• Structural Engineering and Mechanics
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• v.55 no.3
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• pp.473-494
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• 2015

A graded harmonic finite element formulation based on three-dimensional elasticity theory is developed for the structural analysis of 2D functionally graded axisymmetric structures. The mechanical properties of the axisymmetric solid structures composed of two different metals and ceramics are assumed to vary in radial and axial directions according to power law variations as a function of the volume fractions of the constituents. The material properties of the graded element are calculated at the integration points. Effects of material distribution profile on the static deformation, natural frequency and dynamic response analyses of particular axisymmetric solid structures are investigated by changing the power law exponents. It is observed that the displacements, stresses and natural frequencies are severely affected by the variation of axial and radial power law exponents. Good accuracy is obtained with fewer elements in the present study since Fourier series expansion eliminates the need of finite element mesh in circumferential direction and continuous material property distribution within the elements improves accuracy without refining the mesh size in axial and radial directions.

• Communications for Statistical Applications and Methods
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• v.2 no.2
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• pp.166-175
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• 1995

When a neutral particle beam(NPB) aimed at the object and receive a small number of neutron signals at the detector without any errors, it obeys Poisson law. Under the two assumptions that neutral particle scattering distribution and aiming errors have a circular Gaussian distributions that neutral particle scattering distribution and aiming errors have a circular Gaussian distribution respectively, an exact probability distribution of neutral particles vecomes a Poisson-power function distribution. We study and prove some properties, such as limiting distribution, unimodality, stochastical ordering, computational recursion fornula, of this distribution. We also prove monotone likelihood ratio(MLR) property of this distribution. Its MLR property can be used to find a criteria for the hypothesis testing problem.

• Proceedings of the National Institute of Ecology of the Republic of Korea
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• v.3 no.3
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• pp.149-153
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• 2022

The degree distribution of the plant-pollinator network was identified by analyzing the data in the ecosystem and reproduced by a model of the growing bipartite mutualistic networks. The degree distribution of pollinator shows power law or stretched exponential distribution, while plant usually shows stretched exponential distribution. In the growth model, the plant and the pollinator are selected with probability P_p and P_A=1-P_p, respectively. The number of incoming links for the plant and the pollinator is l_p and l_A, respectively. The probability that the link of the plant selects the pollinator of the existing network given as $A_{k_i}=k^{{\lambda}_A}_i/{\sum}_i\;k^{{\lambda}_A}_i$, and the probability that the pollinator selects the plant is $P_{k_i}=k^{{\lambda}_p}_i/{\sum}_i\;k^{{\lambda}_p}_i$. When the nonlinear growth index is 𝛌_X=1 (X=A or P), the degree distribution follows a power law, and if 0≤𝛌_X<1, the degree distribution follows a stretched exponential distribution. The cumulative degree distributions of plants and pollinators of 14 empirical plant-pollinators included in Interaction Web Database were calculated. A set of parameters (P_A,P_P,l_A,l_P) that reproduces these cumulative degree distributions and a growth index 𝛌_X (X=A or P) were obtained. We found that animal takes very heterogenous connections, whereas plant takes a more flexible connection network.

• Structural Engineering and Mechanics
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• v.69 no.6
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• pp.637-649
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• 2019

In the current research paper, a quasi-3D beam theory is developed for free vibration analysis of functionally graded microbeams. The volume fractions of metal and ceramic are assumed to be distributed through a beam thickness by three functions, power function, symmetric power function and sigmoid law distribution. The modified coupled stress theory is used to incorporate size dependency of micobeam. The equation of motion is derived by using Hamilton's principle, however, Navier type solution method is used to obtain frequencies. Numerical results show the effects of the function distribution, power index and material scale parameter on fundamental frequencies of microbeams. This model provides designers with guidance to select the proper distributions and functions.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2001.04a
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• pp.73-76
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• 2001

We have simulated the effect of fracture characteristics on reduction of effective permeability of the fractured rocks due to in-situ bacteria growth. A nutrient is injected continuously for growth of in-situ bacteria. We used a power law for fracture length distribution and a fBm for fracture aperture spatial distribution. The results show that in-situ bacteria growth reduces the Permeability hyperbolically, but the porosity of backbone fracture does not change significantly. It shows that reduction of the permeability proceeds at faster speed for smaller value of length exponent(a) and for larger value of Hurst exponent(H). The fracture length distribution has stronger effect on speed of reduction than the aperture spatial distribution. The time needed to reduce permeability is inversely proportional to the hydraulic gradient.

• Journal of the Korean Ceramic Society
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• v.31 no.12
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• pp.1449-1458
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• 1994

A new analytical model which can discribe the relationship between the bridging stress and the crack opening displacement was proposed to investigate the microstructural effect on the R-curve behavior in a polycrystalline alumina. The crack opening displacement according to the distance behind the stationary crack tip was measured using in-situ fracture technique in an SEM, and then used for a fitting procedure to obtain the distribution of bridging stress. The current model and an empirical power law relation were introduced into the fitting procedure. The results indicated that the bridging stress function and R-curve computed by the current model were consistent with those computed by the power law relation. The microstructural factor, e.g., the distribution of grain size, was also found to be closely related to the bridging stress. Thus, this model explained well the interaction effect between the distribution of bridging stress and the local-fracture-controlling microstructure, providing important information for the systematic interpretation of microfracture mechanism including R-curve behavior of a monolithic alumina.

• Coupled systems mechanics
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• v.11 no.5
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• pp.389-409
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• 2022

During the manufacture of FGM plates, defects such as porosities can appear. Those can change the entire behavior of these plates. This paper aims to investigate the free vibration characteristics of porous functionally graded (FG) plates resting on elastic foundations. The Young's modulus of the plate is assumed to vary continuously through the thickness according to a power-law formulation, and the Poisson ratio is held constant. Different types of porosity distribution rates are considered. To examine the accuracy of the present formulation, several comparison studies are investigated. Effects of variation of porosity distribution rate, foundation parameter, power-law index and thickness ratio on the fundamental frequency of plates have been investigated.

• The Bulletin of The Korean Astronomical Society
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• v.40 no.2
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• pp.42.1-42.1
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• 2015

We model the Spectral Energy Distribution (SED) of Class 0 protostar L1527 IRS using a radiative transfer code RADMC-3D. In addition to the photometry data from literatures, we include the Herschel/PACS data which well covers the far-infrared SED peak of L1527 IRS, providing precise constraints to the density structure and other physical properties of its circumstellar envelope. Previously, Tobin et al. (2013) presented a dust continuum modeling results using a rotating and infalling envelope (Terebey and Shu, & Cassen 1984 ; TSC envelope), which originally describes a power-law density profile (${\rho}{\propto}r-{\alpha}$) with the power-law index (${\alpha}$) of 1.5. However, we find that Herschel/PACS data are better fitted with a shallower power-law density profile. This smaller power-law might be attributed to a inner envelope. Thus, we fit the SED of L1527 IRS with a Bonnor-Ebert sphere, which is a combination of the inner flat-topped and the outer power-law (${\alpha}=2$) density profiles. This Bonnor-Ebert sphere is often used to explain the density profile of prestellar cores, which is considered the earliest stages of star formation. The well-fitted SED with a Bonnor-Ebert sphere suggests that L1527 IRS might have collapsed from a Bonnor-Ebert sphere rather than a singular isothermal sphere.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.7
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• pp.1391-1397
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• 1992

Improved power law flow model was suggested for the calculation of wake flow characteristics around the three dimensional ship stern in case of the formation of bilge vortex in the direction of stern. In comparison with the power law and Coles flow model, the flow velocity calculated based on this study was delayed around the boundary of inner layer and outer layer in reverse flow. More accurate results was obtained with this improved power law flow model by the velocity calculation around ship stern. Accuracy was validated with the comparison of other calculation results and experimental datas.

• Journal of Korea Water Resources Association
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• v.50 no.6
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• pp.359-371
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• 2017

This study generated flood time series of ungauged catchments in the Andongdam catchment using a distributed rainfall-runoff model and data generation method, and extracted the peak flows of 50 catchments to investigate the effect of rainfall spatial variability on peak flow simulation. The model performance statistics for three gauged catchments were reasonable for all events. The flood time series of the 50 catchments were generated using distributed and mean rainfall time series as input. The distribution of the peak flow using the mean rainfall was similar or slightly different to that using the distributed rainfall when the distribution of the distributed rainfall was nearly uniform. However, the distribution of the peak flow using the mean rainfall was reduced significantly compared to that using the distributed rainfall when actual storms moved to the top or bottom of the study catchment, or the rainfall was randomly distributed. These cases were 35% of total number events. Therefore, the spatial variability of rainfall should be considered for flood simulation. In addition, the power law relationship estimated using the peak flow of gauged catchments cannot be used for estimating the peak flow of ungauged independent catchments due to latter's significant variation of the peak flow magnitude.