• Bulletin of the Korean Chemical Society
• /
• v.20 no.1
• /
• pp.35-41
• /
• 1999

Stability characteristics of hyperbolic reaction-diffusion equations with a reversible Brusselator model are investigated as an extension of the previous work. Intensive stability analysis is performed for three important parameters, Nrd, β and Dx, where Nrd is the reaction-diffusion number which is a measure of hyperbolicity, β is a measure of reversibility of autocatalytic reaction and Dx is a diffusion coefficient of intermediate X. Especially, the dependence on Nrd of stability exhibits some interesting features, such as hyperbolicity in the small Nrd region and parabolicity in the large Nrd region. The hyperbolic reaction-diffusion equations are solved numerically by a spectral method which is modified and adjusted to hyperbolic partial differential equations. The numerical method gives good accuracy and efficiency even in a stiff region in the case of small Nrd, and it can be extended to a two-dimensional system. Four types of solution, spatially homogeneous, spatially oscillatory, spatio-temporally oscillatory and chaotic can be obtained. Entropy productions for reaction are also calculated to get some crucial information related to the bifurcation of the system. At the bifurcation point, entropy production changes discontinuously and it shows that different structures of the system have different modes in the dissipative process required to maintain the structure of the system. But it appears that magnitude of entropy production in each structure give no important information related for states of system itself.

• Transactions of Materials Processing
• /
• v.30 no.5
• /
• pp.226-235
• /
• 2021

The strain aging behavior of a low carbon dual phase steel was examined in two conditions: representing room temperature strain aging (100 ℃ × 1 hr after 7.5 % prestrain) and bake hardening process (170 ℃ × 20 min after 2 % prestrain), basing on carbon effective diffusion and dislocation distribution. The first principle calculations revealed that (Mn or Cr)-vacancy-C complexes exhibit the strongest attractive interaction compared to other complexes, therefore, act as strong trapping sites for carbon. For room temperature strain aging condition, the carbon effective diffusion distance is smaller than the dislocation distance in the high dislocation density region near ferrite/martensite interfaces as well as ferrite interior considering the carbon trapping effect of the (Mn or Cr)-vacancy-C complexes, implying ineffective Cottrell atmosphere formation. Under bake hardening condition, the carbon effective diffusion distance is larger compared to the dislocation distance in both regions. Therefore, formation of the Cottrell atmosphere is relatively easy resulting in to a relatively large increase in yield strength under bake hardening condition.

• Communications of the Korean Mathematical Society
• /
• v.21 no.3
• /
• pp.543-558
• /
• 2006

We consider a type of large deviation Principle(LDP) using Freidlin-Wentzell exponential estimates for the solutions to perturbed stochastic differential equations(SDEs) driven by Martingale measure(Gaussian noise). We are using exponential tail estimates and exit probability of a diffusion process. Referring to Freidlin-Wentzell inequality, we want to show another approach to get LDP for the solutions to SDEs.

• Journal of the Korean Geographical Society
• /
• v.36 no.1
• /
• pp.52-65
• /
• 2001

Between 1985 and 1997 the diffusion of private passenger cars first occurred in major cities such as Seoul, Busan, Daegu and the satellite cities of the capital city that enjoyed high incomes and advanced service industries and then it gradually expanded to industrial and major provincial cities while posting a downturn in the major cities. Factor contrbuting to this phenomenon most significantly was the rate of employment in the financial insurance, real estate, and business service sectors in 1985 and 1990. The most ingluential factor in 1997 was the rate of employment in agriculture, hunting, forestry, and fishery. When measured against 1991 as a yardstick, the spatiotemporal ditribution rate of private passenger cars was highly between 1985 and 1990 in Seoul's satellite cities and major regional cities, showing a large inter-regional gap in terms of diffusion rate. The period from 1991 to 1997 showed a high rate of diffusion in cities within the capital region as well as in major regional cities, but inter-regional diffusion rate became similar. Key factors responsible for regional types of the diffusion were {1}the rate of employment in the service industrier and income in the major citier, and (2)the geogtaphic distamce between counties and Seoul plus the size of population in the county regions.

• Bulletin of the Korean Chemical Society
• /
• v.33 no.2
• /
• pp.735-738
• /
• 2012

• Proceedings of the Korea Air Pollution Research Association Conference
• /
• 2006.04a
• /
• pp.259-260
• /
• 2006

• Korean Journal of Mathematics
• /
• v.4 no.1
• /
• pp.39-43
• /
• 1996

Large-time asymptotic behavior of the solutions of interacting population reaction-diffusion systems are considered. Polynomial stability was proved.

• The Bulletin of The Korean Astronomical Society
• /
• v.46 no.2
• /
• pp.47.3-48
• /
• 2021

We studied the large scale dynamo process in a system forced by helical magnetic field. The dynamo process is basically nonlinear, but can be linearized with 𝛼&𝛽 coefficients and large scale magnetic field $\bar{B}$. This is very useful to the investigation of solar (stellar) dynamo. A coupled semi-analytic equations based on statistical mechanics are used to investigate the exact evolution of 𝛼&𝛽. This equation set needs only magnetic helicity ${\bar{H}}_M({\equiv}{\langle}{\bar{A}}{\cdot}{\bar{B}}{\rangle},\;{\bar{B}}={\nabla}{\times}{\bar{A}})$ and magnetic energy ${\bar{E}}_M({\equiv}{\langle}{\bar{B}}^2{\rangle}/2)$. They are fundamental physics quantities that can be obtained from the dynamo simulation or observation without any artificial modification or assumption. 𝛼 effect is thought to be related to magnetic field amplification. However, in reality the averaged 𝛼 effect decreases very quickly without a significant contribution to ${\bar{B}}$ field amplification. Conversely, 𝛽 effect contributing to the magnetic diffusion maintains a negative value, which plays a key role in the amplification with Laplacian ∇²(= - k²) for the large scale regime. In addition, negative magnetic diffusion accounts for the attenuation of plasma kinetic energy E_V(= 〈 U² 〉/2) (U: plasma velocity) when the system is saturated. The negative magnetic diffusion is from the interaction of advective term - U • ∇ B from magnetic induction equation and the helical velocity field. In more detail, when 'U' is divided into the poloidal component U_pol and toroidal one U_tor in the absence of reflection symmetry, they interact with - B • ∇ U and - U • ∇ B from ∇ × 〈 U × B 〉 leading to 𝛼 effect and (negative) 𝛽 effect, respectively. We discussed this process using the theoretical method and intuitive field structure model supported by the simulation result.

• Current Photovoltaic Research
• /
• v.2 no.2
• /
• pp.59-62
• /
• 2014

Minority carrier diffusion length is one of the most important parameters of solar cells, especially for short circuit current density (Jsc). In this report, we proposed the calculating method of the minority carrier diffusion length ($L_n$) in CIGS solar cells through biased quantum efficiency (QE). To verify this method's reliability, we chose two CIGS samples which have different grain size and calculated $L_n$ for each sample. First of all, we calculated out that $L_n$ was 56nm and 97nm for small and large grain sized-cell through this method, respectively. Second, we found out the large grain sized-cell has about 7 times lower defect density than the small grain sized-cell using drive level capacitance profiling (DLCP) method. Consequently, we confirmed that $L_n$ was mainly affected by the micro-structure and defect density of CIGS layer, and could explain the cause of Jsc difference between two samples having same band gap.

• Tribology and Lubricants
• /
• v.28 no.2
• /
• pp.56-61
• /
• 2012

In order to investigate the possibility of Ni-Al based intermetallics coating onto aluminum substrate, the coating process for induction heating has been evaluated by microscopically analyzing the intermetallic layers coated at temperatures lower than the melting temperature of aluminum. The coating layers were divided into two parts with different microstructure along the depth. Hard $NiAl_3$ layer was found at lower parts of the coatings near the interface with aluminum substrate. This layer was formed by the diffusion of aluminum atoms from the substrate into the coating layer across the interface during the induction heating. Meanwhile, at the upper parts of the coating near the surface, a large amount of un-reacted Ni was still remained and surrounded by several Ni-Al based intermetallic compounds, such as $Ni_3Al$, NiAl and $Ni_2Al_3$ formed by the lattice diffusion.