• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.16 no.4
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• pp.249-256
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• 2012

In this work, we analyze the spatial patterns of a predator-prey system with cross diffusion. First we get the critical lines of Hopf and Turing bifurcations in a spatial domain by using mathematical theory. More specifically, the exact Turing region is given in a two parameter space. Our results reveal that cross diffusion can induce stationary patterns which may be useful in understanding the dynamics of the real ecosystems better.

• Proceedings of the KSRS Conference
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• 2002.10a
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• pp.54-58
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• 2002

Mean curvature diffusion (MCD) is a selective smoothing technique that promotes smoothing within a region instead of smoothing across boundaries. By using mean curvature diffusion, noise is eliminated and edges are preserved. In this paper, we propose methods of automatic parameter selection and implementation for the MCD model coupled to min/max flow. The algorithm has been applied to high resolution aerial images and the results show that noise is eliminated and edges are preserved after removal of noise.

• Journal of the Economic Geographical Society of Korea
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• v.1 no.1
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• pp.137-149
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• 1998

It is likely that the spatial structure of the intraurban accessibility as well as the accessibility value of each of the nodes in the subway network is affected by the addition of new linkages. The changes in the accessibility at individual nodes also affect the accessibility in the surrounding areas at some distances away from the nodes. Graph-theoretic algorithms have been developed as a proper measurement scheme for the nodal accessibility in tracked transport networks such as subway networks. However, the graph-theoretic measurements have limitations to estimate the spatial diffusion effect on the surrounding areas. This study proposes a new model for the spatial diffusion effect estimation of nodal accessibility increment in the subway network toward the surrounding areas. Since the distance decay trend of subway station use reflect the spatial diffusion effect of the accessibility of subway station toward the surrounding area. The model is deduced from the subway station use density function which is formulated by the questionnaire survey data.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.385-400
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• 2009

The adverse effect of harmful plankton on the marine ecosystem is a topic of deep concern. To investigate the role of such phytoplankton, a mathematical model containing distinct dynamical equations for toxic and non-toxic phytoplankton is analyzed. Stability analysis of the resulting three equation model is carried out. A continuous time variation in toxin liberation process is incorporated into the model and a stability analysis of the resulting delay model is performed. The distributed delay model is then extended to include the spatial distribution of plankton and the delay-diffusion model is analyzed with spatial and spatiotemporal kernels. Conditions for diffusion-driven instability in both the cases are derived and compared to explore the significance of these kernels. Numerical studies are performed to justify analytical findings.

• Journal of Korean Society of Rural Planning
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• v.20 no.3
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• pp.67-74
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• 2014

The purpose of this study is to estimate regional economic effects of spatial diffusion of wildfire using Cobb-Douglas production function of agriculture and forestry. The analysis is applied to Gangwon and Gyeongbuk provinces where are the most damaged of wildfire in Korea. The damaged areas are derived from multiplied by the occurrence probability of wildfire and diffusion areas of wildfire for micro-spatial unit level with ArcGIS techniques. The models of wildfire provides that the spatial diffusion of wildfire increases with the rising of highest temperature and average wind speed. Through the production function, value added of Agriculture and Forest sectors get damaged where the Cos-converted slope aspect of mountains are toward the South. The production model provides reductions of regional value added by increasing damaged areas of wildfire. It reveals that the most damaged region is Andong city in Gyeongbuk province, where value added loss is 1.25 billion Won, which is about 0.72% of total value added in agriculture and forestry of the city. As a view of policy makers, it needs to be considered to establish prevention policies against wildfires because regional economic losses from wildfire are depending on geographical conditions and performances of the major industry related to wildfire's diffusion such as agriculture or tourism sector according to the result of analysis.

• Environmental Sciences Bulletin of The Korean Environmental Sciences Society
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• v.4 no.4
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• pp.263-271
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• 2000

To investigate the distribution of air pollutants dispersion in the horizontal wind fields, a chaff release experiment was carried out by an airplane. The temporal and spatial variations of a chaff plume from an elevated point source using the WSR-88D(NEXRAD) radar. The observed profiles of radar reflectivity were compared with the Gaussian diffusion model at slightly unstable atmospheric condition. The present study shows that the distributions of radar reflectivity from chaffs and their concentration by the model are in general agreement with time variation. The dispersion coefficients in downwind($\sigma$(sub)x) and crosswind($\sigma$(sub)y) spread data exceeded what has generally been found at Pasquill and Brigg\`s estimates. As a result, it was clearly shown that horizontal and vertical diffusion coefficients are more accurately determined as compared with theoretical coefficients. At longer diffusion distances(than 10km), a radar observation provided the determination of maximum range and diffusion height more qualitatively, too.

• Transactions of the Korean Society of Mechanical Engineers
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• v.11 no.3
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• pp.528-536
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• 1987

In a turbulent free shear flow, the large scale motion is characterized by the intermittent flow which arises from the interaction between the turbulent fluid and the irrotational fluid of the environment through the mean velocity gradient. This large scale motion causes a bulk convection whose effect is similar to the spatial diffusion process. In this paper, the total diffusion process is proposed to be approximated by weighted sum of the bulk convection due to the large scale motion and the usual gradient diffusion due to small scale motion. The diffusion term in conventional .kappa.-.epsilon. model requires on more equation of the intermittency transport equation. A production term of this equation means mass entrainment from the irrotational fluid to the turbulent one. In order to test the validity of the proposed model, a plane jet is predicted by this method. Numerical results of this model is found to yield better agreement with experiment than the standard .kappa.-.epsilon. model and Byggstoyl & Kollmann's model(1986). Present hybrid diffusion model requires further tests for the check of universality of model and for the model constant fix.

• Geomechanics and Engineering
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• v.23 no.2
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• pp.151-163
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• 2020

Grouting method is an effective way of reinforcing cracked rock masses and plugging water gushing. Current grouting diffusion models are generally developed for horizontal cracks, which is contradictory to the fact that the crack generally occurs in rock masses with irregular spatial distribution characteristics in real underground environments. To solve this problem, this study selected a cement-sodium silicate slurry (C-S slurry) generally used in engineering as a fast-curing grouting material and regarded the C-S slurry as a Bingham fluid with time-varying viscosity for analysis. Based on the theory of fluid mechanics, and by simultaneously considering the deadweight of slurry and characteristics of non-uniform spatial distribution of viscosity of fast-curing grouts, a theoretical model of slurry diffusion in an oblique crack in rock masses at constant grouting rate was established. Moreover, the viscosity and pressure distribution equations in the slurry diffusion zone were deduced, thus quantifying the relationship between grouting pressure, grouting time, and slurry diffusion distance. On this basis, by using a 3-d finite element program in multi-field coupled software Comsol, the numerical simulation results were compared with theoretical calculation values, further verifying the effectiveness of the theoretical model. In addition, through the analysis of two engineering case studies, the theoretical calculations and measured slurry diffusion radius were compared, to evaluate the application effects of the model in engineering practice. Finally, by using the established theoretical model, the influence of cracking in rock masses on the diffusion characteristics of slurry was analysed. The results demonstrate that the inclination angle of the crack in rock masses and azimuth angle of slurry diffusion affect slurry diffusion characteristics. More attention should be paid to the actual grouting process. The results can provide references for determining grouting parameters of fast-curing grouts in engineering practice.

• Korean Journal of Mathematics
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• v.13 no.2
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• pp.149-159
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• 2005

We study an age-dependent s-i-s epidemic model with spatial diffusion. The model equations are described by a nonlinear and nonlocal system of integro-differential equations. Finite difference methods along the characteristics in age-time domain combined with finite elements in the spatial variable are applied to approximate the solution of the model. Stability of the discrete periodic solution is investigated.