• Journal of the Korean Mathematical Society
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• v.58 no.3
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• pp.553-569
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• 2021

In this paper, we present and analyze a fully discrete numerical method for solving the time-fractional diffusion wave equation: ∂^β_tu - div(a∇u) = f, 1 < β < 2. We first construct a difference formula to approximate ∂^β_tu by using an interpolation of derivative type. The truncation error of this formula is of O(△t^2+δ-β)-order if function u(t) ∈ C^2,δ[0, T] where 0 ≤ δ ≤ 1 is the Hölder continuity index. This error order can come up to O(△t^3-β) if u(t) ∈ C³ [0, T]. Then, in combinination with the linear finite volume discretization on spatial domain, we give a fully discrete scheme for the fractional wave equation. We prove that the fully discrete scheme is unconditionally stable and the discrete solution admits the optimal error estimates in the H¹-norm and L₂-norm, respectively. Numerical examples are provided to verify the effectiveness of the proposed numerical method.

• Korean Chemical Engineering Research
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• v.59 no.1
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• pp.138-151
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• 2021

The effect of a reactant ratio on the growth of a buoyancy-driven instability in an irreversible A+B→C reaction system is analyzed theoretically and numerically. Taking a non-stoichiometric reactant ratio into account, new linear stability equations are derived without the quasi-steady state assumption (QSSA) and solved analytically. It is found that the main parameters to explain the present system are the Damköhler number, the dimensionless density difference of chemical species and the ratio of reactants. The present initial grow rate analysis without QSSA shows that the system is initially unconditionally stable regardless of the parameter values; however, the previous initial growth rate analysis based on the QSSA predicted the system is unstable if the system is physically unstable. For time evolving cases, the present growth rates obtained from the spectral analysis and pseudo-spectral method support each other, but quite differently from that obtained under the conventional QSSA. Adopting the result of the linear stability analysis as an initial condition, fully nonlinear direct numerical simulations are conducted. Both the linear analysis and the nonlinear simulation show that the reactant ratio plays an important role in the onset and the growth of the instability motion.

• Journal of the Korean GEO-environmental Society
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• v.17 no.4
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• pp.17-31
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• 2016

Many researchers have evaluated the influence of vegetation cover on slope stability. However, due to the extensive variety of site conditions and vegetation types, different studies have often provided inconsistent results, especially when evaluating in different regions. Therefore, additional studies need to be conducted to identify the positive impacts of vegetation cover for slope stabilization. This study used the Transient Rainfall Infiltration and Grid-based Regional Slope-stability Model (TRIGRS) to predict the occurrence of landslides in a watershed in Jinbu-Myeon, Pyeongchang-gun, Korea. The influence of vegetation cover was assessed by spatially and temporally comparing the predicted landslides corresponding to multiple trials of cohesion values (which include the role of root cohesion) and real observed landslide scars to back-calculate the contribution of vegetation cover to slope stabilization. The lower bound of cohesion was defined based on the fact that there are no unstable cells in the raster stability map at initial conditions, and the modified success rate was used to evaluate the model performance. In the next step, the most reliable value representing the contribution of vegetation cover in the study area was applied for landslide assessment. The analyzed results showed that the role of vegetation cover could be replaced by increasing the soil cohesion by 3.8 kPa. Without considering the influence of vegetation cover, a large area of the studied watershed is unconditionally unstable in the initial condition. However, when tree root cohesion is taken into account, the model produces more realistic results with about 76.7% of observed unstable cells and 78.6% of observed stable cells being well predicted.

• Journal of Advanced Marine Engineering and Technology
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• v.26 no.3
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• pp.299-306
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• 2002

The load frequency control(LFC) of power system is one of important subjects in view of system operation and control. That is, even though the rapid load disturbances are applied to the given power system, the stable and reliable power should be supplied to the users, converging unconditionally and rapidly the frequency deviations and the tie-line power flow ones of each area into allowable boundary limits. Nonetheless of such needs, if the internal parameter perturbation and the sudden load variation are given, the unstable phenomena of power systems can be often brought out because of the large frequency deviation and the unsuppressible power line one. So, an optimal modulation controller for UC of multi-area power system is designed by a recursive algorithm that determines the state weighting matrix Q of a linear quadratic performance criterion. The optimal modulation controller is based on optimal control and can obtain the exact dynamic response of the UC of multi-area power system in the time domain. The performances of the resultant optimal modulation control, that is, the steady-state deviations of frequency and tie-line power flow and the related dynamics, were investigated and analyzed in detail by being applied to the UC of multi-area power system in the perturbations of predetermined internal parameters. Through the simulation results tried variously in this paper for disturbance of stepwise load changes, the superiorities of the proposed optimal modulation controller in robustness and stability were proved.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.49 no.3
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• pp.95-106
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• 2000

The load frequency control of power system is one of important subjects in view of system operation and control. That is even though the rapid load disturbances were applied to the given power system, the stable and reliable power should be supplied to the users, converging unconditionally and rapidly the frequency deviations and the tie-line power flow one on each area into allowable boundary limits. Nonetheless of such needs, if the internal parameter perturbation and the sudden load variation were given, the unstable phenomenal of power system can be often brought out because of the large frequency deviation and the unsuppressible power line one. Therefore, it is desirable to design the robust neuro-fuzzy controller which can stabilize effectively the given power system as soon as possible. In this paper the robust neuro-fuzzy controller was proposed and applied to control of load frequency over multi-area power system. The architecture and algorithm of a designed NFC(Neuro-Fuzzy Controller) were consist of fuzzy controller and neural network for auto tuning of fuzzy controller. The adaptively learned antecedent and consequent parameters of membership functions in fuzzy controller were acquired from the steepest gradient method for error-back propagation algorithm. The performances of the resultant NFC, that is, the steady-state deviations of frequency and tie-line power flow and the related dynamics, were investigated and analyzed in detail by being applied to the load frequency control of multi-area power system, when the perturbations of predetermined internal parameters. Through the simulation results tried variously in this paper for disturbances of internal parameters and external stepwise load stepwise load changes, the superiorities of the proposed NFC in robustness and adaptive rapidity to the conventional controllers were proved.

• Structural Engineering and Mechanics
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• v.57 no.2
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• pp.327-355
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• 2016

A new analytical derivation of the elastodynamic point load solutions for an isotropic multi-layered half-space is presented by means of the precise integration method (PIM) and the approach of dual vector. The time-harmonic external load is prescribed either on the external boundary or in the interior of the solid medium. Starting with the axisymmetric governing motion equations in a cylindrical coordinate system, a second order ordinary differential matrix equation can be gained by making use of the Hankel integral transform. Employing the technique of dual vector, the second order ordinary differential matrix equation can be simplified into a first-order one. The approach of PIM is implemented to obtain the solutions of the ordinary differential matrix equation in the Hankel integral transform domain. The PIM is a highly accurate algorithm to solve sets of first-order ordinary differential equations and any desired accuracy of the dynamic point load solutions can be achieved. The numerical simulation is based on algebraic matrix operation. As a result, the computational effort is reduced to a great extent and the computation is unconditionally stable. Selected numerical trials are given to validate the accuracy and applicability of the proposed approach. More examples are discussed to portray the dependence of the load-displacement response on the isotropic parameters of the multi-layered media, the depth of external load and the frequency of excitation.

• Steel and Composite Structures
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• v.53 no.2
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• pp.169-194
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• 2024

Although the excellent characteristics of functionally graded materials (FGMs) cracks could be found due to manufacturing defects or extreme working conditions. The existence of these cracks may threaten the material or structural strength, reliability, and lifetime. Due to high cost and restrictions offered by practical operational features these cracked components couldn't be replaced immediately. Such circumstances lead to the requirement of assessing the dynamic performance of cracked functionally graded structural components especially under moving objects. The present study aims to comprehensively investigate the dynamic behavior of functionally graded cracked Timoshenko beams (FGCTBs) resting on Winkler foundation and subjected to moving load through shear locking free finite elements methodology. The through thickness material distribution is simulated by the exponential gradation law. The geometric discontinuity due to cracks is represented using the massless rotational spring approach. The shear locking phenomena is avoided by using the different interpolation functions orders for both deflections and rotations. Based on Timoshenko beam element, a shear locking free finite elements methodology is developed. The unconditionally stable Newmark procedure is employed to solve the forced vibration problem. Accuracy of the developed procedure is verified by comparing the obtained results with the available results and an excellent agreement is found. Parametric studies are conducted to explore effects of the geometrical, material characteristics, crack geometrical characteristics, the elastic foundation parameter, and the moving load speed on the dynamic behavior for different boundary conditions. Obtained results revealed the significant effect these parameters on the dynamic performance of FGCTBs.

• The Korean Journal of Air & Space Law and Policy
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• v.35 no.2
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• pp.113-136
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• 2020

Worldwide, so-called 'over-booking' of Air Carriers is established in practice. Although not invalid, despite their current contracts, passengers can be refused boarding, which can hinder travel planning. The Korean Supreme Court ruled that an airline carrier who refused to board a passenger due to over-booking was liable for compensation under the "Nonperformance of obligation". But what the court should be thinking about is when the benefit(transport) have been disabled. Thereforeit may be considered that the impossibility of benefit (Transport) due to the rejection of boarding caused by 'Over-booking' may be not the 'subsequent impossibility', but not the 'initialimpossibility '. The legal relationship due to initial impossibility is nullity (imposibilium nulla est obligation). When benefits are initial impossibile, our civil code recognizes liability for damages in accordance with the law of "Culpa in Contrahendo", not "nonperformance of obligation". On this reason, the conclusion that the consumer will be compensated for the loss of boarding due to overbooking by the Air Carrier is the same, but there is a need to review the legal basis for the responsibility from the other side. However, it doesn't matter whether it is non-performance or Culpa in Contrahendo. Rather, the recognition of this compensation is likely to cause confusion due to unstable contractual relationships between both parties. Even for practices permitted by Air Carriers, modifications to current customary overbooking that consumers must accept unconditionally are necessary. At the same time, if Air Carriers continue to be held liable for non-performance of obligations due to overselling tickets, it can be fatal to the airline business environment that requires overbooking for stable profit margins. Therefore, it would be an appropriate measure for both Air Carriers and passengers if the Air Carrier were to be given a clearer obligation to explain (to the consumer) and, at the same time, if the explanation obligation is fulfilled, the Air Carrier would no longer be forced to take responsibility for overbooking.