in space and angle, are compared with the exact solutions. In the heterogeneous problem, the scalar flux distribution obtained by using discontinuous angular and spatical finite elements is in good agreement with that from the ANISN code calculation.

• Journal of Korean Port Research
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• v.14 no.4
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• pp.451-461
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• 2000

The design and maintenance of navigation channel and water facilities of an harbor which is located at the mouth of river or at the estuary area are difficult due to the complexity of estuarial water and sediment circulation. Effects of deepening navigable waterways, of changing coastline configurations, or of discharging dredged material to the open sea are necessary to be investigated and predicted in terms of water quality and possible physical changes to the coastal environment. A borad analysis of the transport mechanism in the estuary area was made in terms of sediment property, falling velocity, concentration and flow characteristics. In order to simulate the transport processes, a two-dimensional finite element model is developed, which includes erosion, transport and deposition mechanism of suspended sediments. Galerkin’s weighted residual method is used to solve the transient convection-diffusion equation. The fluid domain is subdivided into a series of triangular elements in which a quadratic approximation is made for suspended sediment concentration. Model could deal with a continuous aggregation by stipulating the settling velocity of the flocs in each element. The model provides suspended sediment concentration, bed shear stress, erosion versus deposition rate and bed profile at the given time step.

• The Journal of Korea Robotics Society
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• v.17 no.3
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• pp.308-313
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• 2022

This paper proposes a velocity control method for a permanent magnet synchronous motor (PMSM) based on the Koopman operator that does not require model parameter information except for pole-pair of the motor and external load. First, the Koopman operator is derived using observable functions and observation data. Then, the desired q-axis current corresponding to the desired velocity is generated using the relationship between the continuous-time Koopman operator and the dynamics of PMSM. Also, the dynamic equation of PMSM is expressed as a linear form in observable space using the discrete-time Koopman operator. Finally, it is applied to the linear quadratic regulator (LQR) to derive the final form of control input. To verify the proposed method, the conventional cascade PI controller and the LQR controller configured with the existing technique are compared with the proposed method in the viewpoint of q-axis current generation and velocity tracking performance in an environment with noise and external load.

• Korean Journal of Radiology
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• v.22 no.7
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• pp.1194-1202
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• 2021

Objective: To investigate the age-dependent changes in regional cerebral blood flow (CBF) in healthy adults by fitting mathematical models to imaging data. Materials and Methods: In this prospective study, 90 healthy adults underwent pseudo-continuous arterial spin labeling imaging of the brain. Regional CBF values were extracted from the arterial spin labeling images of each subject. Multivariable regression with the Akaike information criterion, link test, and F test (Ramsey's regression equation specification error test) was performed for 7 models in every brain region to determine the best mathematical model for fitting the relationship between CBF and age. Results: Of all 87 brain regions, 68 brain regions were best fitted by cubic models, 9 brain regions were best fitted by quadratic models, and 10 brain regions were best fitted by linear models. In most brain regions (global gray matter and the other 65 brain regions), CBF decreased nonlinearly with aging, and the rate of CBF reduction decreased with aging, gradually approaching 0 after approximately 60. CBF in some regions of the frontal, parietal, and occipital lobes increased nonlinearly with aging before age 30, approximately, and decreased nonlinearly with aging for the rest of life. Conclusion: In adults, the age-related perfusion patterns in most brain regions were best fitted by the cubic models, and age-dependent CBF changes were nonlinear.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.31 no.6B
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• pp.507-514
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• 2011

A numerical model has been developed by employing a finite element method to simulate the depth-averaged 2-D dispersion of the heat pollutant, which is an important pollutant material in natural streams. Among the finite element methods, the Streamline Upwind/Petrov Galerkin (SUPG) method was applied. Also both linear and quadratic elements can be applied so that irregular river boundaries can be easily represented. To show the movement of heat pollutants, the reaction term describing heat transfer was represented as an equation in which sink/source term is proportional to the difference between the equilibrium temperature and water surface temperature. The equation was expressed so that the water surface temperature changes according to the temperature transfer coefficient and the equilibrium temperature. For the calibration of the model developed, analytic and numerical results from a case of rectangular channel with full width continuous injection have been compared in a steady state. The comparisons showed that the numerical results were in good agreement with analytical solutions. The application site was selected from the downstream of Paldang dam to Jamsil submerged weir, and overall length of this site is about 22.5 km. The change of water temperature caused by the discharge from the Guri sewage treatment plant has been simulated, and results were similar to the observed data. Overall it is concluded that the developed model can represent the water temperature changes due to heat transport accurately. But the verification using observed data will further enhance the validity of the model.

• Korean Chemical Engineering Research
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• v.44 no.6
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• pp.650-658
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• 2006

The recycling of TDA from solid waste of TDI plant(TDI-R) by near-critical hydrolysis reaction had been studied by means of a statistical design of experiment. The main and interaction effects of process variables had been defined from the experiments in a batch reactor and the correlation equation with process variables for TDA yield had been obtained from the experiments in a continuous pilot plant. It was confirmed that the effects of reaction temperature, catalyst type and concentration, and the weight ratio of water to TDI-R(WR) on TDA yield were significant. TDA yield decreased with increases in reaction temperature and catalyst concentration, and increased with an increase in WR. As a catalyst, NaOH was more effective than $Na_2CO_3$ for TDA yield. The interaction effects between catalyst concentration and temperature, WR and temperature, catalyst type and reaction time on TDA yield had been defined as significant. Although the effect of catalyst concentration on TDA yield at $300^{\circ}C$ as subcritical water was insignificant, the TDA yield decreased with increasing catalyst concentration at $400^{\circ}C$ as supercritical water. On the other hand, the yield increased with an increase in WR at $300^{\circ}C$ but showed negligible effect with WR at $400^{\circ}C$. The optimization of process variables for TDA yield has been explored with a pilot plant for scale-up. The catalyst concentration and WR were selected as process variables with respect to economic feasibility and efficiency. The effects of process variables on TDA yield had been explored by means of central composite design. The TDA yield increased with an increase in catalyst concentration. It showed maximum value at below 2.5 of WR and then decreased with an increase in WR. However, the ratio at which the TDA yield showed a maximum value increased with increasing catalyst concentration. The correlation equation of a quadratic model with catalyst concentration and WR had been obtained by the regression analysis of experimental results in a pilot plant.