• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.143-154
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• 2003

Analytical solutions for the viscous Cahn-Hilliard equation are considered. Existence and uniqueness of the solution are shown. The exponential decay of the solution in H$^2$-norm, which is an improvement of the result in Elliott and Zheng[5]. We also compare the early stages of evolution of the viscous Cahn-Hilliard equation with that of the Cahn-Hilliard equation, which has been given as an open question in Novick-Cohen[8].

• International Journal of Aeronautical and Space Sciences
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• v.4 no.2
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• pp.17-25
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• 2003

Simple methods are developed to predict temperatures of a satellite box during launch stage. The box is mounted on outer surface of satellite and directly exposed to space thermal environment for the time period from fairing jettison to separation. These simple methods are to solve a 1st order ordinary differential equation (ODE) which is simplified from the governing equation after applying several assumptions. The existence of analytical solution for the 1st order ODE is determined depending on treatment of time-dependent molecular heating term. Even for the case that the analytical solution is not available due to the time dependent term, the 1st order ODE can be solved by relatively simple numerical techniques. The temperature difference between two different approaches (analytical and numerical solutions) is relatively small (Jess than $1^{\circ}C$ along the time line) when they are applied to STSAT-I launch scenario. The present methods can be generally used as tools to quickly check whether a satellite box is safe against space environment during the launch stage for the case that the detailed thermal analysis is not available.

• Journal of the Korean Society of Tobacco Science
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• v.27 no.2
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• pp.207-211
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• 2005

This study was carried out to develop calibration equation of total volatile bases of tobacco leaf using near infrared spectroscopy(NIRS). Burley, imported flue-cured and oriental leaf tobacco samples were collected in 2005 crop year. Calibration equation was developed by modified partial least square method. The standard error of calibration and $R^2$ between traditional analytical method and NIRS analytical method were $0.038\%$, 0.983 for burley and $0.027\%$, 0.986 for imported flue-cured and oriental leaf, respectively. The standard error of performance and $R^2$ between traditional analytical method and NIRS analytical method were $0.048\%$, 0.940 for burley and $0.024\%$, 0.986 for imported flue-cured and oriental leaf, respectively. From these results, the NIRS analytical method seems to be applicable in analyzing total volatile bases of tobacco.

• JSTS:Journal of Semiconductor Technology and Science
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• v.2 no.1
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• pp.59-69
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• 2002

A semi-analytical model based on exact numerical analysis of the 2DEG channel in pseudo-morphic HEMT (PMHEMT) is presented. The exactness of the model stems from solving both Schrodinger's wave equation and Poisson's equation simultaneously and self-consistently. The analytical modeling of the device terminal characteristics in relation to the charge control model has allowed a best fit with the geometrical and structural parameters of the device. The numerically obtained data for the charge control of the channel are best fitted to analytical expressions which render the problem analytical. The obtained good agreement between experimental and modeled current/voltage characteristics and small signal parameters has confirmed the validity of the model over a wide range of biasing voltages. The model has been used to compare both the performance and characteristics of a PMHEMT with a competetive HEMT. The comparison between the two devices has been made in terms of 2DEG density, transfer characteristics, transconductance, gate capacitance and unity current gain cut-off frequency. The results show that PMHEMT outperforms the conventional HEMT in all considered parameters.

• Journal of the Semiconductor & Display Technology
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• v.20 no.3
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• pp.11-17
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• 2021

I performed a semi-analytical numerical analysis of the effects of core size and electric field intensity on the light emission wavelength of CdSe/ZnS quantum dots (QDs). The analysis used a quantum mechanical approach; I solved the Schrödinger equation describing the electron-hole pairs of QDs. The numerical solutions are described using a basis set composed of the eigenstates of the Schrödinger equation; they are thus equivalent to analytical solutions. This semi-analytical numerical method made it simple and reliable to evaluate the dependency of QD characteristics on the QD core size and electric field intensity. As the QD core diameter changed from 9.9 to 2.5 nm, the light emission wavelength of CdSe core-only QDs varied from 262.9 to 643.8 nm, and that of CdSe/ZnS core/shell QDs from 279.9 to 697.2 nm. On application of an electric field of 8 × 10⁵ V/cm, the emission wavelengths of green-emitting CdSe and CdSe/ZnS QDs increased by 7.7 and 3.8 nm, respectively. This semi-analytical numerical analysis will aid the choice of QD size and material, and promote the development of improved QD light-emitting devices.

• Transactions of The Korea Fluid Power Systems Society
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• v.3 no.3
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• pp.1-7
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• 2006

In this paper, a theoretical analysis is carried out to study the lubrication characteristics of sealless piston for hydraulic cylinders. The analytical pressure distributions are obtained solving one-dimensional Reynolds equation with partially tapered moving piston. Nearly analytical expressions for lateral forces acting on the piston and leakage flow rate through the clearance are also presented. Using the analytical expressions, the influence of design parameters on lubrication characteristics can be easily evaluated without numerical analysis. Composite-shaped piston which minimizes the leakage flow rate is the optimum in sealless piston for hydraulic cylinder.

• Fisheries and Aquatic Sciences
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• v.7 no.2
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• pp.90-95
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• 2004

An analytical model for predicting the convection-diffusion of solute dumped in a homogeneous open sea of constant water depth has been developed in a time-integral form. The model incorporates spatially uniform, uni-directional, mean and oscillatory currents for horizontal convection, the settling velocity for the vertical convection, and the anisotropic turbulent diffusion. Two transformations were introduced to reduce the convection-diffusion equation to the Fickian type diffusion equation, and then the Galerkin method was then applied via the expansion of eigenfunctions over the water column derived from the Sturm-Liouville problem. A series of calculations has been performed to demonstrate the applicability of the model.

• Journal of Welding and Joining
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• v.13 no.3
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• pp.116-124
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• 1995

This paper presents an analytical solution to predict the transient temperature distribution in fillet arc welding including the effect of molten metal. The solution is obtained by solving a transient three-dimensional heat conduction equation with convection boundary conditions on the surfaces of a plate, and mapping the infinite plate onto the fillet weld geometry with energy equation. The electric heat input on the fillet weld and on the infinite plate is assumed to have a combination of two bivariate Gaussian distribution. To check the validity of the solution. FCA welding experiments were performed under various welding conditions. The actual isotherms of the weldment cross-sections at various distances from the arc start point are compared with those of simulation result.

• Steel and Composite Structures
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• v.14 no.5
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• pp.511-521
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• 2013

In this study we have considered the governing nonlinear equation of an eccentrically reinforced cylindrical shell. A new analytical method called He's Variational Approach (VA) is used to obtain the natural frequency of the nonlinear equation. This analytical representation gives excellent approximations to the numerical solution for the whole range of the oscillation amplitude, reducing the respective error of angular frequency in comparison with the variation approach method. It has been proved that the variational approach is very effective, convenient and does not require any linearization or small perturbation. Additionally it has been demonstrated that the variational approach is adequately accurate to nonlinear problems in physics and engineering.

• Steel and Composite Structures
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• v.26 no.4
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• pp.453-461
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• 2018

In this paper, nonlinear vibrations of the unsymmetrical laminated composite beam (LCB) on a nonlinear elastic foundation are studied. The governing equation of the problem is derived by using Galerkin method. Two different end conditions are considered: the simple-simple and the clamped-clamped one. The Hamiltonian Approach (HA) method is adopted and applied for solving of the equation of motion. The advantage of the suggested method is that it does not need any linearization of the problem and the obtained approximate solution has a high accuracy. The method is used for frequency calculation. The frequency of the nonlinear system is compared with the frequency of the linear system. The influence of the parameters of the foundation nonlinearity on the frequency of vibration is considered. The differential equation of vibration is solved also numerically. The analytical and numerical results are compared and is concluded that the difference is negligible. In the paper the new method for error estimation of the analytical solution in comparison to the exact one is developed. The method is based on comparison of the calculation energy and the exact energy of the system. For certain numerical data the accuracy of the approximate frequency of vibration is determined by applying of the suggested method of error estimation. Finally, it has been indicated that the proposed Hamiltonian Approach gives enough accurate result.