• Bulletin of the Korean Chemical Society
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• v.7 no.4
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• pp.283-288
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• 1986

A nonlinear analysis is presented for the treatment of fluctuations near the critical point in the presence of diffusion in the Schlogl models. The two time scaling method is used to obtain an evolution equation for the amplitude of fluctuations. It is shown that the fluctuations decay to zero in the stable region and they are enhanced to a finite value as time goes to infinity in the unstable region.

• Proceedings of the Korean Nuclear Society Conference
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• 1998.05b
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• pp.160-165
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• 1998

Under the heavy irradiation, when the production and the recombination of interstitials and vacancies are included, the diffusion equations become nonlinear. An effort has been made to arrange an appropriated transformation of these nonlinear differential equations to soluble Poisson's equations, so that analytical solutions for simultaneously calculating the concentrations of interstitials and vacancies in the angular dependent Cottrell's potential of the edge dislocation have been derived from the well-known Green's theorem and perturbation theory.

• Computers and Concrete
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• v.13 no.3
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• pp.361-375
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• 2014

The moisture transport in underground concrete was experimentally investigated and the nonlinear model of moisture transport considering the effects of water diffusion, hydration of cementicious materials and water permeability was proposed. The consumed moisture content by self-desiccation could be firstly calculated according to evolved hydration degree of cement and mineral admixtures. Furthermore, the finite differential method was adopted to solve the moisture transport model by linearizing the nonlinear moisture diffusion coefficient. The comparison between experimental and calculated results showed a good agreement, which indicated that the proposed moisture model could be used to predict moisture content evolution in underground concrete members with drying-wetting boundaries.

• Bulletin of the Korean Chemical Society
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• v.7 no.3
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• pp.224-228
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• 1986

A nonlinear theory is presented for the fluctuations of intermediates in the Brusselator near the critical point caused by diffusion. The method used is the two time scaling method different from the conventional method in the sense that a slight nonlinear effect is included in the initial time region where the linear approximation is conventionally valid. The result obtained by the nonlinear theory shows that fluctuations close to the critical point approach the value of a stable steady state or deviate infinitely from an unstable steady state, as time goes to infinity, while the linear theory gives approximately time-independent fluctuations. A brief discussion is given for the correlation at a time between fluctuating intermediates when the system approaches a stable steady state.

• Progress in Superconductivity and Cryogenics
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• v.5 no.1
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• pp.81-86
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• 2003

This paper presents a numerical analysis of transient magnetic diffusion in a melt-cast-processed BSCCO-2212 tube subjected to sinusoidal applied fields. The nonlinear f-$\lrcorner$ relation obtained by experiments in liquefied $N_2$ is used to find the magnetic diffusion coefficient. The magnetic flux density, shield current density and p-J$^2$ loss are considered. According to the result of this study, the shielding current density is varied with external applied field and coordinate in the superconductor tube. The result of analysis can be used to explain the response of a Supercon -ductor-Shield-Core-Reactor subjected to sinusoidal applied fields.

• Water Engineering Research
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• v.2 no.3
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• pp.187-196
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• 2001

An approximate analytical solution of a nonlinear hydro-thermo coupled diffusion equation is derived using the dimensionless form of the equation and transformation method. To derive an analytical solution, it is drastically assumed that the product of first order derivatives in the non-dimensionalized governing equation has little influence on the solution of heat and moisture behavior problem. The validity of this drastic assumption is demonstrated. Some numerical simulation is performed to investigate the applicability of a derived approximate analytical solution. The results show a good agreement between analytical and numerical solutions. The proposed solution may provide a useful tool in the verification process of the numerical models. Also, the solution can be used for the analysis of one-dimensional coupled heat and moisture movements in unsaturated porous media.

• Journal of the Korean Mathematical Society
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• v.51 no.3
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• pp.635-654
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• 2014

We consider the Cauchy problem for a Keller-Segel-fluid model with degenerate diffusion for cell density, which is mathematically formulated as a porus medium type of Keller-Segel equations coupled to viscous incompressible fluid equations. We establish the global-in-time existence of weak solutions and bounded weak solutions depending on some conditions of parameters such as chemotactic sensitivity and consumption rate of oxygen for certain range of diffusive exponents of cell density in two and three dimensions.

• Transactions on Control, Automation and Systems Engineering
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• v.1 no.1
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• pp.75-86
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• 1999

An air-data estimator for generic air-breathing hypersonic vehicles (AHSVs) is developed and demonstrated with an example vehicle configuration. The AHSV air-data estimation strategy emphasized improvement of the angle of attack estimate accuracy to a degree necessitated by the stringent operational requirements of the air-breathing propulsion. the resulting estimation problem involves highly nonlinear diffusion process (propagation); consequently, significant distortion of a posteriori conditional density is suspected. A simulation based statistical analysis tool is developed to characterize the nonlinear diffusion process. The statistical analysis results indicate that the diffusion process preserves the symmetry and unimodality of initial probability density shape state variables, and provide the basis for applicability of an Extended Kalman Filter (EKF). An EKF is designed for the AHSV air-data system and the air data estimation capabilities are demonstrated.

• Proceedings of the KSME Conference
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• 2003.11a
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• pp.320-325
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• 2003

Acoustic-Pressure Response of diluted hydrogen-air diffusion flames is investigated numerically by adopting a fully unsteady analysis of flame structures. In the low-pressure regime, the amplification index remains low and constant at low frequencies. As acoustic frequency increases, finite-rate chemistry is enhanced through a nonlinear accumulation of heat release rate, leading to a high amplification index. Finally, the flame responses decrease at high frequency due to the response lag of the transport zone. For a medium-pressure operation and low-frequency excitation, the amplification index is low and constant. It then decreases at moderate frequencies. As frequency increases further, the amplification index increases appreciably due to an intense accumulation effect.

• Communications for Statistical Applications and Methods
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• v.14 no.1
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• pp.241-254
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• 2007

This paper propose a new short-term interest rate model having a different nonlinear drift function and the same diffusion coefficient with Chan et al. (1992) model. The fractional polynomial power of the drift function in our model is linked to the local volatility elasticity of the diffusion coefficient. While the nonlinear drift function estimated by $A\"{\i}t$-Sahalia (1996a) and others has a feature that higher interest rates tend to revert downward and low rates upward, the drift function estimated by our nonlinear model shows that higher interest rate mean-reverts strongly, but, medium rates has almost zero drift and low rates has a very small drift. This characteristic coincides the empirical result based on the nonparametric methodology by Stanton (1997) and the implication by the scatter plot of the short rate data.