• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.1
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• pp.43-55
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• 2011

We here investigate the Liouville type theorems of slow diffusion differential inequality and its coupled system with variable coefficients in cone. First, we give the definition of global weak solution, and then we establish the universal estimate (does not depend on the initial value) of solution by constructing test function. At last, we obtain the nonexistence of non-negative non-trivial global weak solution within the appropriate critical exponent. The main feature of this method is that we need not use comparison theorem or the maximum principle.

• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.185-201
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• 2014

In this paper, we construct a numerical method to solve singularly perturbed one-dimensional parabolic convection-diffusion problems. We use Euler method with uniform step size for temporal discretization and exponential-spline scheme on spatial uniform mesh of Shishkin type for full discretization. We show that the resulting method is uniformly convergent with respect to diffusion parameter. An extensive amount of analysis has been carried out to prove the uniform convergence with respect to the singular perturbation parameter. The obtained numerical results show that the method is efficient, stable and reliable for solving convection-diffusion problem accurately even involving diffusion parameter.

• Advances in nano research
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• v.6 no.2
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• pp.113-133
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• 2018

In this work, free vibration characteristics of functionally graded piezoelectric (FGP) nanobeams based on third order parabolic shear deformation beam theory are studied by presenting a Navier type solution as the first attempt. Electro-mechanical properties of FGP nanobeam are supposed to change continuously throughout the thickness based on power-law model. To capture the small size effects, Eringen's nonlocal elasticity theory is adopted. Using Hamilton's principle, the nonlocal governing equations for third order shear deformable piezoelectric FG nanobeams are obtained and they are solved applying analytical solution. By presenting some numerical results, it is demonstrated that the suggested model presents accurate frequency results of the FGP nanobeams. The influences of several parameters including, external electric voltage, power-law exponent, nonlocal parameter and mode number on the natural frequencies of the size-dependent FGP nanobeams is discussed in detail.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.21 no.1
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• pp.66-73
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• 2011

This paper deals with free vibrations of the tapered beams with the constant surface area. The surface area of the objective beams are always held constant regardless shape functions of the cross-sectional depth. The shape functions are chosen as the linear and parabolic ones. Ordinary differential equations governing free vibrations of such beams are derived and solved numerically for determining the natural frequencies. In the numerical examples, hinged-hinged, hinged-clamped and clamped-clamped end constraints are considered. As the numerical results, the relationships between non-dimensional frequency parameters and various beam parameters such as section ratio, surface area ratio, end constraint and taper type are reported in tables and figures. Especially, section ratios of the strongest beam are calculated, under which the maximum frequencies are achieved.

• Proceedings of the Korean Institute of Navigation and Port Research Conference
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• 2000.04a
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• pp.75-81
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• 2000

Water waves propagate over irregular bottom bathymetry are transformed by refraction, diffraction, shoaling, reflection etc. Principal factor of wave transform is bottom bathymetry, but in case of current field, current is another important factor which effect wave transformation. The governing equation of this study is develop as wave-current equation type to investigate the effect of wave-current interaction. This wave-current model was applied to the Kwangan beach which is located at Pusan. The numerical simulation results of this model show the characteristics of wave transformation and flow pattern around the Kwangan beach fairly well.

• Advances in aircraft and spacecraft science
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• v.5 no.6
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• pp.671-689
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• 2018

Bending, buckling and free vibration responses of functionally graded (FG) higher-order beams resting on two parameter (Winkler-Pasternak) elastic foundation are studied using a new inverse hyperbolic beam theory. The material properties of the beam are graded along the thickness direction according to the power-law distribution. In the present theory, the axial displacement accounts for an inverse hyperbolic distribution, and the transverse shear stress satisfies the traction-free boundary conditions on the top and bottom surfaces of the beams. Hamilton's principle is employed to derive the governing equations of motion. Navier type analytical solutions are obtained for the bending, bucking and vibration problems. Numerical results are obtained to investigate the effects of power-law index, length-to-thickness ratio and foundation parameter on the displacements, stresses, critical buckling loads and frequencies. Numerical results by using parabolic beam theory of Reddy and first-order beam theory of Timoshenko are specially generated for comparison of present results and found in excellent agreement with each other.

• 한국연소학회:학술대회논문집
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• 2000.05a
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• pp.35-44
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• 2000

It was numerically studied that NOx emission characteristics of confined $CH_{4}$ jet flames with the variation of the diameter of inner fuel nozzle, the flow rate of $CH_{4}$ and equivalence ratio. Parabolic type equations were adopted in the calculation and GRI-2.1I mechanism was used for the chemical reaction. NOx emission index (EINOx) was introduced to evaluate NOx emission quantitatively in parametrically varied flames and the contribution of Thermal and Prompt NO mechanism was discussed. The results showed that Total EINOx varied sensitively with the variation of the flow rate of$CH_{4}$ but it was not sensitive to the variation of the diameter of inner fuel nozzle. Thermal EINOx showed the similar tendency to total EINOx and Prompt EINOx showed insensitivity to the variation of the diameter of inner fuel nozzle and the flow rate of $CH_{4}$.

• Proceedings of the KIEE Conference
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• 1989.07a
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• pp.134-137
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• 1989

A digital controller for a discrete-data control system can take many forms. For example, they can be passive RC networks, general purpose digital computers, special purpose of mini-computer, and delay lines. With the recent advent of the microprocessor, its use as a digital controller is evident. This work discusses the hardware and software development of a microprocessor-based digital controller for a discrete-data control system. A second-order, Type 1 system is implemented on an analog computer; a Intel 80-286 microprocessor is used to implemented the controller; and, output response are obtained for step, ramp, and parabolic inputs. The results demonstrate that the microprocessor has potential as a digital controller. Finally, a brief discussion on the results indicate possible areas of improvement of the controller and future investigation.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.14 no.10
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• pp.1089-1095
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• 2003

In this paper, the 26 GHz band omnidirectional antenna that produces an isotropic radiation pattern in the azimuth plane and a directive radiation pattern in the elevation plane was designed by using reflector antennas. To investigate the reliability of the designed antenna, that was analyzed by using the aperture field method and the calculated value was compared with the measured value. An good agreement was achieved between the calculated characteristics and the experimental performance. We found that the designed antenna in this paper can be used as the omnidirectional antenna with reflectors and the analysis method in this paper can be used for the analysis of this type antenna.

• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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• pp.48-49
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• 2003

In the present research a high order Gudonov-type method has been used for the simulation of very high pressure flow fields, as well as the capturing of strong shocks, which usually occur in explosion of high explosives. The treatment strong shocks and the flow field behind the shocks needs a very high resolution scheme. To resolve accurately the shock and the release waves behind the shock the piece­wise parabolic method (PPM) of Colella [1] was utilized in this research. A major problem which encountered in very high pressure problems is the equation of state which differs completely form the ideal-gas equation of state (EOS). Here, the original PPM is extended for real gas effect consideration.