• Nuclear Engineering and Technology
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• 제55권6호
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• pp.2172-2194
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• 2023

A variational nodal method (VNM) with unstructured-mesh is presented for solving steady-state and dynamic neutron diffusion equations. Orthogonal polynomials are employed for spatial discretization, and the stiffness confinement method (SCM) is implemented for temporal discretization. Coordinate transformation relations are derived to map unstructured triangular nodes to a standard node. Methods for constructing triangular prism space trial functions and identifying unique nodes are elaborated. Additionally, the partitioned matrix (PM) and generalized partitioned matrix (GPM) methods are proposed to accelerate the within-group and power iterations. Neutron diffusion problems with different fuel assembly geometries validate the method. With less than 5 pcm eigenvalue (k_eff) error and 1% relative power error, the accuracy is comparable to reference methods. In addition, a test case based on the kilowatt heat pipe reactor, KRUSTY, is created, simulated, and evaluated to illustrate the method's precision and geometrical flexibility. The Dodds problem with a step transient perturbation proves that the SCM allows for sufficiently accurate power predictions even with a large time-step of approximately 0.1 s. In addition, combining the PM and GPM results in a speedup ratio of 2-3.

• Journal of the Korean Data and Information Science Society
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• 제27권1호
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• pp.265-274
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• 2016

In this paper, we consider a diffusion risk process, in which, its surplus process behaves like a Brownian motion in-between adjacent epochs of claims. We assume that the claims occur following a Poisson process and their sizes are independent and exponentially distributed with the same intensity. Our main goal is to derive the exact formula of the joint moment generating function of the ruin time and the total amount of aggregated claim sizes until ruin in the diffusion risk process. We also provide a method for computing the related first and second moments using the joint moment generating function and the augmented matrix exponential function.

• 대한치과보철학회지
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• 제30권4호
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• pp.481-492
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• 1992

Author measured the bonding strength between Dental Porcelain and Nonprecious Dental Alloy and analyzed diffusion Phenomena at the interfaceby by Auger electron spectroscopy and also Electron spectroscopy for Chemical Analysis. The each specimen was sputtered with Al, Cr, In and Sn. 1. Ni whic is the main element of the matris of dental nonprecious alloy diffuse more than the other element and the Ni diffusion rate of each specimen was well coordinated with the bonding strength of each. 2. The Sn thin film suppress the diffusion rate of Ni of matrix into the Dental Porcelain than the In or Cr thin films. 3. The Al thin film suppress the diffusion rate of Ni than the Sn thin film. 4. The main coponent of dental porcelain : Al, Si, Mo diffused into the matrix of alloy. It means that the each element of dental alloy and dental porelain diffused into the each other part.

• 한국원자력학회:학술대회논문집
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• 한국원자력학회 2001년도 추계학술발표회요약집
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• pp.276.1-276
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• 2001

• Journal of applied mathematics & informatics
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• 제6권2호
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• pp.455-466
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• 1999

In this note we present a numerical scheme for finding an approxximate solution of an equation which can be viewed as a model for spatial diffusion of age-depednent biological populations. Discretization of the model yields a linear system with a block tridi-agonal matrix. Our main concern will be discussion of stability for this scheme by examining the eigenvalues of the block tridiagonal matrix. Numerical results are presented.

• Bulletin of the Korean Chemical Society
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• 제12권6호
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• pp.692-698
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• 1991

The reaction path Smoluchowski equation approach developed in a recent work to calculate the rate constant for a diffusive multidimensional barrier crossing process is extended to incorporate the configuration-dependent diffusion matrix. The resulting formalism is then applied to the investigation of stilbene photoisomerization dynamics. Adapting a model two-dimensional potential and a model diffusion matrix proposed by Agmon and Kosloff [J. Phys. Chem.,91 (1987) 1988], we derive an eigenvalue equlation for the relaxation rate constant of the stilbene photoisomerization. This eigenvalue equation is solved numerically by using the finite element method. The advantages and limitations of the present method are discussed.

• Nuclear Engineering and Technology
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• 제34권3호
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• pp.218-231
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• 2002

Using a three-dimensional numerical code, B3R developed for nuclide transport of an arbitrary length of decay chain in the buffer between the canister and adjacent rock in a high- level radioactive waste repository by adopting a finite difference method utilizing the control- volume scheme, some illustrative calculations have been done. A linear sorption isotherm, nuclide transport due to diffusion in the buffer and the rock matrix, and advection and dispersion along thin rigid parallel fractures existing in a saturated porous rock matrix as well as diffusion through the fracture wall into the matrix is assumed. In such kind of repository, buffer and rock matrix are known to be important physico-chemical harriers in nuclide retardation. To show effects of buffer and rock matrix on nuclide transport in HLW repository and also to demonstrate usefulness of B3R, several cases of breakthrough curves as well as three- dimensional plots of concentration isopleths associated with these two barriers are introduced for a typical case of decay chain of $^{234}$ Ulongrightarrow$^{230}$ Thlongrightarrow$^{226}$ Ra, which is the most important chain as far as the human environment is concerned.

• Corrosion Science and Technology
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• 제8권2호
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• pp.81-88
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• 2009

Chloride induced corrosion of steel reinforcement inside concrete is a major concern for concrete structures exposed to a marine environment. It is well known that transport of chloride ions in concrete occurs mainly through ionic/molecular diffusion, as a gradient of chloride concentration in the concrete pore solution is set. In the process of chloride transport, a portion of chlorides are bound in cement matrix then to be removed in the pore solution, and thus only the rest of chlorides which are not bound (i.e. free chlorides) leads the ingress of chlorides. However, since the measurement of free/bound chloride content is much susceptible to environmental conditions, chloride profiles expressed in total chlorides are evaluated to use in many studies In this study, the capacity of chloride binding in cement matrix was monitored for 150 days and then quantified using the Langmuir isotherm to determine the portions of free chlorides and bound chlorides at given total chlorides and the redistribution of free chlorides. Then, the diffusion of chloride ion in concrete was modeled by considering the binding capacity for the prediction of chloride profiles with the redistribution. The predicted chloride profiles were compared to those obtained from conventional model. It was found that the prediction of chloride profiles obtained by the model has shown slower diffusion than those by the conventional ones. This reflects that the prediction by total chloride may overestimate the ingress of chlorides by neglecting the redistribution of free chlorides caused by the binding capacity of cement matrix. From the evaluation, it is also shown that the service life prediction using the free chloride redistribution model needs different expression for the chloride threshold level which is expressed by the total chlorides in the conventional diffusion model.

• 한국콘크리트학회:학술대회논문집
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• 한국콘크리트학회 2003년도 봄 학술발표회 논문집
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• pp.711-714
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• 2003

Factors causing deterioration of concrete structures under marine environment are various, especially penetration and diffusion of chloride ion, carbon dioxide, and water through pore effects on the durability of concrete as well as mechanical properties of concrete. Pore of porous materials like concrete can be classified as micro-, meso-, and macro-pore. And pore of cement matrix is classified as pore which occupied by water, air void, and ITZ between cement paste and aggregates. In this study, to verify the relationship between pore of cement matrix and the property of chloride ion diffusivity, the regression analysis is producted. From the result of regression analysis, the average pore diameter more than total pore volume effects on the diffusivity of chloride ion.

• Journal of applied mathematics & informatics
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• 제38권5_6호
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• pp.489-506
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• 2020

The spatial fractional diffusion equation can be discretized by employing the implicit finite difference scheme using the shifted Grünwald formula. The discretized linear system is obtained, whose the coefficient matrix has a diagonal-plus-Toeplitz structure. In order to solve the diagonal-plus-Toeplitz linear system, on the basis of circulant and skew-circulant splitting (CSCS splitting), we construct a new and efficient iterative method, called DSCS iterative methods, which have two parameters. Than we prove the convergence of DSCS methods. As a focus, we derive the simple and effective values of two optimal parameters under some restrictions. Some numerical experiments are carried out to illustrate the validity and accuracy of the new methods.