• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.2
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• pp.108-120
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• 2022

We considered qualitative behaviour of the generalization of Einstein's model of Brownian motion when the key parameter of the time interval of free jump degenerates. Fluids will be characterised by number of particles per unit volume (density of fluid) at point of observation. Degeneration of the phenomenon manifests in two scenarios: a) flow of the fluid, which is highly dispersing like a non-dense gas and b) flow of fluid far away from the source of flow, when the velocity of the flow is incomparably smaller than the gradient of the density. First, we will show that both types of flows can be modeled using the Einstein paradigm. We will investigate the question: What features will particle flow exhibit if the time interval of the free jump is inverse proportional to the density and its gradient ? We will show that in this scenario, the flow exhibits localization property, namely: if at some moment of time t₀ in the region, the gradient of the density or density itself is equal to zero, then for some T during time interval [t₀, t₀ + T] there is no flow in the region. This directly links to Barenblatt's finite speed of propagation property for the degenerate equation. The method of the proof is very different from Barenblatt's method and based on the application of Ladyzhenskaya - De Giorgi iterative scheme and Vespri - Tedeev technique. From PDE point of view it assumed that solution exists in appropriate Sobolev type of space.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.15 no.12
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• pp.4567-4583
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• 2021

This study proposes an analytical approximation algorithm based on extreme value theory (EVT) for the inverse of the power of the incomplete Gamma function. First, the Gumbel function is used to approximate the power of the incomplete Gamma function, and the corresponding inverse problem is transformed into the inversion of an exponential function. Then, using the tail equivalence theorem, the normalized coefficient of the general Weibull distribution function is employed to replace the normalized coefficient of the random variable following a Gamma distribution, and the approximate closed form solution is obtained. The effects of equation parameters on the algorithm performance are evaluated through simulation analysis under various conditions, and the performance of this algorithm is compared to those of the Newton iterative algorithm and other existing approximate analytical algorithms. The proposed algorithm exhibits good approximation performance under appropriate parameter settings. Finally, the performance of this method is evaluated by calculating the thresholds of space-time block coding and space-frequency block coding pattern recognition in multiple-input and multiple-output orthogonal frequency division multiplexing. The analytical approximation method can be applied to other related situations involving the maximum statistics of independent and identically distributed random variables following Gamma distributions.

• Structural Engineering and Mechanics
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• v.85 no.5
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• pp.621-633
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• 2023

The major objective of this paper is to study the receding contact problem between two functional graded layers under a flat indenter. The gravity is assumed negligible, and the shear moduli of both layers are assumed to vary exponentially along the thickness direction. In the absence of body forces, the problem is reduced to a system of Fredholm singular integral equations with the contact pressure and contact size as unknowns via Fourier integral transform, which is transformed into an algebraic one by the Gauss-Chebyshev quadratures and polynomials of both the first and second kinds. Then, an iterative speediest descending algorithm is proposed to numerically solve the system of algebraic equations. Both semi-analytical and finite element method, FEM solutions for the presented problem validate each other. To improve the accuracy of the numerical result of FEM, a graded FEM solution is performed to simulate the FGM mechanical characteristics. The results reveal the potential links between the contact stress/size and the indenter size, the thickness, as well as some other material properties of FGM.

• The Bulletin of The Korean Astronomical Society
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• v.45 no.1
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• pp.48.4-49
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• 2020

We reconstruct the expansion history of the universe using type Ia supernovae (SN Ia) in a manner independent of any cosmological model assumptions. To do so, we implement a nonparametric iterative smoothing method on the Joint Light-curve Analysis (JLA) data while exploring the SN Ia light-curve hyperparameter space by Markov Chain Monte Carlo (MCMC) sampling. We test to see how the posteriors of these hyperparameters depend on cosmology, whether using different dark energy models or reconstructions shift these posteriors. Our constraints on the SN Ia light-curve hyperparameters from our model-independent analysis are very consistent with the constraints from using different parameterizations of the equation of state of dark energy, namely the flat ΛCDM cosmology, the Chevallier-Polarski-Linder model, and the Phenomenologically Emergent Dark Energy (PEDE) model. This implies that the distance moduli constructed from the JLA data are mostly independent of the cosmological models. We also studied that the possibility the light-curve parameters evolve with redshift and our results show consistency with no evolution. The reconstructed expansion history of the universe and dark energy properties also seem to be in good agreement with the expectations of the standard ΛCDM model. However, our results also indicate that the data still allow for considerable flexibility in the expansion history of the universe. This work is published in ApJ.

• Journal of the Earthquake Engineering Society of Korea
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• v.28 no.4
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• pp.223-231
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• 2024

For the OPR1000, a standard power plant in Korea, an analytical model of the containment building considering voids and deterioration was built with multilayer shell elements. Voids were placed in the vulnerable parts of the analysis model, and the deterioration effects of concrete and rebar were reflected in the material model. To check the impact of voids and deterioration on the seismic performance of the containment building, iterative push-over analysis was performed on four cases of the analytical model with and without voids and deterioration. It was found that the effect of voids with a volume ratio of 0.6% on the seismic performance of the containment building was insignificant. The effect of strength reduction and cross-sectional area loss of reinforcement due to deterioration and the impact of strength increase of concrete due to long-term hardening offset each other, resulting in a slight increase in the lateral resistance of the containment building. To determine the limit state that adequately represents the seismic performance of the containment building considering voids and deterioration, the Ogaki shear strength equation, ASCE 43-05 low shear wall allowable lateral displacement ratio, and JEAC 4601 shear strain limit were compared and examined with the analytically derived failure point (ultimate point) in this study.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.11 no.4
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• pp.103-112
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• 1991

In this study, a numerical model was established and applied to simulate the steady-state groundwater and heat flow in an isotropic, heterogeneous, three dimensional aquifer system with uniform thermal properties and no change of state. This model was developed as an aid in screening large groundwater-flow systems as prospects for underground waste storage. Driving forces on the system are external hydrologic conditions of recharge from precipitation and fixed hydraulic head boundaries. Heat flux includes geothermal heat-flow, conduction to the land surface, advection from recharge, and advection to or from fixed-head boundaries. The model uses an iterative procedure that alternately solves the groundwater-flow and heat-flow equations, updating advective flux after solution of the groundwater-flow equation, and updating hydraulic conductivity after solution of the heat-flow equation. Dierect solution is used for each equation. Travel time is determined by particle tracking through the modeled space. Velocities within blocks are linear interpolations of velocities at block faces. Applying this model to the groundwater-flow system located in Jigyung-ri. Songla-myun, Youngil-gun. Kyungsangbuk-do, the groundwater-flow system including distribution of head, temperature and travel time and flow line, is analyzed.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.33 no.2
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• pp.549-557
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• 2013

An flood inundation map is able to convey spatial distribution of inundation to a decision maker for flood risk management. A roughness coefficient with unclear values and a discharge obtained from the stage-discharge rating equation are key sources of uncertainty in flood inundation mapping by using a hydraulic model. Also, the uncertainty analysis needs an observation for the flood inundation, and satellite images is useful to obtain spatial distribution of flood. Accordingly, the objective of this study is to quantify uncertainty arising roughness and discharge in flood inundation mapping by using a hydraulic model and a satellite image. To perform this, flood inundations were simulated by HEC-RAS and terrain analysis, and ISODATA (Iterative Self-Organizing Data Analysis) was used to classify waterbody from Landsat 5TM imagery. The classified waterbody was used as an observation to calculate F-statistic (likelihood measure) in GLUE (Generalized Likelihood Uncertainty Estimation). The results from GLUE show that flood inundation areas are 74.59 $km^2$ for lower 5 % uncertainty bound and 151.95 $km^2$ for upper 95% uncertainty bound, respectively. The quantification of uncertainty in flood inundation mapping will play a significant role in realizing the efficient flood risk management.

• Journal of the Korean Institute of Telematics and Electronics T
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• v.35T no.2
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• pp.20-27
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• 1998

This paper describes color clustering method based on color difference in the uniform Munsell color space obtained from hue, saturation, and value. The proposed method operates in the uniform HSV color space which is approximated using ${L^*}{a^*}{b^*}$ coordinate system based on the RGB inputs. A clustering and color difference evaluation are proposed by thresholding NBS unit which is likely to Balinkin color difference equation. Region segmentation and isolation process are carried out ISO DATA algorithm which is a self iterative clustering technique. Through the clustering of 2 input images according to the threshold value, satisfactory results are obtained. So, in conclusion, it is possible to extract result of better region segmentation using human color perception of the objects.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.17 no.2 s.105
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• pp.158-164
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• 2006

In this paper, we proposed a new algorithm of the inverse scattering for the reconstruction of unknown dielectric scatterers using the finite-difference time-domain method and the design sensitivity analysis. We introduced the design sensitivity analysis based on the gradient information for the fast convergence of the reconstruction. By introducing the adjoint variable method for the efficient calculation, we derived the adjoint variable equation. As an optimal algorithm, we used the steepest descent method and reconstructed the dielectric targets using the iterative estimation. To verify our algorithm, we will show the numerical examples for the two-dimensional $TM^2$ cases.

• Journal of the Korean Society of Industry Convergence
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• v.19 no.1
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• pp.1-9
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• 2016

In this paper, we propose a new learning control scheme for various walk motion control of biped robot with same learning-base by neural network. We show that learning control algorithm based on the neural network is significantly more attractive intelligent controller design than previous traditional forms of control systems. A multi layer back propagation neural network identification is simulated to obtain a dynamic model of biped robot. Once the neural network has learned, the other neural network control is designed for various trajectory tracking control with same learning-base. The biped robots have been received increased attention due to several properties such as its human like mobility and the high-order dynamic equation. These properties enable the biped robots to perform the dangerous works instead of human beings. Thus, the stable walking control of the biped robots is a fundamentally hot issue and has been studied by many researchers. However, legged locomotion, it is difficult to control the biped robots. Besides, unlike the robot manipulator, the biped robot has an uncontrollable degree of freedom playing a dominant role for the stability of their locomotion in the biped robot dynamics. From the simulation and experiments the reliability of iterative learning control was illustrated.