• Journal of Electrical Engineering and Technology
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• v.8 no.6
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• pp.1530-1541
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• 2013

The coexistence and extinction of species are important concepts for biological systems and can be distinguished by an investigation of stability. When determining local stability of nonlinear systems, Lyapunov indirect method based on the Jacobian linearization has been widely employed due to its simplicity. Despite such popularity, it is not applicable to singular systems whose Jacobian has at least one eigenvalue that is equal to zero. In such singular cases, an appropriate Lyapunov function should be sought to determine the stability of systems, which is rather difficult and quite involved. In this paper, we seek for a simple criterion to determine stability of the equilibrium that is located at the boundary of the positive orthant, when one of eigenvalues of the Jacobian is zero. The goal of the paper is to present a generalized condition for the equilibrium to attract all trajectories that starting from initial condition in the positive orthant and near the equilibrium. Unlike the Lyapunov direct method, the proposed method requires just a simple algebraic computation for checking the stability of the critical point. Our approach is applied to various biological systems to show the effectiveness of the proposed method.

• 사회경제평론
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• no.38
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• pp.51-83
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• 2012

Consider an n goods production economy. Assume the equilibrium condition of Sraffa's price system, a balanced growth condition and the goods market clearing conditions. If both equations are given to determine a real wage rate and investment, the economic system is over-determined. It suggests that there exists no long-period equilibrium to satisfy both labor market and goods market conditions. This paper interprets this situation of over-determinacy as a disequilibrium state, and attempts to solve it through disequilibrium dynamics. It constructs a model of accumulation and real wage rates consistent with Lotka-Volterra system, and shows that the overall growth path fluctuates endogenously around a resting point of long-period disequilibrium.

• Journal of Technology Innovation
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• v.13 no.1
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• pp.113-139
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• 2005

The purpose of this study is to analyse the diffusion process of personal computer (PC) in Korea during the 1990's. To achieve the goal, five research steps have been done such as the literature survey of diffusion theory, set-up of theoretic equilibrium model of supply and demand, derivation of an equilibrium path using Hamiltonian, and empirical analysis. The empirical analysis has been performed based on that equilibrium path. The results can be summarized as follows : First, technological attribute of diffusing product influences the diffusion speed of Product. It has been proven that the size of the network has a significant effect on the diffusion of PC in empirical study Second, supply factors have an important role in the diffusion process. According to the empirical analysis, decreasing cost of production as a result of technological advance promotes the speed of diffusion. This point seems to be manifest theoretically, but existing empirical models have not included supply factors explicitly, Third, it has been found out that expectation of decreasing cost would influence the speed of diffusion negatively as expected ex ante. Theoretically this result is supported by arbitrage condition of purchasing timing.

• Proceedings of the KSME Conference
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• 2007.05b
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• pp.2797-2802
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• 2007

It has been confirmed that implementation of the no-slip boundary conditions for the lattice-Boltzmann method play an important role in the overall accuracy of the numerical solutions as well as the stability of the solution procedure. We in this paper propose a new algorithm, i.e. the method of the dynamic boundary condition for no-slip boundary condition. The distribution functions on the wall along each of the links across the physical boundary are assumed to be composed of equilibrium and nonequilibrium parts which inherit the idea of Guo's extrapolation method. In the proposed algorithm, we apply a dynamic equation to reflect the computational slip velocity error occurred on the actual wall boundary to the correction; the calculated slip velocity error dynamically corrects the fictitious velocity on the wall nodes which are subsequently employed to the computation of equilibrium distribution functions on the wall nodes. Along with the dynamic selfcorrecting process, the calculation efficiently approaches the steady state. Numerical results show that the dynamic boundary method is featured with high accuracy and simplicity.

• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.731-770
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• 1997

We study Diriclet forms and related subjects for the Gibbs measures of classical unbounded sping systems interacting via potentials which are superstable and regular. For any Gibbs measure $\mu$, we construct a Dirichlet form and the associated diffusion process on $L^2(\Omega, d\mu), where \Omega = (R^d)^Z^\nu$. Under appropriate conditions on the potential we show that the Dirichlet operator associated to a Gibbs measure $\mu$ is essentially self-adjoint on the space of smooth bounded cylinder functions. Under the condition of uniform log-concavity, the Gibbs measure exists uniquely and there exists a mass gap in the lower end of the spectrum of the Dirichlet operator. We also show that under the condition of uniform log-concavity, the unique Gibbs measure satisfies the log-Sobolev inequality. We utilize the general scheme of the previous works on the theory in infinite dimensional spaces developed by e.g., Albeverio, Antonjuk, Hoegh-Krohn, Kondratiev, Rockner, and Kusuoka, etc, and also use the equilibrium condition and the regularity of Gibbs measures extensively.

• Journal of the Korean Mathematical Society
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• v.42 no.5
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• pp.1071-1086
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• 2005

In this paper, we introduce a discrete time to the model to describe the time between infection of a CD4$^{+}$ T-cells, and the emission of viral particles on a cellular level. We study the effect of the time delay on the stability of the endemically infected equilibrium, criteria are given to ensure that the infected equilibrium is asymptotically stable for all delay. We also obtain the condition for existence of an orbitally asymptotically stable periodic solution.

• International Journal of Aerospace System Engineering
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• v.2 no.1
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• pp.12-17
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• 2015

Aero-optical effects induced by the flow around the optical window degrade the performance of the IR seeker, especially for the hypersonic flow. For the thermochemical non-equilibrium flow, index of refraction model and optical transmission calculation method are developed to predict the aero-optical effects. The optical distortion is discussed for the typical optical widow shape and flow condition. The influence on aero-optical effects is analyzed.

• Journal of Radiation Protection and Research
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• v.26 no.4
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• pp.399-408
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• 2001

The variation characteristics of radon concentration, equilibrium equivalent concentration and equilibrium factor in some houses and laboratory buildings have been studied. The variation of equilibrium factor and the unattached fraction of radon progeny with ventilation condition have been also estimated. The averages of radon concentration, equilibrium equivalent concentration and equilibrium factor were $30\;Bq\;m^{-3},\;19.6\;Bq\;m^{-3}$ and 0.65 in seven houses, while $55.0\;Bq\;m^{-3},\;31.9\;Bq\;m^{-3}$ and 0.58 in three laboratory buildings, respectively. The diurnal variation of radon concentration, equilibrium equivalent concentration and equilibrium factor in indoor showed a typical pattern that the radon concentration, equilibrium equivalent concentration and equilibrium factor increased at dawn and morning, while decreased at midday and evening. While the equilibrium factor rate deceased in the indoor environment which was well ventilated, the unattached traction of radon progeny increased. The equilibrium factor was in proportion to air pressure and humidity of indoor, whereas in Inverse proportion to temperature.

• The Korean Journal of Ceramics
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• v.2 no.4
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• pp.221-225
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• 1996

In diamond synthesis by metal film growth method under high pressure and high temperature, the nucleation and growth of diamond was observed dependent on the carbon source variation from graphite powder to the heat treated powders of lamp black carbon. At the low driving force condition near equilibrium pressure and temperature line, nucleation of diamond did not occur but growth of seed diamond appeared in the synthesis from lamp black carbon while both nucleation and growth of diamond took place in the synthesis from graphite. Growth morphology change of diamond occurred from cubo-octahedron to octahedron in the synthesis from graphite but very irregular growth of seed diamond occurred in the synthesis from lamp block carbon. Lamp black carbon transformed to recrystallized graphite first and very nucleation of diamond was observed on the recrystallized graphite surface. Growth morphology of diamond on the recrystallized graphite was clear cubo-octahedron even at higher pressure departure condition from equilibrium pressure and temperature line.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1993.10a
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• pp.212-217
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• 1993

A 2-dimensional FEM/GEM program was developed for analyzing forming processes of an arbitrarily shaped draw-die, in which plane strain condition is assumed and linear line elements are employed. FEM formulation adopted a new algorithm for solving force equilibrium as well as non-penetration condition simultaneously. For the case of numerical divergence at nearly final forming stages and the initial guess in Newton-Raphson iterations, geometric force equilibrium method(GEM) is also introduced. The developed program was tested with the simulation of stamping processes of automotive bonnet inner pannel in order to verify the usefulness and validity of FEM/GEM formulation.