• Bulletin of the Korean Mathematical Society
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• v.31 no.2
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• pp.309-318
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• 1994

The approach presented in this paper is based on the transformation of the Stefan problem in one space dimension to an initial-boundary value problem for the heat equation in a fixed domain. Of course, the problem is non-linear. The finite element approximation adopted here is the standared continuous Galerkin method in time. In this paper, only the regular case is discussed. This means the error analysis is based on the assumption that the solution is sufficiently smooth. The aim of this paper is the existence of the solution in a finite Galerkin system of ordinary equations.

• Journal of applied mathematics & informatics
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• v.41 no.2
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• pp.311-320
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• 2023

In this article, a new penalty and different ranking algorithms are used to find the lowest transportation costs for the fuzzy transportation problem. This approach utilises different ranking techniques when dealing with triangular fuzzy numbers. Also, we find that the fuzzy transportation solution of the proposed method is the same as the Fuzzy Modified Distribution Method (FMODI) solution. Finally, examples are used to show how a problem is solved.

• Journal of Korea Water Resources Association
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• v.41 no.7
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• pp.669-679
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• 2008

The present study examines similarity of behavior between an overtopping wave generated by a plunging wave and a dam-break flow through hydraulic model tests. The dam-break flow has been employed to estimate the overtopping effect on the basis of the dam-break flow's behavior similar to the overtopping. In this study, the overtopping velocity was measured by a modified image technique using bubble and bubble texture images called bubble image velocitmetry. From the measurements, the vertical profiles of horizontal overtopping velocity at cross-sections along the deck were presented and discussed. Maximum velocity and depth-averaged velocity at each cross-section were compared with an analytical solution solving the dam-break flow, Ritter's solution. The initial water depth of importance for the solution was determined from the tested wave condition and the overtopping measurements. The comparison shows that the solution with the initial water depth estimated using the front velocity of the overtopping wave is in good agreements with the measurements.

• Journal of Environmental Science International
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• v.8 no.3
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• pp.399-409
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• 1999

The three domestic natural zeolites(Yong dong-ri (Y), Daesin-ri (D), Seogdong-ri (S)) harvested in Kyeongju-shi and Pohang-shi, Kyungsangbug-Do, were pretreatd with each of the NaOH, $Ca(OH)_2$ and NaOH following HCl solutions, and the removal performances of divalent haevy metals(Cu, Mn, Pb, and Sr) for natural and pretreated zeolites were investigated and compared in the single and mixed solutions. The natural zeolite-heavy metal system attained the final equilibrium plateau within 20 min, irrespective of initial heavy metal concentration. The heavy metal uptakes increased with increasing initial heavy metal concentration and pH. The heavy metal uptakes for natural zeolites decreased in the following sequences : D>Y>S among the natural zeolites; Pb>Cu>Sr>Mn among the heavy metals. The pretreated zeolites showed higher heavy metal removal performances than natural zeolites and decreased in the order of NaOH, NaOH following HCl, $Ca(OH)_2$ treatment among the pretreatment methods. The heavy metal ion exchange capacity by natural and pretreated zeolites was described either by Freundlich equation or Langmuir equation, but it followed the former better than the latter. The heavy metal uptakes for natural zeolites decreased in the mixed solution, in comparing with those in the single solution and especially, the manganese uptake decreased greatly in the mixed solution. The pretreated zeolites showed the improved removal performances of heavy metals in the mixed solution than in the single solution and the heavy metal uptakes by those in the mixed solution showed the same trends in the single solution among the chemical treatment methods and heavy metals.

• Carbon letters
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• v.13 no.4
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• pp.248-253
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• 2012

Dielectrophoretic filtering and alignment of single-walled carbon nanotubes (SWCNTs) were tested using deuterium oxide as a solvent. A solution of deuterium oxide-SWCNTs was dropped on top of a silicon chip and an ac electric field was applied between pre-defined electrodes. Deuterium oxide was found to be a better solvent than hydrogen oxide for the dielectrophoresis process with higher efficiency of filtering. This was demonstrated by comparing Raman spectra measured on the initial solution with those measured on the filtered solution. We found that the aligned nanotubes along the electric field were not deposited on the substrate but suspended in solution, forming chain-like structures along the field lines. This so-called pearl chain formation of CNTs was verified by electrical measurements through the aligned tubes. The solution was frozen in liquid nitrogen prior to the electrical measurements to maintain the chain formation. The current-voltage characteristics for the sample demonstrate the existence of conduction channels in the solution, which are associated with the SWCNT chain structures.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.73-80
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• 2006

In order to examine the validity of an asymptotic solution for nonlinear interaction in asymmetric vibration modes of a perfect circular plate, we obtain the numerical solution. The motion of the plate is governed by nonlinear partial differential equation. The initial and boundary value problem is solved by using the finite difference method. The numerical solution is compared with the asymptotic solution. It is found that traveling waves relating clockwise and counterclockwise as well as standing wave are depicted by the numerical solution.

• Journal of applied mathematics & informatics
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• v.31 no.1_2
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• pp.131-145
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• 2013

In this paper, we present an initial value technique for solving singularly perturbed differential difference equations with a boundary layer at one end point. Taylor's series is used to tackle the terms containing shift provided the shift is of small order of singular perturbation parameter and obtained a singularly perturbed boundary value problem. This singularly perturbed boundary value problem is replaced by a pair of initial value problems. Classical fourth order Runge-Kutta method is used to solve these initial value problems. The effect of small shift on the boundary layer solution in both the cases, i.e., the boundary layer on the left side as well as the right side is discussed by considering numerical experiments. Several numerical examples are solved to demonstate the applicability of the method.

• Journal of Advanced Marine Engineering and Technology
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• v.21 no.5
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• pp.527-534
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• 1997

Freezing of an aqueous sodium cWoride solution (Nacl- H20) saturating a packed bed with ini¬tial salt concentrations of 5, 10, 15(k by weight is investigated experimentally in a rectangular cav¬ity. The system was cooled from the top, bottom and a vertical side wall. For the freezing experi¬ments from below, there was little effect of the initial salt concentration throughout the freezing process, and the global freezing rate was not affected by the initial salt concentration. For the freezing from above, the size of the mush region decreased and the mushlliquid interface became flatter as the initial liquid concentration is decreased. For the freezing from vertical side wall, reheating of the mixture was intensified with an increase in the initial salt concentration. For Ci= 5%, supercooling was observed only at the early times of freezing process, but for Ci= 15% small supercooling was observed throughout the freezing process.

• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.141-152
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• 2007

In this paper a numerical method is presented to solve singularly perturbed two points boundary value problems for second order ordinary differential equations consisting a discontinuous source term. First, in this method, an asymptotic expansion approximation of the solution of the boundary value problem is constructed using the basic ideas of a well known perturbation method WKB. Then some initial value problems and terminal value problems are constructed such that their solutions are the terms of this asymptotic expansion. These initial value problems are happened to be singularly perturbed problems and therefore fitted mesh method (Shishkin mesh) are used to solve these problems. Necessary error estimates are derived and examples provided to illustrate the method.

• Journal of the Korean Chemical Society
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• v.64 no.5
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• pp.249-258
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• 2020

The potential use of egg shell and calcined egg shell as adsorbent was evaluated and compared to remove Cd²⁺ from aqueous solution. The samples were characterized using Thermogravimetry and Differential Thermal Analysis (TG/DTA), Scanning Electron Microscope (SEM), X-ray Diffractometer (XRD), Energy Dispersive X-ray Spectrometer (EDX) and BET Surface Analyzer. The batch-type adsorption experiment was conducted by varying diverse variables such as contact time, pH, initial Cd²⁺ concentrations and adsorbent dosage. The results showed that, under the initial Cd²⁺ concentrations ranged from 25 to 200 mg g^-1, the removal efficiencies of Cd²⁺ by egg shell powder (ESP) were decreased steadily from 96.72% to 22.89% with increase in the initial Cd²⁺ concentration at 2.5 g of dosage and 8 h of contact time. However, on the contrary to this, calcined egg shell powder (CESP) showed removal efficiencies above 99% regardless of initial Cd²⁺ concentration. The difference in the adsorption behavior of Cd²⁺ may be explained due to the different pH values of ESP and CESP in solution. Cd²⁺ seems to be efficiently removed from aqueous solution by using the CESP with a basicity nature of around pH 12. It was also observed that an optimum dosage of ESP and CESP for nearly complete removal of Cd²⁺ from aqueous solution is approximately 5.0 g and 1.0 g, respectively. Consequently, Cd²⁺ is more favorably adsorbed on CESP than ESP in the studied conditions. Adsorption data were applied by the pseudo-first-order and pseudo-second-order kinetics models and Freundlich and Langmuir isotherm models, respectively. With regard to adsorption kinetics tests, the pseudo-second-order kinetics was more suitable for ESP and CESP. The adsorption pattern of Cd²⁺ by ESP was better fitted to Langmuir isotherm model. However, by contrast with ESP, CESP was described by Freundlich isotherm model well.