• Journal of the Korean Operations Research and Management Science Society
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• v.34 no.4
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• pp.123-138
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• 2009

This study examined the first- and second-best pricing by stable dynamics in congested transportation networks. Stable dynamics, suggested by Nesterov and de Palma (2003), is a new model which describes and provides a stable state of congestion in urban transportation networks. The first-best pricing in user equilibrium models introduces user-equilibrium in the system-equilibrium by tolling the difference between the marginal social cost and the marginal private cost on each link. Nevertheless, the second-best pricing, which levies the toll on some, but not all, links, is relevant from the practical point of view. In comparison with the user equilibrium model, the stable dynamic model provides a solution equivalent to system-equilibrium if it is focused on link flows. Therefore the toll interval on each link, which keeps up the system-equilibrium, is more meaningful than the first-best pricing. In addition, the second-best pricing in stable dynamic models is the same as the first-best pricing since the toll interval is separately given by each link. As an effect of congestion pricing in stable dynamic models, we can remove the inefficiency of the network with inefficient Braess links by levying a toll on the Braess link. We present a numerical example applied to the network with 6 nodes and 9 links, including 2 Braess links.

• Journal of the Korean Operations Research and Management Science Society
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• v.32 no.3
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• pp.63-80
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• 2007

This study is a generalization of 'stable dynamics' recently suggested by Nesterov and de Palma[29]. Stable dynamics is a new model which describes and provides a stable state of congestion in urban transportation networks. In comparison with user equilibrium model that is common in analyzing transportation networks, stable dynamics requires few parameters and is coincident with intuitions and observations on the congestion. Therefore it is expected to be an useful analysis tool for transportation planners. An equilibrium in stable dynamics needs only maximum flow in each arc and Wardrop[33] Principle. In this study, we generalize the stable dynamics into the model with multiple traffic classes. We classify the traffic into the types of vehicle such as cars, buses and trucks. Driving behaviors classified by age, sex and income-level can also be classes. We develop an equilibrium with multiple traffic classes. We can find the equilibrium by solving the well-known network problem, multicommodity minimum cost network flow problem.

• Journal of the Korean Regional Science Association
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• v.13 no.2
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• pp.45-54
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• 1997

A regional economy is characterized as a spatial economy. However the literature shows that it has been treated as a point economy since space is little recognized in regional modeling due to mathematical complication. This leads to the fact that regional model does not sufficiently represent regional characteristic. This paper attempts to construct a regional growth model in a partial equilibrium framework specifically taking into consideration land as a primary factor. The model is formulated largely neoclassical. Labor is assumed to move in response to differences in the wage rate, while capital is perfectly mobile across regions. The paper shows that two growth equilibrium points exist, one stable equilibrium point and the other unstable equilibrium point. The unstable growth equilibrium indicates the existence of minimum threshold that a region must overcome the minimum threshold to grow constantly. Consequently, directions of regional growth are characterized by two growth paths depending on the initial condition of a region. That is to say, a region below the minimum threshold is converging toward the lower stable equilibrium point over time. When a regional economy initially lies above the minimum threshold, it will grow forever. A regional economy is not thus necessarily converging a stationary is not thus necessarily converging a stationary equilibrium point through factor movement. Finally, the impacts of the presence of agglomeration economies and diseconomies are analyzed through the phase diagram. The paper also shows that agglomeration economies result in lowering the minimum threshold and in escalating the level of stable equilibrium However, when agglomeration diseconomies prevail, the results are opposite, i.e., rising the minimum threshold of growth and lowering the growth level of stable equilibrium.

• 연구논문집
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• s.27
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• pp.183-200
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• 1997

We have calculated the energy of three distinct grain configurations, namely completely connected, partially connected and unconnected configurations, evolving during a spheroidization of polycrystalline thin film by extending a geometrical model due to Miller et al. to the case of spheroidization at both the surface and film-substrate interface. "Stabilitl" diagram defining a stable region of each grain configuration has been established in terms of the ratio of grain size to film thickness vs. equilibrium wetting or dihedral angles at various interface energy conditions. The occurrence of spheroidization at the film-substrate interface significantly enlarges the stable region of unconnected grain configuration thereby greatly facilitating the occurrence of agglomeration. Complete separation of grain boundary is increasingly difficult with a reduction of equilibrium wetting angle. The condition for the occurrence of agglomeration differs depending on the equilibrium wetting or dihedral angles. The agglomeration occurs, at low equilibrium angles, via partially connected configuration containing stable holes centered at grain boundary vertices, whereas it occurs directly via completely connected configuration at large equilibrium angles except for the case having small surface and/or film-substrate interface energy. The initiation condition of agglomeration is defined by the equilibrium boundary condition between the partially connected and unconnected configurations for the former case, whereas it can, for the latter case, largely deviate from the equilibrium boundary condition between the completely connected and unconnected configurations because of the presence of a finite energy barrier to overcome to reach the unconnected grain configuration.

• Journal of the Korean Operations Research and Management Science Society
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• v.32 no.4
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• pp.19-35
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• 2007

This study is for detecting the Braess Paradox by stable dynamics in general transportation networks. Stable dynamics, suggested by Nesterov and de Palma[18], is a new model which describes and provides a stable state of congestion in urban transportation networks. In comparison with user equilibrium model based on link latency function in analyzing transportation networks, stable dynamics requires few parameters and is coincident with intuitions and observations on the congestion. Therefore it is expected to be an useful analysis tool for transportation planners. The phenomenon that increasing capacity of a network, for example creating new links, may decrease its performance is called Braess Paradox. It has been studied intensively under user equilibrium model with link latency function since Braess[5] demonstrated a paradoxical example. However it is an open problem to detect the Braess Paradox under stable dynamics. In this study, we suggest a method to detect the Paradox in general networks under stable dynamics. In our model, we decide whether Braess Paradox will occur in a given network. We also find Braess links or Braess crosses if a network permits the paradox. We also show an example how to apply it in a network.

• Journal of Korean Association for Spatial Structures
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• v.18 no.3
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• pp.83-91
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• 2018

In this study, we investigated the dynamic stability of the system and the semi-analytical solution of the shallow arch. The governing equation for the primary symmetric mode of the arch under external load was derived and expressed simply by using parameters. The semi-analytical solution of the equation was obtained using the Taylor series and the stability of the system for the constant load was analyzed. As a result, we can classify equilibrium points by root of equilibrium equation, and classified stable, asymptotical stable and unstable resigns of equilibrium path. We observed stable points and attractors that appeared differently depending on the shape parameter h, and we can see the points where dynamic buckling occurs. Dynamic buckling of arches with initial condition did not occur in low shape parameter, and sensitive range of critical boundary was observed in low damping constants.

• Journal of the Korean Operations Research and Management Science Society
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• v.34 no.1
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• pp.61-83
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• 2009

This study developed a variable demand traffic assignment model by stable dynamics. Stable dynamics, suggested by Nesterov and do Palma[19], is a new model which describes and provides a stable state of congestion in urban transportation networks. In comparison with the user equilibrium model, which is based on the arc travel time function in analyzing transportation networks, stable dynamics requires few parameters and is coincident with intuitions and observations on congestion. It is therefore expected to be a useful analysis tool for transportation planners. In this study, we generalize the stable dynamics into the model with variable demands. We suggest a three stage optimization model. In the first stage, we introduce critical travel times and dummy links and determine variable demands and link flows by applying an optimization problem to an extended network with the dummy links. Then we determine link travel times and path flows in the following stages. We present a numerical example of the application of the model to a given network.

• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1117-1127
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• 2011

In this paper, a class of more general delayed viral infection model with lytic immune response is proposed by Song et al.[1] ([Journal of Mathematical Analysis Application 373 (2011), 345-355). We derive the basic reproduction numbers $R_0$ and $R_0^*$ 0 for the viral infection, and establish that the global dynamics are completely determined by the values of $R_0$ and $R_0^*$. If $R_0{\leq}1$, the viral-free equilibrium $E_0$ is globally asymptotically stable; if $R_0^*{\leq}1$ < $R_0$, the immune-free equilibrium $E_1$ is globally asymptotically stable; if $R_0^*$ > 1, the chronic-infection equilibrium $E_2$ is globally asymptotically stable by using the method of Lyapunov function.

• Structural Engineering and Mechanics
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• v.19 no.4
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• pp.413-423
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• 2005

This paper presents the solution of large static deflection due to uniformly distributed self weight and the critical or maximum applied uniform loading that a simply supported beam with variable-arc-length can resist. Two analytical approaches are presented and validated experimentally. The first approach is a finite-element discretization of the span length based on the variational formulation, which gives the solution of large static sag deflections for the stable equilibrium case. The second approach is the shooting method based on an elastica theory formulation. This method gives the results of the stable and unstable equilibrium configurations, and the critical uniform loading. Experimental studies were conducted to complement the analytical results for the stable equilibrium case. The measured large static configurations are found to be in good agreement with the two analytical approaches, and the critical uniform self weight obtained experimentally also shows good correlation with the shooting method.

• Journal of the Korean Society for Precision Engineering
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• v.29 no.1
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• pp.72-78
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• 2012

In this research an equilibrium point of a Wheeled Inverted Pendulum (WIP) running on an inclined road is derived and validated by some experiments. Generally, The WIP has stable and unstable equilibrium point. Only unstable equilibrium point is interested in the research. To keep the WIP on the unstable equilibrium point, the WIP is consistently controlled. A controller for the WIP needs a reference state for the equilibrium point. The reference state can be obtained by studying an equilibrium point of the WIP. This research is deriving dynamic equations of the WIP running on the inclined road and equilibrium of it based on statics. Several experiments are carried out to show the validation of the equilibrium point.