• Journal of Korean Society for Atmospheric Environment
• /
• v.8 no.3
• /
• pp.162-168
• /
• 1992

Numerical solutions to the advection equations used for long-range transport air pollution models are calculated using three numerical methods; Antidiffusion correction method(Smolarkiewicz, 1983), Positive definite advecton scheme obtained by nonlinear renormalization of the advective fluxes(Bott, 1989), and Positive definite pseudospectral method(Bartnicki, 1989). Accuracy, numerical diffusion and computational time requirement are compared for two-dimensional transport calculations in a uniform rotational flow field. The solutions from three methods are positive definite. Bartnicki(1989)'s method is most conservative but requires approximately 10 times as much computational time as Smolarkiewicz(1983)'s method of which numerical diffusion is the largest. All three methods are more conservative for a cone shape initial condition than for a rectangular block initial condition with a steep gradient.

• Journal of the Korean Mathematical Society
• /
• v.36 no.1
• /
• pp.229-241
• /
• 1999

The fractal space is often associated with natural phenomena with many length scales and the functions defined on this space are usually not differentiable. First we define a $\sigma$-multifractal from $\sigma$-iterated function systems with probability. We introduce the measure derivative through the invariant measure of the $\sigma$-multifractal. We show that the non-differentiable function on the $\sigma$-multifractal can be differentiable with respect to this measure derivative. We apply this result to some examples of ordinary differential equations and diffusion processes on $\sigma$-multifractal spaces.

• Proceedings of the Korea Concrete Institute Conference
• /
• 1996.04a
• /
• pp.123-128
• /
• 1996

Water in concrete has an effect on properties of concrete very much, such as shrinkage, creep, fire resistance, durability, freezing and thawing resistance. Therefore predicting the moisture distribution in concrete is very important. And since the diffusion process of water in concrete is strongly dependent on the temperature and pore humidity, the process is highly nonlinear phenomena. In this study, a finite element program which was capable of simulating the moisture distribution in concrete was developed, and differential drying shrinkage due to the water diffusion process was measured at the different positions of concrete. This F.E.M. program is shown that the analytical results of this study are in good agreement with experimental data. Shrinkage strain caused by moisture distribution was increased with the decrease of pore relative humidity.

• KIEE International Transactions on Electrophysics and Applications
• /
• v.3C no.6
• /
• pp.246-251
• /
• 2003

We report the theory of thin-sample Z -scan for materials, viz. diffusion-dominated photorefractives, having a nonlinearly induced phase that may be proportional to the spatial derivative of the intensity profile. The on-axis far-field intensity is approximately an even function of the scan distance on different positive and negative values for phase shift $\Delta$$\Phi$$_{o}$. In case of positive phase shift, the Z -scan graph shows a minimum and two maxima, while for the negative value, only one minimum is observed. The fact is that far-field beam profiles display beam distortion and shift of the peak as compared with Kerr-type or photovoltaic nonlinearities.s.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.11 no.3
• /
• pp.7-20
• /
• 2007

We examined the steady state solution for a strongly exothermic mixtures in some class A geometries subjected to different boundary conditions under Arrhenius, Bimolecular and Sensitised reactions. The solution of the governing nonlinear reaction diffusion equation was obtained using the variational method formulation executed in Mathematica package. The paper elucidates the influence of geometry, boundary conditions and types of reaction on the thermal ignition of the reactive mixture. Apart from validating known results in literature, the solution gave further insight into the influence of material properties and conditions on the occurrence of thermal ignition.

• Bulletin of the Korean Chemical Society
• /
• v.15 no.3
• /
• pp.209-213
• /
• 1994

Two unknown values among three electrochemical values, i.e. electrode area, diffusion coefficient, and concentration, are simultaneously obtained by nonlinear regression analysis of a single chronoamperometric faradaic current curve at a microdisk electrode. The approach is an analytical application of the semi-empirical equation presented by Shoup and Szabo for the chronoamperometric response at a disk electrode. To demonstrate the usefulness and accuracy of this approach, the chronoamperometric current at a platinum disk electrode of 50 ${\mu}m$ radius in solutions of $Ru(NH_3)_6^{3+},\;ferrocene,\;Fe(CN)_6^{3-},\;and\;C_{60}$, were analyzed.

• Computers and Concrete
• /
• v.30 no.6
• /
• pp.409-419
• /
• 2022

The purpose of this study is to examine the effectiveness of biological repairing mortars on restoring the structural performance of a sewage culvert deteriorated by sulfate attack. The biological mortars were developed for protecting concrete structures exposed to sulfate attack based on the block membrane action of the bacterial glycocalyx. The diffusion coefficient of sulfate ions in the biological mortars was determined from the natural diffusion cell tests. The effect of sulfate-attack-induced concrete deterioration on the structural performance of culverts was examined by using the moment-curvature relationship predicted based on the nonlinear section lamina approach considering the sulfuric-acid-induced degradation of the structure. Typical analytical assessments showed that biological mortars were quite effective in increasing the sulfate-resistant service life of sewage culverts.

• Kyungpook Mathematical Journal
• /
• v.48 no.4
• /
• pp.593-611
• /
• 2008

Global attractivity and oscillatory behavior of the following nonlinear impulsive parabolic differential equation which is a general form of many population models $$\array{\{{{\frac {{\partial}u(t,x)}{{\partial}t}=\Delta}u(t,x)-{\delta}u(t,x)+f(u(t-\tau,x)),\;t{\neq}t_k,\\u(t^+_k,x)-u(t_k,x)=g_k(u(t_k,x)),\;k{\in}I_\infty,}\;\;\;\;\;\;\;\;(*)$$ are considered. Some new sufficient conditions for global attractivity and oscillation of the solutions of (*) with Neumann boundary condition are established. These results no only are true but also improve and complement existing results for (*) without diffusion or impulses. Moreover, when these results are applied to the Nicholson's blowflies model and the model of Hematopoiesis, some new results are obtained.

• Computers and Concrete
• /
• v.1 no.2
• /
• pp.131-150
• /
• 2004

We present in this work a coupled phenomenological chemo-mechanical model that represents the degradation of concrete-like materials. The chemical behaviour is described by the nowadays well known simplified calcium leaching approach. And the mechanical damage behaviour is described by a continuum damage model which involves the gradient of the damage quantity. The coupled nonlinear problem at hand is addressed within the context of the finite element method. For the equation governing the calcium dissolution-diffusion part of the problem, special care is taken to treat the highly nonlinear calcium conductivity and solid calcium functions. The algorithmic design is based on a Newton-type iterative scheme where use is made of a recently proposed relaxed linearization procedure. And for the equation governing the damage part of the problem, an augmented Lagrangian formulation is used to take into account the damage irreversibility constraint. Finally, numerical simulations are compared with experimental results on cement paste.

• Proceedings of the Korean Nuclear Society Conference
• /
• 1998.05a
• /
• pp.79-86
• /
• 1998

The nonlinear analytic function expansion nodal (AFEN) method is applied to the solution of the time-dependent neutron diffusion equation. Since the AFEN method requires both the particular solution and the homogeneous solution to the transient fixed source problem, the derivation solution method is focused on finding the particular solution efficiently. To avoid complicated particular solutions, the source distribution is approximated by quadratic polynomials and the transient source is constructed such that the error due to the quadratic approximation is minimized. In addition, this paper presents a new two-node solution scheme that is derived by imposing the constraint of current continuity at the interface corner points. The method is verified through a series of applications to the NEACRP PWR rod ejection benchmark problem.