• 대한수학회보
• /
• 제54권2호
• /
• pp.655-666
• /
• 2017

In this paper, we study the pattern formation to a general Degn-Harrison reaction model. We show Turing instability happens by analyzing the stability of the unique positive equilibrium with respect to the PDE model and the corresponding ODE model, which indicate the existence of the non-constant steady state solutions. We also show the existence periodic solutions of the PDE model and the ODE model by using Hopf bifurcation theory. Numerical simulations are presented to verify and illustrate the theoretical results.

• 대한수학회논문집
• /
• 제33권3호
• /
• pp.1039-1048
• /
• 2018

In this paper we study the dynamics of a general ${\omega}-periodic$ model. Necessary and sufficient conditions for the global stability of zero steady state of the model are given. The conditions under which there exists a unique periodic solutions to the model are determined. We also show that the unique periodic solution is the global attractor of all other positive solutions. Some applications to mathematical models for cancer and tumor growth are given.

• 대한기계학회:학술대회논문집
• /
• 대한기계학회 2003년도 추계학술대회
• /
• pp.1654-1659
• /
• 2003

This paper introduces a fast Fourier transform (FFT)-based spectral analysis method for the transient responses as well as the steady-state responses of linear discrete systems. The force vibration of a viscously damped three-DOF system is considered as the illustrative numerical example. The proposed spectral analysis method is evaluated by comparing with the exact analytical solutions as well as with the numerical solutions obtained by the Runge-Kutta method.

• 대한전기학회:학술대회논문집
• /
• 대한전기학회 1986년도 하계학술대회논문집
• /
• pp.609-613
• /
• 1986

The resonance frequency and the gain for oscillation of external cavity diode lasers are derived by approximating the phase and the gain conditions. By modifying single mode rate equations for the external cavity diode laser, steady state solutions and their stability are studied.

• Structural Engineering and Mechanics
• /
• 제52권4호
• /
• pp.787-813
• /
• 2014

Starting with Hamilton's variational principle, the governing field equations for the steady state response of thin-walled beams under harmonic forces are derived. The formulation captures shear deformation effects due to bending and warping, translational and rotary inertia effects and as well as torsional flexural coupling effects due to the cross section mono-symmetry. The equations of motion consist of four coupled differential equations in the unknown displacement field variables. A general closed form solution is then developed for the coupled system of equations. The solution is subsequently used to develop a family of shape functions which exactly satisfy the homogeneous form of the governing field equations. A super-convergent finite element is then formulated based on the exact shape functions. Key features of the element developed include its ability to (a) isolate the steady state response component of the response to make the solution amenable to fatigue design, (b) capture coupling effects arising as a result of section mono-symmetry, (c) eliminate spatial discretization arising in commonly used finite elements, (d) avoiding shear locking phenomena, and (e) eliminate the need for time discretization. The results based on the present solution are found to be in excellent agreement with those based on finite element solutions at a small fraction of the computational and modelling cost involved.

• 전기학회논문지
• /
• 제58권5호
• /
• pp.873-878
• /
• 2009

When the transmission lines are initially energized for power system restoration, the power system suffers the various overvoltages that can be classified as steady-state, transient, and dynamic overvoltages. For the accurate analyses of these overvoltages, many researchers utilize different simulation tools such as Power System Simulator for Engineering(PSS/E). Although PSS/E provides good solutions in steady-state and dynamic overvoltages, it is not suitable for transient overvoltages. Therefore, transient overvoltages are simulated by using Electro-Magnetic Transients Program(EMTP) developed for the analysis of transients in the power system. Recently, EMTP can be also used to simulate dynamic behavior of the system. In order to analyze the transient overvoltages with steady-state and dynamic overvoltages, the authors adopt EMTP as the simulation tool for the analysis of overvoltages. This paper presents the simulation results for the analyses of various overvoltages, and the possibility of EMTP to be used for these types of analyses.

• Nuclear Engineering and Technology
• /
• 제45권2호
• /
• pp.191-202
• /
• 2013

A numerical analysis of thermal stratification in the upper plenum of the MONJU fast breeder reactor was performed. Calculations were performed for a 1/6 simplified model of the MONJU reactor using the commercial code, CFX-13. To better resolve the geometrically complex upper core structure of the MONJU reactor, the porous media approach was adopted for the simulation. First, a steady state solution was obtained and the transient solutions were then obtained for the turbine trip test conducted in December 1995. The time dependent inlet conditions for the mass flow rate and temperature were provided by JAEA. Good agreement with the experimental data was observed for steady state solution. The numerical solution of the transient analysis shows the formation of thermal stratification within the upper plenum of the reactor vessel during the turbine trip test. The temporal variations of temperature were predicted accurately by the present method in the initial rapid coastdown period (~300 seconds). However, transient numerical solutions show a faster thermal mixing than that observed in the experiment after the initial coastdown period. A nearly homogenization of the temperature field in the upper plenum is predicted after about 900 seconds, which is a much shorter-term thermal stratification than the experimental data indicates. This discrepancy may be due to the shortcoming of the turbulence models available in the CFX-13 code for a natural convection flow with thermal stratification.

• 전자공학회논문지A
• /
• 제31A권5호
• /
• pp.134-148
• /
• 1994

A full two-dimensional MOSFET simulator utilizing the Mixed Particle Monte Carlo method is introduced. Particle simulation for both electrons and holes are self-consistently coupled with Poisson 's equation. To demonstrate the performance of the simulator, steady state and transient state solutions of the terminal characteristics and the internal physical quantities are obtained for 0.25$\mu$m MOSFETs with three different structures` conventional single drain, LDD and GOLD MOSFET structures.

• Structural Engineering and Mechanics
• /
• 제62권2호
• /
• pp.171-178
• /
• 2017

Nonlinear vibrations of an Euler-Bernoulli beam resting on a nonlinear elastic foundation are discussed. In search of approximate analytical solutions, the classical multiple scales (MS) and the multiple scales Lindstedt Poincare (MSLP) methods are used. The case of primary resonance is investigated. Amplitude and phase modulation equations are obtained. Steady state solutions are considered. Frequency response curves obtained by both methods are contrasted with each other with respect to the effect of various physical parameters. For weakly nonlinear systems, MS and MSLP solutions are in good agreement. For strong hardening nonlinearities, MSLP solutions exhibit the usual jump phenomena whereas MS solutions are not reliable producing backward curves which are unphysical.

• Wind and Structures
• /
• 제4권1호
• /
• pp.31-44
• /
• 2001

Mean concentrations of ammonia gas released as a tracer from an isolated low-rise building have been measured and predicted. Predictions were calculated using computational fluid dynamics (CFD) and two dispersion models: a diffusion model and a Lagrangian particle tracking technique. Explicit account was taken of the natural variation of wind direction by a technique based on the weighted summation of individual steady state wind direction results according to the probability density function of the wind direction. The results indicated that at distances >3 building heights downstream the weighted predictions from either model are satisfactory but that in the near wake the diffusion model is less successful. Weighted solutions give significantly improved predictions over unweighted results. Lack of plume spread is identified as the main cause of inaccuracies in predictions and this is linked to inadequate resolution of flow features and mixing in the CFD model. Further work on non-steady state simulation of wake flows for dispersion studies is recommended.