• Bulletin of the Korean Mathematical Society
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• v.59 no.3
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• pp.745-756
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• 2022

We study a nonlinear wave equation on finite connected weighted graphs. Using Rothe's and energy methods, we prove the existence and uniqueness of solution under certain assumption. For linear wave equation on graphs, Lin and Xie [10] obtained the existence and uniqueness of solution. The main novelty of this paper is that the wave equation we considered has the nonlinear damping term |u_t|^p-1·u_t (p > 1).

• Journal of Photoscience
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• v.8 no.1
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• pp.33-37
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• 2001

Picosecond absorption spectroscopy has been employed in the study of the solvent dynamics of 1, 2, 4, 5-tetracyanobenzene/biphenyl derivative radical ion pairs, and the resulting rates of radical ion pair separation are faster in acetonitrile than in dichloromethane. In an effort to account quantitatively for such solvent effect on the rate of radical ion pair separation, an equation for the rate of radical ion pair separation is introduced, in which the rate depends exponentially on the electrostatic interaction energy in the radical ion pair. In our analysis of the types of electrostatic interaction energy based on the conducting spheres in dielectric continuum was chosen, and the rate equation employing this electrostatic energy provided information on the distance on the distance of radical ion pair separation and solvation energy of the radical ion pair, thereby providing quantitative explanation for the observed solvent effect on the rate of radical ion pair sepaaration.

• Fire Protection Technology
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• s.23
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• pp.15-19
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• 1997

The objective of this paper is to present a equation which can give some insight of the behavior of droplet in a fire plume. The equation is derived with a number of engineering relations drawn from the literature for calculating properties of fire plume. Plume properties considered here include temperatures, velocities and virtual origin. In addition, the drag force for a sphere and the energy equation are considered.

• Transactions on Electrical and Electronic Materials
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• v.13 no.4
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• pp.204-207
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• 2012

Epoxy nanocomposite was synthesized through the exfoliation of organoclay in an epoxy matrix, which was composed of diglycidyl ether of bisphenol A (DGEBA), 4,4'-methylene dianiline (MDA) and malononitrile (MN). Organoclay was prepared by treating the montmorillonite with octadecyl trimethyl ammonium bromide (ODTMA). The exfoliation of the organoclay was estimated by wide angle X-ray diffraction (WAXD) analysis. In order to measure the cure rate of DGEBA/MDA (30 phr)/MN (5 phr)/organoclay (3 phr), differential scanning calorimetry (DSC) analysis was performed at various heating rates, and the data were interpreted by Kissinger equation. Thermal degradation kinetics of the epoxy nanocomposite were studied by thermogravimetric analysis (TGA), and the data were introduced to the Ozawa equation. The activation energy for cure reaction was 45.8 kJ/mol, and the activation energy for thermal degradation was 143 kJ/mol.

• Transactions of the Korean Society of Automotive Engineers
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• v.8 no.4
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• pp.177-185
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• 2000

The deformation characteristics is one of the major factors to resume the crash configuration in collision accident reconstruction. Crash analysis are carried out using finite element method and body stiffness equations representing force-deformation relationship are derived, Two different crash conditions : 1) frontal barrier impact 2) frontal impact between cars are given for the derivation of the equations. The stiffness coefficient of equation by method 2) is larger than that by method. 1). Crash analysis between two vehicles is accomplished with three crash angles and three velocities for each angle condition. The deformations are measured for six selected points and deformation energies are calculated using the derived equations. Equation by method 2) results in better estimation of deformation energy than that by method 1) for all crush configurations. The estimated energies can be utilized as one of indices to identify the type of the collision accident result.

• New & Renewable Energy
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• v.2 no.2 s.6
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• pp.50-59
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• 2006

An experimental and numerical study is carried out to investigate the performance and the efficiency humidifying Membrane Electrolyte Assembly and having the double-layered catalyst in a fuel cell system which is taken into account the physical and thermal concept. Based on the principals of the problem, the equation of electronic charge conservation equation, gas-phase continuity equation, and mass balance equation are used for the numerical calculation. A unit cell for $200cm^2$ MEA is assembled and measured for finding better operational situation. After finding the optimal condition, 10 cell stacked PEMFC is fabricated. For the performance evaluation, V-I and power curves are examined in detail by changing the condition of humidity, temperature, pressure, thickness of catalyst and oxidant. It is found that the power is maximized around 500W at 80A.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.4
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• pp.967-976
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• 1994

A tensor invariant model equation for the turbulent energy dissipation rate is proposed in the present study, which is able to simulate secondary straining effects such as curvature effects without the introduction of additional empirical input. The source term in this model has a combined form of the generation term due to the mean vorticity with the conventional one due to the mean strain rate. An extended low-Reynolds-number $k-\epsilon$ turbulence model involving this new model equation is tested for a turbulent Coutte flow between coaxial cylinders with inner cylinder rotated, which is a well defined example of curved flows. The predicted results indicate that the present model works much better for this flow, compared with previous models.

• Transactions of the Korean Society of Automotive Engineers
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• v.11 no.2
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• pp.157-163
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• 2003

This work was undertaken for the numerical analysis of defrosting phenomena of automobile windshield. To analyze the defrost, the flow and temperature field of cabin interior, heat transfer through the windshield glass, and phase change of the frost should be analyzed simultaneously. The flow field was obtained by solving the 3-D unsteady Navier-Stokes equation and the temperature field was computed by energy equation. The phase-change process of Stefan problem was solved by enthalpy method. For code validation, the temperature field of the driven cavity was calculated. The result of calculation shows a good agreement with the other numerical results. Then, the present code was applied to the defrosting analysis of a real automobile and, also, a good agreement with experiment was obtained.

• Nuclear Engineering and Technology
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• v.35 no.1
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• pp.45-54
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• 2003

A hyperbolic two-phase, two-fluid equation system developed in the previous work has been implemented in an existing nuclear safety analysis code, MARS. Although the implicit treatment of interfacial pressure force term introduced in momentum equation of the hyperbolic equation system is required to enhance the numerical stability, it is very difficult to implement in the code because it is not possible to maintain the existing numerical solution structure. As an alternative, two-step approach with stabilizer momentum equations has been selected. The results of a linear stability analysis by Von-Neumann method show the equivalent stability improvement with fully-implicit solution method. To illustrate the applicability, the new solution scheme has been implemented into the best-estimate thermal-hydraulic analysis code, MARS. This paper also includes the comparisons of the simulation results for the perturbation propagation and water faucet problems using both two-step method and the original solution scheme.

• Journal of Energy Engineering
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• v.15 no.4 s.48
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• pp.250-255
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• 2006

In this study, the discrete ordinates method which has been widely used in the solution of neutron transport equation is applied to the solution of the time dependent radiative transfer equation. The self-adjoint form of the second order radiation intensity equation is used to enhance the stability of the solution, and a new multi-step linearization method is developed to avoid the nonlinearity in the material temperature equation. This new solution method is applied to the well known Marshak wave problem, and the numerical result is compared with that of the conventional Monte-Carlo method.