• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제13권1호
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• pp.21-29
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• 2009

This paper treats the conditions for the existence and stability properties of stationary solutions of a predator-prey interaction with self and cross-diffusion. We show that at a certain critical value a diffusion driven instability occurs, i.e. the stationary solution stays stable with respect to the kinetic system (the system without diffusion) but becomes unstable with respect to the system with diffusion and that Turing instability takes place. We note that the cross-diffusion increase or decrease a Turing space (the space which the emergence of spatial patterns is holding) compared to the Turing space with self-diffusion, i.e. the cross-diffusion response is an important factor that should not be ignored when pattern emerges.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제17권2호
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• pp.129-138
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• 2013

A spatio-temporal models as systems of ODE which describe two-species Beddington - DeAngelis type predator-prey system living in a habitat of two identical patches linked by migration is investigated. It is assumed in the model that the per capita migration rate of each species is influenced not only by its own but also by the other one's density, i.e. there is cross diffusion present. We show that a standard (self-diffusion) system may be either stable or unstable, a cross-diffusion response can stabilize an unstable standard system and destabilize a stable standard system. For the diffusively stable model, numerical studies show that at a critical value of the bifurcation parameter the system undergoes a Turing bifurcation and the cross migration response is an important factor that should not be ignored when pattern emerges.

• 대한수학회논문집
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• 제21권2호
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• pp.293-320
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• 2006

Using calculus inequalities and embedding theorems in $R^1$, we establish $W^1_2$-estimates for the solutions of prey-predator population model with cross-diffusion and self-diffusion terms. Two cases are considered; (i) $d_1\;=\;d_2,\;{\alpha}_{12}\;=\;{\alpha}_{21}\;=\;0$, and (ii) $0\;<\;{\alpha}_{21}\;<\;8_{\alpha}_{11},\;0\;<\;{\alpha}_{12}\;<\;8_{\alpha}_{22}$. It is proved that solutions are bounded uniformly pointwise, and that the uniform bounds remain independent of the growth of the diffusion coefficient in the system. Also, convergence results are obtained when $t\;{\to}\;{\infty}$ via suitable Liapunov functionals.

• 대한수학회보
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• 제43권2호
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• pp.443-459
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• 2006

The prey-predator system with a single cross-diffusion pressure is known to possess a local solution with the maximal existence time $T\;{\leq}\;{\infty}$. By obtaining the bounds of $W\array_2^1$-norms of the local solution independent of T we establish the global existence of the solution. And the long-time behaviors of the global solution are analyzed when the diffusion rates $d_1\;and\;d_2$ are sufficiently large.

• 대한수학회논문집
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• 제23권2호
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• pp.211-227
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• 2008

As a mathematical model proposed to understand the behaviors of interacting species, cross-diffusion systems with functional responses of prey-predator type are considered. In order to obtain $W^{1_2}$-estimates of the solutions, we make use of several forms of calculus inequalities and embedding theorems. We consider the quasilinear parabolic systems with the cross-diffusion terms, and without the self-diffusion terms because of the simplicity of computations. As the main result we derive the uniform $W^{1_2}$-bound of the solutions and obtain the global existence in time.

• 대한수학회보
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• 제41권2호
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• pp.371-385
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• 2004

In this paper, we investigate the uniqueness of positive solutions to weak competition models with self-cross diffusion rates under homogeneous Dirichlet boundary conditions. The methods employed are upper-lower solution technique and the variational characterization of eigenvalues.

• 한국연소학회지
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• 제4권1호
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• pp.105-115
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• 1999

The structure of a non-axisymmetric propane diffusion flame was investigated. Tomographic reconstruction method to convert the line-integrated self-emission data of a fuel-rich diffusion flame with square cross-section was applied to get the spatially reconstructed emission data. Modified Shepp-Logan filter and concentric squares raster were chosen for reconstructing arbitrarily shaped object in this process. Spatially reconstructed emission data were then interpreted to several physical quantities, such as flame edge, FWHM, perimeter and 3-D flame temperature distribution. Necessary assumptions were discussed and the results were interpreted. In comparison with axisymmetric flame, flame edge was developed higher, and sooting region of upstream was broader than in this non-axisymmetric one. At some height, the flame was shrunk very rapidly and finally formed circular cross-section.

• 한국해안해양공학회지
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• 제19권6호
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• pp.596-605
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• 2007

본 연구에서는 파랑이 존재하는 수역에서 수평방향으로 분사되는 비부력 원형 난류제트의 거동을 검토하기 위해 수리실험을 수행하였다. 난류제트의 유속은 PIV(particle image velocimetry)기법을 이용하여 측정하였으며, 측정된 순간유속장을 위상평균하여 평균유속장으로 계산하였다. 수리실험에서는 상대적으로 작은 파고의 규칙파가 사용되었으며, 파랑의 분산이 난류제트의 확산현상에 미치는 영향을 제트의 중심선유속과 횡단면유속의 변화를 통하여 관찰하였다. 또한 파랑의 위상변화에 따른 제트 거동을 파악하기 위하여 다른 세 위상순간에서 제트의 거동을 비교하였다. 제트의 중심선유속은 파고가 커짐에 따라 감소하였으며, 횡단면의 폭은 증가함을 알 수 있었다. 제트의 횡단면유속분포 특성인 자기상사성은 파고가 증가할수록 약해졌으나 축방향으로의 단면폭의 변화는 크지 않았다. 또한 파고에 대한 제트의 변화에 비해 파랑 위상에 대해서는 변화가 작음을 알 수 있었다.

• 한국막학회:학술대회논문집
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• 한국막학회 1999년도 The 7th Summer Workshop of the Membrane Society of Korea
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• pp.27-30
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• 1999

Poly(phenylene oxide)s were used to prepare flat, integrally skinned self-supporthed asymmetric membranes by dry-wet phase separption. The intrinsic ideal gas selectivity of poly- (2,6-dimethy-1,4-phenylene oxide) (PMPO) was retained in the membranes, and improved by a coating with silicone rubber. Polymers of the same class were coated of UF supports with a silicon rubber gutter layer, yielding composite membranes with high flux but lower selectivity. The effect of th glutaraldehyde cross-linking of sodium alginate (SA) membranes on the mobility of water and ethanol has been studied with pfg nmr. Crosslinking reduces water self-diffusion, and does not seem to be stable on the timescale of weeks.

• 소성∙가공
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• 제17권8호
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• pp.558-563
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• 2008

The initial strain, the applied stress exponent, the activation energy, and rupture time in AZ31 magnesium alloy have been measured in order to predict the deformation mechanism and rupture life of creep over the temperature range of 423-443K. Creep tests were carried out under constant applied stress and temperature, and the lever type tester and automatic temperature controller was used for it, respectively. The experimental results showed that the applied stress exponent was about 9.74, and the activation energy for creep, 113.6KJ/mol was less than that of the self diffusion of Mg alloy including aluminum. From the results, the mechanism for creep deformation seems to be controlled by cross slip at the temperature range of 423-443K. Also the higher the applied stress and temperature, the higher the initial strain. And the rupture time for creep decreased as quadratic function with increasing the initial strain in double logarithmic axis.