• Structural Engineering and Mechanics
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• 제1권1호
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• pp.47-60
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• 1993

The eigen-equation of a wave traveling over repetitive structure is derived directly form the stiffness matrix formulation, in a form which can be used for the case of the cross stiffness submatrix $K_{ab}$ being singular. The weighted adjoint symplectic orthonormality relation is proved first. Then the general method of solution is derived, which can be used either to find all the eigensolutions, or to find the main eigensolutions for large scale problems.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제21권1호
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• pp.1-16
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• 2017

The Allen-Cahn equation is solved numerically by operator splitting Fourier spectral methods. The basic idea of the operator splitting method is to decompose the original problem into sub-equations and compose the approximate solution of the original equation using the solutions of the subproblems. The purpose of this paper is to characterize higher order operator splitting schemes and propose several higher order methods. Unlike the first and the second order methods, each of the heat and the free-energy evolution operators has at least one backward evaluation in higher order methods. We investigate the effect of negative time steps on a general form of third order schemes and suggest three third order methods for better stability and accuracy. Two fourth order methods are also presented. The traveling wave solution and a spinodal decomposition problem are used to demonstrate numerical properties and the order of convergence of the proposed methods.

• 한국연소학회지
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• 제10권3호
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• pp.25-33
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• 2005

Fast-time instability is investigated for diffusion flames with Lewis numbers greater than unity by employing the numerical technique called the Evans function method. Since the time and length scales are those of the inner reactive-diffusive layer, the problem is equivalent to the instability problem for the $Li\tilde{n}\acute{a}n#s$ diffusion flame regime. The instability is primarily oscillatory, as seen from complex solution branches and can emerge prior to reaching the upper turning point of the S-curve, known as the $Li\tilde{n}\acute{a}n#s$ extinction condition. Depending on the Lewis number, the instability characteristics is found to be somewhat different. Below the critical Lewis number, $L_C$, the instability possesses primarily a pulsating nature in that the two real solution branches, existing for small wave numbers, merges at a finite wave number, at which a pair of complex conjugate solution branches bifurcate. For Lewis numbers greater than $L_C$, the solution branch for small reactant leakage is found to be purely complex with the maximum growth rate found at a finite wave number, thereby exhibiting a traveling nature. As the reactant leakage parameter is further increased, the instability characteristics turns into a pulsating type, similar to that for L < $L_C$.

• Geomechanics and Engineering
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• 제18권6호
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• pp.605-614
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• 2019

The present paper seeks to investigate propagation and reflection of waves at free surfaces of homogeneous, anisotropic and rotating micropolar fibre-reinforced medium with voids. It has been observed that, in particular when P-wave is incident on the free surface, there exist four coupled reflected plane waves traveling in the medium; quasi-longitudinal displacement (qLD) wave, quasi-transverse displacement (qTD) wave, quasi-transverse microrotational wave and a wave due to voids. Normal mode Analysis usually called harmonic solution method is adopted in concomitant with Snell's laws and appropriate boundary conditions in determination of solution to the micropolar fibre reinforced modelled problem. Amplitude ratios which correspond to reflected waves in vertical and horizontal components are presented analytically. Also, the Reflection Coefficients are presented using numerical simulated results in graphical form for a particular chosen material by the help of Mathematica software. We observed that the micropolar fibre-reinforced, voids and rotational parameters have various degrees of effects to the modulation, propagation and reflection of waves in the medium. The study would have impact to micropolar fibre-reinforecd rotational-acoustic machination fields and future works about behavior of seismic waves.

• 충청수학회지
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• 제30권3호
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• pp.323-329
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• 2017

In this paper, by rigorous calculations, we consider $L^2({\mathbb{R}})-spectrum$ of linear differential operators with periodic coefficients. These operators are usually seen in linearization of nonlinear partial differential equations about spatially periodic traveling wave solutions. Here, by using the solution operator obtained from Floquet theory, we prove rigorously that $L^2({\mathbb{R}})-spectrum$ of the linear operator is determined by the eigenvalues of Floquet matrix.

• Nuclear Engineering and Technology
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• 제49권6호
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• pp.1157-1164
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• 2017

The Monte Carlo criticality simulation of decoupled systems, as for instance in large reactor cores, has been a challenging issue for a long time. In particular, due to limited computer time resources, the number of neutrons simulated per generation is still many order of magnitudes below realistic statistics, even during the start-up phases of reactors. This limited number of neutrons triggers a strong clustering effect of the neutron population that affects Monte Carlo tallies. Below a certain threshold, not only is the variance affected but also the estimation of the eigenvectors. In this paper we will build a time-dependent diffusion equation that takes into account both spatial correlations and population control (fixed number of neutrons along generations). We will show that its solution obeys a traveling wave dynamic, and we will discuss the mechanism that explains this biasing of local tallies whenever leakage boundary conditions are applied to the system.

• Journal of Mechanical Science and Technology
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• 제16권10호
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• pp.1303-1313
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• 2002

Effects of the reduced frequency of upstream wake on downstream unsteady boundary layer flow were simulated by using a Wavier-Stokes code. The Wavier-Stokes code is based on an unstructured finite volume method and uses a low Reynolds number turbulence model to close the momentum equations. The geometry used in this paper is the MIT flapping foil experimental set-up and the reduced frequency of the upstream wake is varied in the range of 0.91 to 10.86 to study its effect on the unsteady boundary layer flow. Numerical solutions show that they can be divided into two categories. One is so called the low frequency solution, and behaves quite similar to a Stokes layer. Its characteristics is found to be quite similar to those due to either a temporal or spatial wave. The low frequency solutions are observed clearly when the reduced frequency is smaller than 3.26. The other one is the high frequency solution. It is observed for the reduced frequency larger than 7.24. It shows a sudden shift of the phase angle of the unsteady velocity around the edge of the boundary layer. The shift of phase angle is about 180 degree, and leads to separation of the boundary layer flow from corresponding outer flow. The high frequency solution shows the characteristics of a temporal wave whose wave length is half of the upstream frequency. This characteristics of the high frequency solution is found to be caused by the strong interaction between unsteady vortices. This strong interaction also leads to destroy of the upstream wake strips inside the viscous sublayer as well as the buffer layer.

• International Union of Geodesy and Geophysics Korean Journal of Geophysical Research
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• 제25권1호
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• pp.47-56
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• 1997

We present a theoretical study on how the plasmasphere responses to the sudden impulses in the magnetosphere. A mechanism on how Pi 2 pulsations are excited in the magnetosphere is also proposed. When impulsive disturbances associated with the substorm onset are assumed in the magnetotail, their propagation toward the sunward direction is investigated with a wave equation. The propagation speed undergoes serious variations owing to the existence of the plasmasphere, which results in various reflection and tunneling of traveling disturbances at the plasmapause. In order to examine the effect of the plasmapause on initial impulsive disturbances, we analytically solve the wave equation based on the model of reasonable Alfven speed profile. The exact solution shows that virtual resonant states exist inside the plasmaspheric cavity. We obtain the result that these unique modes strongly persist for arbitrary incoming impulses from the source in the magnetotail, which quantitatively corresponds to the signature of PI 2 pulsations.

• 한국방재학회 논문집
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• 제8권1호
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• pp.133-138
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• 2008

외해에서 내습하는 파랑 자료를 분석하는 일은 연안에서 발생하는 문제를 해결함에 있어 기본이 되기 때문에 매우 중요하다. 파랑을 해석하는 방법에는 크게 수치 모델을 이용하는 방법과 해석 해를 이용하는 방법이 있다. 수치 모델의 경우, 다양한 지형과 파랑 조건에 대해 적용할 수 있다는 장점이 있지만 수치 오차를 고려해야 하는 번거로움이 있다. 반면, 해석 해의 경우 수치 오차 없이 빠르고 정확하게 해를 구할 수 있다는 장점이 있지만 특정한 지형 및 파랑 조건에서만 성립한다는 단점이 있다. 본 연구에서는 수치적인 기법과 해석적인 접근을 혼합하여 수치 오차를 최소화시키면서 다양한 조건에 적용이 가능한 완경사 방정식의 해를 유도하였다. 유도된 해를 기존의 수치 해와 비교한 결과 매우 잘 일치한다는 알 수 있었다.

• Nuclear Engineering and Technology
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• 제45권6호
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• pp.731-744
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• 2013

Energy security is a topic of high importance to many countries throughout the world. Countries with access to vast energy supplies enjoy all of the economic and political benefits that come with controlling a highly sought after commodity. Given the desire to diversify away from fossil fuels due to rising environmental and economic concerns, there are limited technology options available for baseload electricity generation. Further complicating this issue is the desire for energy sources to be sustainable and globally scalable in addition to being economic and environmentally benign. Nuclear energy in its current form meets many but not all of these attributes. In order to address these limitations, TerraPower, LLC has developed the Traveling Wave Reactor (TWR) which is a near-term deployable and truly sustainable energy solution that is globally scalable for the indefinite future. The fast neutron spectrum allows up to a ~30-fold gain in fuel utilization efficiency when compared to conventional light water reactors utilizing enriched fuel. When compared to other fast reactors, TWRs represent the lowest cost alternative to enjoy the energy security benefits of an advanced nuclear fuel cycle without the associated proliferation concerns of chemical reprocessing. On a country level, this represents a significant savings in the energy generation infrastructure for several reasons 1) no reprocessing plants need to be built, 2) a reduced number of enrichment plants need to be built, 3) reduced waste production results in a lower repository capacity requirement and reduced waste transportation costs and 4) less uranium ore needs to be mined or purchased since natural or depleted uranium can be used directly as fuel. With advanced technological development and added cost, TWRs are also capable of reusing both their own used fuel and used fuel from LWRs, thereby eliminating the need for enrichment in the longer term and reducing the overall societal waste burden. This paper describes the origins and current status of the TWR development program at TerraPower, LLC. Some of the areas covered include the key TWR design challenges and brief descriptions of TWR-Prototype (TWR-P) reactor. Selected information on the TWR-P core designs are also provided in the areas of neutronic, thermal hydraulic and fuel performance. The TWR-P plant design is also described in such areas as; system design descriptions, mechanical design, and safety performance.