• Journal of the Korean Mathematical Society
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• v.49 no.5
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• pp.1083-1096
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• 2012

For a given ideal I of a Noetherian ring R and an arbitrary integer ${\kappa}{\geq}-1$, we apply the concept of ${\kappa}$-regular sequences and the notion of ${\kappa}$-depth to give some results on modules called ${\kappa}$-Cohen Macaulay modules, which in local case, is exactly the ${\kappa}$-modules (as a generalization of f-modules). Meanwhile, we give an expression of local cohomology with respect to any ${\kappa}$-regular sequence in I, in a particular case. We prove that the dimension of homology modules of the Koszul complex with respect to any ${\kappa}$-regular sequence is at most ${\kappa}$. Therefore homology modules of the Koszul complex with respect to any filter regular sequence has finite length.

• Earthquakes and Structures
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• v.11 no.3
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• pp.505-516
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• 2016

This paper evaluates the scaling of ground motions recorded from nine intermediate-depth earthquakes produced in the Vrancea seismic zone in Romania. The considered ground motion database consists of 363 horizontal recordings obtained on soil classes B and C (according to Eurocode 8). An analysis of the inter- and intra-event spectral accelerations is performed in order to gain information regarding the magnitude and distance scaling of the Vrancea ground motions. The analyses reveal a significant influence of the earthquake magnitude and focal depth on the distance scaling and different magnitude and distance scaling for the two soil classes. A linear magnitude and distance scaling is inferred from the results for the range of magnitudes $5.2{\leq}M_W{\leq}7.1$. The results obtained are checked through stochastic simulations and the influence of the stress drop and kappa values on the ground motion levels is assessed. In addition, five ground motion models which were tested in other studies using recordings from Vrancea earthquakes are analyzed in order to evaluate their corresponding host stress drop and kappa. The results show generally a direct connection between the host kappa values and the host stress drop values. Moreover, all the ground motion models depict magnitude dependent host kappa and stress drop levels.

• Bulletin of the Society of Naval Architects of Korea
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• v.17 no.2
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• pp.11-16
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• 1980

For vibration analysis of stiffened plates the orthotropic plate analogy is commonly accepted. As to stiffened plates in contact with water, however, there is still much uncertainty in estimation of the added mass because of the lack of direct methods. The authors, considering that for added mass of plates there are many reliable data derived theoretically or experimentally available, suggest a method to estimate the added mass of a stiffened plate by combining the mass increase factor, $\beta$, of an equivalent orthotropic plate and the correction factor, $\kappa$, for the effects of stiffeners. The latter is to be derived from systematic experimental investigations. Then, the natural frequency in water, f', can be calculated from that in air, f, by the equation $f'=f/\sqrt{1+\kappa\beta}$. To investigate practical applicability of this method, a systematic experiment was carried out with five uniaxially stiffened plates. Each of them had a plate of same size, $600mm{\times}600mm{\times}3.2mm$, but stiffeners of different size in the web-depth, 41.6mm, 51.2mm or 66.8mm and of different spacing 75mm, 100mm, or 150mm. Natural frequencies were measured under simply supported-edge conditions in both air and water, and corresponding $\kappa$ values derived. In spite of wide variations of web-depth and spcae of stiffeners, the experimental results show that the diversity of $\kappa$ values is not remarkable; mean values of $\kappa$ are 1.31 with standard deviation of 0.025 for the first modes and 1.27 with that 0.077 for the second modes. Hence, the authors concluded that the above $\kappa$ values can be used generally for the cases of uniaxially stiffened plates both sides of which contact with water, and that $\kappa$ values of general use for the cases of cross-stiffened plates may also be obtainable from similar experiments.

• Water for future
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• v.29 no.2
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• pp.199-207
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• 1996

To evaluate the usage of $\kappa-\imath$ turbulence closure for the analysis of thermal discharge behavior, a two-dimensional depth-integrated numerical model is developed. The developed model is applied to a steady flow in an open channel with simle geometry and the numerical results agree well with existing experimental data. The adequate simulation of recirculation, reattachment, and excess temperature rise at downstream of the outlet in the channel attributes to the correct calculation of turbulent eddy viscosity and diffusivity by $\kappa-\imath$ turbulence model. For an accurate prediction of thermal discharge behavior, the introduction of buoyancy production term, the modification of source/sink, and the correct input of turbulence constants of the $\kappa-\imath$ turbulence model are required.

• Geophysics and Geophysical Exploration
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• v.17 no.2
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• pp.66-73
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• 2014

To estimate the shear-velocity ($v_s$) structure beneath the WIZ station on White Island in New Zealand, we applied receiver function (RF) inversion and H-${\kappa}$ stacking methods to 362 teleseismic events (Mw > 5.5) recorded during April 20, 2007 to September 6, 2013. Using 71 RFs with errors less than 20% after 200 iterative computations, we determined that the depth to Moho of $v_s$ = 4.35 km/s is $24{\pm}1km$ within a 15 km radius of the station. In an 1-d $v_s$ model derived by RF inversions, a 4-km thick low-velocity layer (LVL) at depths of 18 ~ 22 km was identified in the lower crust. This LVL, which is 0.15 km/s slower than the rocks above and below it, may indicate the presence of a deep magma reservoir. The H-${\kappa}$ stacking method yielded an estimate of the depth to the Moho of 24.5 km, which agrees well with the depth determined by RF inversions. The low $v_p/v_s$ ratio of 1.64 may be due to the presence of gas-filled rock or hot crystallizing magma.

• 한국지구물리탐사학회:학술대회논문집
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• 2008.10a
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• pp.173-178
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• 2008

In this paper, we will introduce rock physics modeling technique, which interrelate reservoir properties with seismic properties, and apply the technique to the Donghae-1 gas reservoir. From well-log data analysis, we obtained velocityporosity (Vp-$\phi$) relations for each formation. These relations can used to predict porosity from seismic data. In addition, we analyzed permeability data, which were obtained from core measurements and computational rock physics simulations. We then obtained permeability-porosity ($\kappa-\phi$) relations. Combining $\kappa-\phi$ with Vp-$\phi$ relations, we finally present quantitative Vp-$\kappa$ relations. As to Vp-$\phi$ modeling, we found that the degree of diagenesis and clay contents increase with depth. As to Vp-$\kappa$ relations, though \kappa-\phi relations are almost identical for all formations, we could obtain distinct Vp-$\kappa$ relations due to Vp-$\phi$ variations. In conclusion, the rock physics modeling, which bridges between seismic properties and reservoir properties, can be a very robust tool for quantitative reservoir characterization with less uncertainty.

• Journal of Mechanical Science and Technology
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• v.18 no.12
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• pp.2265-2272
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• 2004

The aquaculture tank is used for breeding fish in sea water which was pumped up to land. The flow characteristics in the aquaculture were investigated with varying the tank geometry and flow rate. The numerical analysis has been employed for calculating the velocity and temperature distributions in a water tank of rectangular type. The finite volume method and SIMPLE algorithm with 3-dimensional standard $\kappa$-$\varepsilon$ turbulence model were used for the numerical analysis. For comparison with experimental results, the PIV system was applied to visualize the flow patterns quantitatively. The numerical results showed good agreements with the experimental results. The mean velocity and temperature versus aquarium depth were represented for various circulating flow rates. Especially, the aquaculture environment is recommended that the aquarium depth has to be d=0.5 m, and this case is the condition of higher velocity and temperature in winter season.

• 한국전산유체공학회:학술대회논문집
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• 2006.10a
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• pp.181-184
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• 2006

High-speed flight vehicle have various cavities. The supersonic cavity flow is complicated due to vortices, flow separation and reattachment, shock and expansion waves. The general cavity flow phenomena include the formation and dissipation of vortices, which induce oscillation and noise. The oscillation and noise greatly affect flow control, chemical reaction, and heat transfer processes. The supersonic cavity' flow with high Reynolds number is characterized by the pressure oscillation due to turbulent shear layer, cavity geometry, and resonance phenomenon based on external flow conditions, The resonance phenomena can damage the structures around the cavity and negatively affect aerodynamic performance and stability. In the present study, we performed numerical analysis of cavities by applying the unsteady, compressible three dimensional Reynolds-Averaged Navier-Stokes(RANS) equations with the ${\kappa}-{\omega}$ turbulence model. The cavity model used for numerical calculation had a depth(D) of 15mm cavity aspect ratio(L/D) of 3, width to spanwise ratio(W/D) of 1.0 to 5.0. Based on the PSD(Power Spectral Density) and CSD(Cross Spectral Density) analysis of the pressure variation, the dominant frequency was analyized and compared with the results of Rossiter's Eq.

• Journal of computational fluids engineering
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• v.11 no.4 s.35
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• pp.62-66
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• 2006

High-speed flight vehicle have various cavities. The supersonic cavity flow is complicated due to vortices, flow separation, reattachment, shock waves and expansion waves. The general cavity flow phenomena includes the formation and dissipation of vortices, which induce oscillation and noise. The oscillation and noise greatly affect flow control, chemical reaction, and heat transfer processes. The supersonic cavity flow with high Reynolds number is characterized by the pressure oscillation due to turbulent shear layer, cavity geometry, and resonance phenomenon based on external flow conditions. The resonance phenomena can damage the structures around the cavity and negatively affect aerodynamic performance and stability. In the present study, we performed numerical analysis of cavities by applying the unsteady, compressible three dimensional Reynolds-Averaged Navier-Stokes(RANS) equations with the ${\kappa}-{\omega}$ turbulence model. The cavity model used for numerical calculation had a depth(D) of 15mm cavity aspect ratio (L/D) of 3, width to spanwise ratio(W/D) of 1.0 to 5.0. Based on the PSD(Power Spectral Density) and CSD(Cross Spectral Density) analysis of the pressure variation, the dominant frequency was analyzed and compared with the results of Rossiter's Eq.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.29 no.3B
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• pp.247-257
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• 2009

In the present paper, turbulent open-channel flows with alternate vegetated zones are numerically simulated using threedimensional model. The Reynolds-averaged Navier-Stokes Equations are solved with the ${\kappa}-{\varepsilon}$ model. The CFD code developed by Olsen(2004) is used for the present study. For model validation, the partly vegetated channel flows are simulated, and the computed depth-averaged mean velocity and Reynolds stress are compared with measured data in the literature. Comparisons reveal that the present model successfully predicts the mean flow and turbulent structures in vegetated open-channel. However, it is found that the ${\kappa}-{\varepsilon}$ model cannot accurately predict the momentum transfer at the interface between the vegetated zone and the non-vegetated zone. It is because the ${\kappa}-{\varepsilon}$ model is the isotropic turbulence model. Next, the open channel flows with alternate vegetated zones are simulated. The computed mean velocities are compared well with the previously reported measured data. Good agreement between the simulated results and the experimental data was found. Also, the turbulent flows are computed for different densities of vegetation. It is found that the vegetation curves the flow and the meandering flow pattern becomes more obvious with increasing vegetation density. When the vegetation density is 9.97%, the recirculation flows occur at the locations opposite to the vegetation zones. The impacts of vegetation on the flow velocity and the water surface elevation are also investigated.