• 대한수학회논문집
• /
• 제21권4호
• /
• pp.701-717
• /
• 2006

The positive coexistence of a simple food chain model with ratio-dependent functional response and cross-diffusion is discussed. Especially, when a cross-diffusion is small enough, the existence of positive solutions of the system concerned can be expected. The extinction conditions for all three interacting species and for one or two of three species are studied. Moreover, when a cross-diffusion is sufficiently large, the extinction of prey species with cross-diffusion interaction to predator occurs. The method employed is the comparison argument for elliptic problem and fixed point theory in a positive cone on a Banach space.

• 대한수학회지
• /
• 제57권1호
• /
• pp.249-281
• /
• 2020

A reaction-diffusion model with spatiotemporal delay modeling the dynamical behavior of a single species is investigated. The parameter regions for the local stability, global stability and instability of the unique positive constant steady state solution are derived. The conditions of the occurrence of Turing (diffusion-driven) instability are obtained. The existence of time-periodic solutions, the existence and nonexistence of nonconstant positive steady state solutions are proved by bifurcation method and energy method. Numerical simulations are presented to verify and illustrate the theoretical results.

• Computers and Concrete
• /
• 제15권1호
• /
• pp.127-140
• /
• 2015

The process of chloride ingress in saturated concrete was presented by a previous study that used a mathematical model for the same as that concrete. This model is to be studied chloride ion diffusion which is considered as a chemical phenomenon and is to be represented the chloride diffusion process to be a nonlinear partial differential equation (PDE). In this paper, this nonlinear PDE is solved by the Kirchhoff transformation to render into a linear PDE. This linear PDE associated with initial and boundary conditions is also solved by the Laplace transformation to obtain an analytical solution. To verify the serviceability and reliability of this proposed method, the practical application should be supplied. The input parameters were cited from the previous study. The free chloride concentration profiles obtained by the analytical solution of mathematical model for saturated concretes after 24 and 120 hrs of exposure were compared with the previous study. The predicted results obtained from proposed method have a tendency with experimental results obtained by the previous study and trend toward numerical results approximated by finite difference technique.

• 대한기계학회논문집B
• /
• 제23권9호
• /
• pp.1185-1191
• /
• 1999

Radiation-induced oscillatory instability in diffusion flames is numerically investigated with nonlinear dynamics considered. As the simplest flame model, a diffusion flame established in the stagnant mixing layer is employed with optically thin gas-phase radiation and unity Lewis numbers for all species. Attention is focused on the radiation-induced extinction regime, which occurs at large $Damk\ddot{o}hler$ number. Once the steady flame structure is obtained for a prescribed value of the initial $Damk\ddot{o}hler$ number, transient solution of the flame is calculated after a finite amount of the $Damk\ddot{o}hler$-number perturbation is imposed on the steady flame. Transient evolution of the flame exhibits three types of flame-evolution behaviors, namely decaying oscillatory solution, diverging solution to extinction and stable limit-cycle solution. A dynamic extinction boundary is identified for laminar flamelet library.

• 대한수학회보
• /
• 제57권3호
• /
• pp.677-690
• /
• 2020

In this article, we study a reaction-diffusion system with homogeneous Dirichlet boundary conditions, which describing a three-species food chain model. Under some conditions, the predator-prey subsystem (u₁ ≡ 0) has a unique positive solution (${\bar{u_2}}$, ${\bar{u_3}}$). By using the birth rate of the prey r1 as a bifurcation parameter, a connected set of positive solutions of our system bifurcating from semi-trivial solution set (r₁, (0, ${\bar{u_2}}$, ${\bar{u_3}}$)) is obtained. Results are obtained by the use of degree theory in cones and sub and super solution techniques.

• 한국초전도ㆍ저온공학회논문지
• /
• 제5권2호
• /
• pp.66-70
• /
• 2003

Transient magnetic diffusion process in a melt-cast Bi2Sr2CaCu20X(Bi-2212) tube was studied by experimental and numerical analyses. The transient diffusion partial differential equation is transformed into an ordinary differential equation by integral method. The penetration depth of magnetic field into a superconducting tube is obtained by solving the differential equation numerically. The results show that the penetration depth as a function of time which is somewhat different from the results by Bean's critical state model. The reason of the difference between the present results and that of Bean's model is discussed and compared in this paper. This experiment measure the magnetic flux density in the supercondutor after supply direct-current of Bi-2212 rounded by copper coil. This study was discussed of valid of a previous numerical solution which is compared by the penetrate time and the magnetic flux density difference of between the present results and the numerical solution.

• 통합자연과학논문집
• /
• 제4권2호
• /
• pp.130-136
• /
• 2011

This study investigated the adsorption characteristics of nickel, zinc and cadmium ions from the aqueous solution onto the alginate bead. Adsorption equilibrium capacities of the heavy metal ions increased with increasing initial pH of the solution. The adsorption equilibrium isotherm of the heavy metal ions was well represented by Langmuir equation. The magnitude of adsorption capacity of the heavy metal ions onto alginate bead was the order of cadmium > zinc > nickel. Kinetic parameters were measured in a batch adsorber to analyze the adsorption rates of the heavy metal ions. The internal diffusion coefficient of the heavy metal ions in the intraparticle were determined by comparing the experimental concentration curves with those predicted from the surface diffusion model (SDM) and pore diffusion model (PDM). The internal diffusion of the heavy metal ions in the intraparticles was explained by PDM.

• 대한기계학회논문집B
• /
• 제25권1호
• /
• pp.29-35
• /
• 2001

Radiation-induced oscillatory instability in CH$_4$/Air diffusion flames is numerically investigated by adopting detailed chemistry. Counterflow diffusion flame is employed as a model flamelet and optically thin gas-phase radiation is assumed. Attention is focused on the extinction regime induced by radiative heat loss, which occurs at low strain rate. Once a steady flame structure is obtained for a prescribed value of initial strain rate, transient solution of the flame is calculated after a finite amount of strain-rate perturbation is imposed on the steady flame. Depending on the initial strain rate and the amount of perturbed strain rate, transient evolution of the flame exhibits various types of flame-evolution behaviors. Basically, the dynamic behaviors can be classified into two types, namely oscillatory decaying solution and diverging solution leading to extinction.

• 한국결정학회지
• /
• 제5권1호
• /
• pp.33-38
• /
• 1994

Hen egg white Iysozyme과 equine serum albumin을 모델 단백질로 하여 'heterogeneous' vapor diffusion실험을 수행하였다. 즉, droplet과 reseroir용액에 각각 다른 침전제를 사용하여 vapor diffusion에 의하여 평형에 이르도록 하였다. 실험 결과는 NSI 혹은 ammonium sulfate 대신 polyethylene glycol이 reservoir 용액에 포함되므로써 droplet과 reservoir 용액 사이의 평형 속도가 감소되는 것을 보여 주었다. Heterogeneous vapor diffusion 법을 통하여 reservoir용액에 포함된 이온성 염과 비이온성 침전제의 양을 적절히 조절하여 평형속도를 조절할 수 있음을 보였다.

• Journal of applied mathematics & informatics
• /
• 제26권1_2호
• /
• pp.29-44
• /
• 2008

By employing the continuation theorem of coincidence degree theory, we derive a sufficient condition for the existence and attractricity of a positive periodic solution for a generalized predator-prey model with diffussion feedback controls.