• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.141-152
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• 2007

In this paper a numerical method is presented to solve singularly perturbed two points boundary value problems for second order ordinary differential equations consisting a discontinuous source term. First, in this method, an asymptotic expansion approximation of the solution of the boundary value problem is constructed using the basic ideas of a well known perturbation method WKB. Then some initial value problems and terminal value problems are constructed such that their solutions are the terms of this asymptotic expansion. These initial value problems are happened to be singularly perturbed problems and therefore fitted mesh method (Shishkin mesh) are used to solve these problems. Necessary error estimates are derived and examples provided to illustrate the method.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2017.05a
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• pp.47-53
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• 2017

One of the most common causes of failure of space launch vehicles is combustion instability. Combustion instability is a phenomenon that the pressure perturbation inside the combustion chamber is greatly amplified due to the interaction of the pressure perturbation inside the combustion chamber and the heat release perturbation. When this phenomenon becomes worse, an engine failure or launch vehicle crash occurs. In order to predict and avoid such combustion instability, understanding of the phenomenon is indispensable, and numerical, theoretical, and experimental approaches to combustion instability have been carried out worldwidely.

• Nuclear Engineering and Technology
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• v.49 no.6
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• pp.1181-1188
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• 2017

This paper proposes the adoption of Monte Carlo perturbation theory to approximate the Jacobian matrix of coupled neutronics/thermal-hydraulics problems. The projected Jacobian is obtained from the eigenvalue decomposition of the fission matrix, and it is adopted to solve the coupled problem via the Newton method. This avoids numerical differentiations commonly adopted in Jacobian-free Newton-Krylov methods that tend to become expensive and inaccurate in the presence of Monte Carlo statistical errors in the residual. The proposed approach is presented and preliminarily demonstrated for a simple two-dimensional pressurized water reactor case study.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.300-306
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• 2004

This paper is concerned with the application of perturbation method to the dynamic analysis of free-free beam. In general, the rigid-body motions and elastic vibrations are analyzed separately. However, the rigid-body motions cause vibrations and elastic vibrations also affect rigid-body motions in turn, which indicates that the rigid-body motions and elastic vibrations are coupled in nature. The resulting equations of motion are hybrid and nonlinear. We can discretize the equations of motion by means of admissible functions but still we have to cope with nonlinear equations. In this paper, we propose the use of .perturbation method to the coupled equations of motion. The resulting equations consist of zero-order equations of motion which depict the rigid-body motions and first-order equations of motion which depict the perturbed rigid-body motions and elastic vibrations. Numerical results show the efficacy of the proposed method.

• Advances in nano research
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• v.15 no.5
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• pp.385-399
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• 2023

Hexagonal boron nitride (h-BN), commonly referred to as Boron Nitride Nanoribbons (BNNRs), is an electrical insulator characterized by high thermal stability and a wide bandgap semiconductor property. This study delves into the electronic properties of two BNNR configurations: Armchair BNNRs (ABNNRs) and Zigzag BNNRs (ZBNNRs). Utilizing the nearest-neighbour tight-binding approach and numerical methods, the electronic properties of BNNRs were simulated. A simplifying assumption, the Hamiltonian matrix is used to compute the electronic properties by considering the self-interaction energy of a unit cell and the interaction energy between the unit cells. The edge perturbation is applied to the selected atoms of ABNNRs and ZBNNRs to simulate the electronic properties changes. This simulation work is done by generating a custom script using numerical computational methods in MATLAB software. When benchmarked against a reference study, our results aligned closely in terms of band structure and bandgap energy for ABNNRs. However, variations were observed in the peak values of the continuous curves for the local density of states. This discrepancy can be attributed to the use of numerical methods in our study, in contrast to the semi-analytical approach adopted in the reference work.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.35 no.3
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• pp.287-291
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• 2011

We solve the simple physical model for liquid pool spreading with vaporization semi-analytically for the first time, using perturbation techniques. The results are compared with those obtained using numerical methods. We use the evaporation rate per unit area as a perturbation parameter, and first-order solutions are obtained for continuous and instantaneous release. The two solutions are nearly identical with respect to the pool radius. The pool volumes are nearly the same at the early stage of the spread and then start to diverge.

• Journal of Institute of Control, Robotics and Systems
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• v.18 no.11
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• pp.989-996
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• 2012

The purpose of this paper is to analyze GPS (Global Positioning System) satellite orbital mechanics, and then to propose a novel long-term GPS satellite orbit prediction scheme including virtual planet perturbation. The GPS orbital information is a necessary prerequisite to pinpointing the location of a GPS receiver. When a GPS receiver has been shut down for a long time, however, the time needed to fix it before its reuse is too long due to the long-standing GPS orbital information. To overcome this problem, the GPS orbital mechanics was studied, such as Newton's equation of motion for the GPS satellite, including the non-spherical Earth effect, the luni-solar attraction, and residual perturbations. The residual perturbations are modeled as a virtual planet using the least-square algorithm for a moment. Through the modeling of the virtual planet with the aforementioned orbital mechanics, a novel GPS orbit prediction scheme is proposed. The numerical results showed that the prediction error was dramatically reduced after the inclusion of virtual planet perturbation.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1992.10a
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• pp.117-123
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• 1992

In recent years, the finite element method has become one of the most popular numerical technique for obtaining solutions of engineering science problems. However, there exist various uncertainties in modeling the problems, such as the dimensions(geometry shape), the material properties, boundary conditions, etc. The consideration for the uncertainties inherent in the problems can be made by understanding the influences of uncertain parameters[1]. Determining the influences of uncertainties as statistical quantities using the standard finite element method requires enormous computing time, while the probabilistic finite element method is realized as an efficient scheme[2,3] yielding statistical solution with just a few direct computations. In this paper, a formulation of the probabilistic fluid-structure interaction problem accounting for the first order perturbation of geometric shape is derived, and especially probabilistical acoustic pressure scattering from the structure with surrounding fluid is focused on. In Section 2, governing equations for the fluid-structure problems are given. In Section 3, a finite element formulation, based on the functional, is presented. First order perturbation of geometric shape with randomness is incorporated into the finite element formulation in conjunction with discretization of the random fields in Section 4 and 5. Finally, the proposed formulation is applied to a acoustic pressure scattering problem from an infinitely long cylindrical shell structure with randomness of radial perturbation.

• Journal of Astronomy and Space Sciences
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• v.22 no.4
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• pp.513-526
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• 2005

The objectives of this study are to perform extensive analysis on internal mass motion for a wider parameter space and to provide suitable design criteria for a broader applicability for the class of spinning space vehicles. In order to examine the stability criterion determined by a perturbation method, some numerical simulations will be performed and compared at various parameter points. In this paper, Ince-Strutt diagram for determination of stable-unstable regions of the internal mass motion of the spinning thrusting space vehicle in terms of design parameters will be obtained by an analytical method. Also, phase trajectories of the motion will be obtained for various parameter values and their characteristics are compared.

• Journal of the Chungcheong Mathematical Society
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• v.6 no.1
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• pp.25-43
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• 1993

This paper introduces a numerical method approximating the minimum norm solution to the first kind integral equation Kf = g with its kernel satisfying a certain property, where g belongs to the range space of K. Most of the existing expansion methods suffer from choosing a set of basis functions, whereas this method automatically provides an optimal set of basis functions approximating the minimum norm solution of Kf = g. Perturbation results and numerical experiments are also provided to analyze this method.