• Journal of applied mathematics & informatics
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• v.10 no.1_2
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• pp.309-323
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• 2002

This paper studies the parameter estimation problem for a steady state flow in an inhomogeneous medium. Our approximation scheme could be used when the diffusion coefficient is singular. The function space parameter estimation convergence(FSPEC) is considered and numerical simulations are performed.

• Journal of the Institute of Electronics and Information Engineers
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• v.54 no.4
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• pp.91-98
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• 2017

Electrical impedance tomography is a nondestructive imaging technique to reconstruct unknown conductivity distribution based on applied current data and measured voltage data through an array of electrodes attached on the periphery of a domain. In this paper, an inverse method based on truncated singular value decomposition is proposed to solve the inverse problem with the generalized Tikhonov regularization and to reconstruct the conductivity distribution. In order to reduce the inverse computational time, truncated singular value decomposition is applied to the inverse term after the generalized regularization matrix is taken out from the inverse matrix term. Numerical experiments and phantom experiments have been performed to verify the performance of the proposed method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.8 s.251
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• pp.949-956
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• 2006

The method of Greenwood and Williamson is extended to obtain a solution to the coupled non-linear problem of steady-state electrical and thermal conduction across a crack in a conductive layer, for which the electrical resistivity and thermal conductivity are functions of temperature. The problem can be decomposed into the solution of a pair of non-linear algebraic equations involving boundary values and material properties. The new mixed-boundary value problem given from the thermal and electrical boundary conditions for the crack in the conductive layer is reduced in order to solve a singular integral equation of the first kind, the solution of which can be expressed in terms of the product of a series of the Chebyshev polynomials and their weight function. The non-existence of the solution for an infinite conductor in electrical and thermal conduction is shown. Numerical results are given showing the temperature field around the crack.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.4
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• pp.509-517
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• 1997

Results of flat plate compressible boundary layer calculation, based on discrete formulation of DSMC method, are presented in low Mach number and low Knudsen number range. The free stream is a uniform flow of pure nitrogen at various Mach numbers in low pressures (i.e. rarefied gas). Complete thermal accommodation and diffuse molecular reflections are used as the wall boundary condition, replacing unreal no-slip condition used in continuum calculations. In the discrete formulation of DSMC method, there is no need to use ad hoc assumptions on transport properties like viscosity and thermal conductivity, instead viscosity is calculated from values of other field variables (velocity and shear stress). Also the results are compared with existing self-similar continuum solutions. In all Mach number cases computed, velocity slip is most pronounced in regions near the leading edge where continuum formulation renders the solution singular. As the boundary layer develops further downstream, velocity slips asymptote to values that are between 10 to 20% of the magnitude of free stream velocity. When the free stream number density is reduced, so the gas more rarefied, the velocity slip increases as expected.

• Journal of Ocean Engineering and Technology
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• v.10 no.2
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• pp.106-119
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• 1996

The ceramic has various high mechanical properties such as heat, abrasion, corrosion resistance and high temperature strength compared with metal. It also has low speciffic weight, low thermal expansibillity, low thermal conductivity. However, it could not be used as structural material since it is brittle and difficult for the machining. Therefore, there have been many researches to attempt to join ceramic with metal which is full of ductillity in order to compensate the weakness of ceramic.The problem is that residual stress develops around the joint area while the ceramic/metal joint material is cooled from high joining temperature to room temperature due to remarkable difference of thermal expansion coefficients between ceramic and metal. Especially, the residual stress at both edges of the specimen reduces the strngth of joint to a large amount by forming a singular stress field. In this study, two dimensional finite element method is attempted for the thermal elastic analysis. The joint residual stress of ceramic/metal developed in the cooling process is investigated and the change of joint residual stress resulted from the repetitive heat cycle is also examined. In addition, it is attempted to clarify the joint stress distribution of the case of tensile load and of the case of superposition of residual stress and actual loading stress.

• Journal of The Korean Astronomical Society
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• v.36 no.3
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• pp.89-95
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• 2003

Observations of dark matter dominated dwarf and low surface brightness disk galaxies favor density profiles with a flat-density core, while cold dark matter (CDM) N-body simulations form halos with central cusps, instead. This apparent discrepancy has motivated a re-examination of the microscopic nature of the dark matter in order to explain the observed halo profiles, including the suggestion that CDM has a non-gravitational self-interaction. We study the formation and evolution of self-interacting dark matter (SIDM) halos. We find analytical, fully cosmological similarity solutions for their dynamics, which take proper account of the collisional interaction of SIDM particles, based on a fluid approximation derived from the Boltzmann equation. The SIDM particles scatter each other elastically, which results in an effective thermal conductivity that heats the halo core and flattens its density profile. These similarity solutions are relevant to galactic and cluster halo formation in the CDM model. We assume that the local density maximum which serves as the progenitor of the halo has an initial mass profile ${\delta}M / M {\propto} M^{-{\epsilon}$, as in the familiar secondary infall model. If $\epsilon$ = 1/6, SIDM halos will evolve self-similarly, with a cold, supersonic infall which is terminated by a strong accretion shock. Different solutions arise for different values of the dimensionless collisionality parameter, $Q {\equiv}{\sigma}p_br_s$, where $\sigma$ is the SIDM particle scattering cross section per unit mass, $p_b$ is the cosmic mean density, and $r_s$ is the shock radius. For all these solutions, a flat-density, isothermal core is present which grows in size as a fixed fraction of $r_s$. We find two different regimes for these solutions: 1) for $Q < Q_{th}({\simeq} 7.35{\times} 10^{-4}$), the core density decreases and core size increases as Q increases; 2) for $Q > Q_{th}$, the core density increases and core size decreases as Q increases. Our similarity solutions are in good agreement with previous results of N-body simulation of SIDM halos, which correspond to the low-Q regime, for which SIDM halo profiles match the observed galactic rotation curves if $Q {\~} [8.4 {\times}10^{-4} - 4.9 {\times} 10^{-2}]Q_{th}$, or ${\sigma}{\~} [0.56 - 5.6] cm^2g{-1}$. These similarity solutions also show that, as $Q {\to}{\infty}$, the central density acquires a singular profile, in agreement with some earlier simulation results which approximated the effects of SIDM collisionality by considering an ordinary fluid without conductivity, i.e. the limit of mean free path ${\lambda}_{mfp}{\to} 0$. The intermediate regime where $Q {\~} [18.6 - 231]Q_{th}$ or ${\sigma}{\~} [1.2{\times}10^4 - 2.7{\times}10^4] cm^2g{-1}$, for which we find flat-density cores comparable to those of the low-Q solutions preferred to make SIDM halos match halo observations, has not previously been identified. Further study of this regime is warranted.

• Proceedings of the Korea Water Resources Association Conference
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• 2015.05a
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• pp.244-244
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• 2015

Managed Aquifer Recharge (MAR) in the form of Aquifer Storage and Recovery (ASR) systems are being applied for numerous water augmentation projects both in developed and developing countries. Given the onset of Climate Change and its influence on weather patterns and land use, it has been acknowledged the utilization of this technology will be ever increasing. This technique like all others does have its drawbacks or disadvantages, whereby to overcome these drawbacks or disadvantages it is recommended that logical planning process be followed. In this study, we developed a decision framework known as "Decision framework for the planning, designing, construction/testing and implementation of subsurface water storage system" to further standardize the planning and design process of subsurface water storage system to increase the probability of having a successful ASR/ASTR project. The formulation of this framework was based on earlier frameworks, guidelines, published papers and technical reports which were compiled into a data collection database. The database of which consider both qualitative and quantitative aspect for example recharge objectives, site location, water chemistry of the native, source and recovered water, aquifer characteristics(hydraulic conductivity, transmissivity, porosity), injection/pumping rate, ecological constraints, societal restrictions, regulatory restrictions etc. The assimilation of these factors into a singular framework will benefit the broad spectrum of stakeholder as it maps the chronological order under which ASR project should be undertaken highlighting at each stage the feasibility of the project. The final stage of which should result in fully operational ASR system. The framework was applied to two case studies and through the application of a modified ASR site selection suitability index (Brown et al., 2005) a score was derived to identify the performance of each site. A high score of which meant a maximize chance of success given the reduce presence of project constraints.