• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.505-519
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• 2018

In this paper we define a (p, q)-Laplace transform. By using this definition, we obtain many properties including the linearity, scaling, translation, transform of derivatives, derivative of transforms, transform of integrals and so on. Finally, we solve the differential equation using the (p, q)-Laplace transform.

• Korean Chemical Engineering Research
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• v.57 no.5
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• pp.652-665
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• 2019

Analytical solutions of the reactant concentration inside porous spherical catalytic particles were obtained from unsteady reaction-diffusion equation by applying eigenfunction expansion method. Various surface concentrations as exponentially decaying or oscillating function were considered as boundary conditions to solve the unsteady partial differential equation as a function of radial distance and time. Dirac delta function was also used for the instantaneous injection of the reactant as the surface boundary condition to calculate average reactant concentration inside the particles as a function of time by Laplace transform. Besides spherical morphology, other geometries of particles, such as cylinder or slab, were considered to obtain the solution of the reaction-diffusion equation, and the results were compared with the solution in spherical coordinate. The concentration inside the particles based on calculation was compared with the bulk concentration of the reactant molecules measured by photocatalytic decomposition as a function of time.

• Journal of the Korean Applied Science and Technology
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• v.23 no.1
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• pp.54-62
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• 2006

Kelvin equation is revisited, which accounts for important phenomena observed frequently in nano-dispersion systems. They include vapor pressure increase for curved interfaces, nucleation, capillary condensation, Ostwald ripening and so on. The smaller the radius of curvature is, the more significant Kelvin equation becomes. Therefore, its meaning, curvature effect, and importance are examined and discussed.

• Proceedings of the KIEE Conference
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• 2001.11a
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• pp.284-287
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• 2001

유한체적법(Finite Volume Method)은 기계공학분야에서 열, 유체현상을 수치해석하는 방법으로 널리 쓰이고 있다. 열전달(Heat Transfer)문제의 지배방정식은 에너지방정식(Energy equation)으로써 그 중 순수 전도문제의 경우 지배방정식은 라플라스(Laplace)방정식의 형태를 띄고 있다. 전계해석의 지배방정식 역시 라플라스 방정식의 형태이다. 수학적으로 동일한 지배방정식을 갖는 다는 것은 물리적으로 같은 현상을 나타내고 있다는 것을 의미하며 이러한 점에 착안을 하여 본 논문에서는 유한체적법을 사용하여 2차원 모델에 대한 전계해석을 수행하였다.

• Proceedings of the KSME Conference
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• 2007.05b
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• pp.2113-2118
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• 2007

In this study, a mathematical model for a thermal analysis of a flat heat pipe with a grooved wick structure is presented. The effects of the liquid-vapor interfacial shear stress, the contact angle, and the amount of liquid charge have been included in the proposed model. In particular, the axial variations of the wall temperature and the evaporation/condensation rates are considered by solving the one-dimensional conduction and the augmented Young-Laplace equations, respectively. In order to verify the model, the results obtained from the model are compared to existing experimental data.

• Journal for History of Mathematics
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• v.21 no.3
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• pp.1-30
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• 2008

The success of Newton's Gravitational Theory has influenced the theory of capillarity, beginning in the early nineteenth century, by providing a major model of molecular attraction. He used the equation of the attraction of spheroids, which is expressed by second order partial differential equations, to utilize this analogy as the same kind of a particle's force, between gravitational, refractive force of light, and capillarity. The solution of the differential equation corresponds to the geometrical figure of the vessel and the contact angle which is made by the fluid. Unknown abstract functions $\varphi(f)$ represent interaction forces between molecules, giving their potential functions. By conducting several kinds of experimental conditions, it was found that the height of the ascending fluid in the tube is inversely proportional to the rayon of the tube or the distance of the plate. This model is an essential element in the theory of capillarity. Laplace has brought Newtonian mechanics to completion, which relates to the standard model of gravitational theory. Laplace-Young's equation of capillarity is applicable to minimal surfaces in mathematics, to surface tensional phenomena in physics, and to soap bubble experiments.

• Laser Solutions
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• v.5 no.1
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• pp.23-31
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• 2002

The uniform metal droplet generation using Nd-YAG laser was studied and experiment was carried out. The shape and volume of developed droplet was measured and the Young-Laplace equation and equilibrium condition of force were applied this model. The differential equation predicting shape of droplet using equilibrium condition of force instead of Navier-stokes equation was induced and numerical solution of differential equation compared with experimentation data. The differential equation was solved by Runge-Kutta method. Surface tension coefficient of droplet was determined with numerical solution relate to experimental result under the statical condition. In case of dynamic vibration, metal droplet shape and detaching critical volume are predicted by recalculating proposed model. The result revealed that this model could reasonably describe the behavior of molten metal droplet on vibration.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.47 no.12
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• pp.17-23
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• 2010

In this paper, a new analytical model for deriving the threshold voltage of a short-channel bulk-type MOSFET is suggested. Using the Fourier coefficient method, the Laplace equation in the oxide region and the Poisson equation in the depleted silicon region have been solved two-dimensionally. Making use of them, the minimum surface potential is derived to describe the threshold voltage. Simulation results show good agreement with the dependencies of the threshold voltage on the various device parameters and applied bias voltages.

• Nuclear Engineering and Technology
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• v.26 no.4
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• pp.453-460
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• 1994

The migration equation is modified for a three-member decay chain in the fracture and porous matrix Analytical solutions are obtained by utilizing Laplace transform the initial conditions of Delta function and Bateman equation. The concentrations for each nuclide of Np$^{237}$ -U$^{233}$ -Th$^{229}$ and U$^{234}$ -Th$^{230}$ -Ra$^{226}$ chains selected from the 4n＋1 and 4n＋2 chains are plotted by utilizing analytical solutions in the fracture. Retardation coefficient of the nuclides are obtained using those of the granite. The results indicate that the daughter nuclides such as U$^{233}$ , Th$^{229}$ , Th$^{230}$ and Ra$^{226}$ become important at the far field from the repository though there is very small initial inventory in the waste solid or spent fuel, for they are produced by the mother nuclides decayed in the fracture and porous matrix.

• Proceedings of the Korean Society of Laser Processing Conference
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• 2001.11a
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• pp.43-47
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• 2001

This paper presents a study of the uniform metal droplet generation using laser. The theoretical model, based on the variational principle instead of solving the Wavier-Stokes equation with moving boundaries, is developed. Our model is considered the Young-Laplace equation and force equilibrium conditions. Surface tension coefficient is determined under the statical condition with induced differential equation by using experimental result. In case of dynamic vibration, metal droplet shape and critical detaching volume are predicted by recalculating of proposed model. The simulation result revealed that the developed model could reasonably describe the molten metal droplet behavior on vibration with metal wire.