• Journal of applied mathematics & informatics
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• v.35 no.3_4
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• pp.241-260
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• 2017

An analysis is made to study the solute transport in a Casson fluid flow through an annulus in presence of oscillatory flow field and determine how this flow influence the solute dispersion along the annular region. Axial dispersion coefficient and the mean concentration expressions are calculated using the generalized dispersion model. Dispersion coefficient in oscillatory flow is found to be a function of frequency parameter, Schmidt number, and the pressure fluctuation component besides its dependency on yield stress of the fluid, annular gap and time in the case of steady flow. Due to the oscillatory nature of the flow, the dispersion coefficient changes cyclically and the amplitude and magnitude of the dispersion increases initially with time and reaches a non - transient state after a certain critical time. This critical value varies with frequency parameter and independent of the other parameters. It is found that the presence of inner cylinder and increase in the size of the inner cylinder inhibits the dispersion process. This model may be used in understanding the dispersion phenomenon in cardiovascular flows and in particular in catheterized arteries.

• Journal of Korea Water Resources Association
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• v.36 no.4
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• pp.673-689
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• 2003

Field tests were conducted to investigate characteristics of the transverse mixing and to evaluate the dispersion coefficients in the meandering natural streams. The Sum River and the Cheong-mi Creek, tributaries of Han River, were selected as the test site, and measurements of the hydraulic and dispersion data were performed. In the tracer tests, the radioisotope was used as a tracer and injected into a flow on the instantaneous point source. Using the measured data, the longitudinal and transverse dispersion coefficients were evaluated and compared with the previous studies. The longitudinal dispersion coefficients, which were evaluated by application of the analytical solution, were about 0.5 $m^2$/s at the Sum River and 0.2 $m^2$/s at the Cheong -mi Creek. The transverse dispersion coefficients, which were evaluated by the analytical solution and the moment method, were ranging from 0.01 to 0.06 $m^2$/s for the Sum River and from 0.01 to 0.05 $m^2$/s for the Cheong-mi Creek.

• Water for future
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• v.28 no.4
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• pp.195-204
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• 1995

New dispersion coefficient equation which can be used to estimate dispersion coefficient by using only hydraulic data easily obtained in natural streams has been developed. Dimensional analysis was performed to select physically meaningful parameters, One-Step Huber method, which is one of the nonlinear multi-regression method, was applied to derive a regression equation of dispersion coefficient. 59 measured hydraulic data which were collected in 26 streams in the United States and were analyzed in the Part I of this study, were used in developing new dispersion coefficient equation. Among 59 measured data sets, 35 data sets were used in deriving regression equation, and 24 data sets are used for verification. The new dispersion coefficient equation, which has been developed in this study was proven to be superior in explaining dispersion characteristics of natural streams more precisely compared to existing dispersion coefficient equations.

• Korean Journal of Hydrosciences
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• v.6
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• pp.51-66
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• 1995

Various Eulerian-Lagerangian numerical models for the one-dimensional longtudinal dispersion equation are studied comparatively. In the models studied, the transport equation is decoupled into two component parts by the operator-splitting approach ; one part governing advection and the other dispersion. The advection equation has been solved using the method of characteristics following flud particles along the characteristic line and the result are interpolated onto an Eulerian grid on which the dispersion equation is solved by Crank-Nicholson type finite difference method. In solving the advection equation, various interpolation schemes are tested. Among those, Hermite interpo;ation po;ynomials are superor to Lagrange interpolation polynomials in reducing both dissipation and dispersion errors.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.8
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• pp.1165-1173
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• 2003

The effects of (1) phonon dispersion on thermal conductivity model and (2) differentiation of group velocity and phase velocity are examined for germanium. The results show drastic change of thermal conductivity regardless of the same relaxation time model. Also the contribution of transverse acoustic (TA) phonon and longitudinal acoustic (LA) phonon on the thermal conductivity at high temperatures is reassessed by considering more rigorous dispersion model. Holland model, which is commonly used for modeling thermal conductivity, underestimates the scattering rate for TA phonon at high frequency. This leads the conclusion that TA is dominant heat transfer mode at high temperatures. But according to the rigorous consideration of phonon dispersion, the reduction of thermal conductivity is much larger than the estimation of Holland model, thus the TA at high frequency is expected to be no more dominant heat transfer mode. Another heat transfer mechanism may exist at high temperatures. Two possible explanations we the roles of (1) Umklapp scattering of LA phonon at high frequency and (2) optical phonon.

• The Journal of the Acoustical Society of Korea
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• v.20 no.4E
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• pp.45-51
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• 2001

This paper examines the dispersion relation governing the wave propagation on cylindrical shells. The assumption of thin shells allows the dispersion relation to be separated into three relations related to the propagation of flexural waves and two types of membrane waves. Those relations are used to identify the characteristics of the wave number curves. The dispersion relation provides two and three closed wave number curves below and above the ring frequency. Above the ring frequency three wave number curves are clearly identified to be those of flexural, shear and longitudinal waves, respectively. Below the ring frequency, the characteristics of two wave number curves are identified with dependence of the direction of wave propagation.

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.1627-1632
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• 2003

The effect of (1) phonon dispersion in thermal conductivity model and (2) the differentiation of group velocity and phase velocity for Ge is examined. The results show drastic change of thermal conductivity regardless of using same relaxation time model. Also the contribution of transverse acoustic (TA) phonon and longitudinal acoustic (LA) phonon is changed by considering more rigorous dispersion model. Holland model underestimates the scattering rate for high frequency TA, so misleading conclusion, i.e. TA is dominant heat transfer mode at high temperature. But the actual reduction of thermal conductivity is much larger than the estimation by Holland model and high frequency TA is no more dominant heat transfer mode. Another heat transfer mechanism may exist for high temperature. Two possible explanations are (1) high frequency LA by Umklapp scattering and (2) optical phonon.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.11a
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• pp.615-618
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• 2004

For successful guided-wave damage inspection, the appropriate signal processing of measured wave signals is very important. The objective of this paper is to introduce an efficient signal processing technique especially suitable for the guided-waves used for damage detection. The key idea of this technique is to model guided-waves by chirp functions of special form considering the dispersion phenomenon. To determine the parameter of the chirp functions simulating guided-waves, the matching pursuit algorithm is employed. The damage information in waveguides can be extracted by pulse-characterizing parameters. The effectiveness of present method is checked with the longitudinal wave-based damage inspection.

• Structural Engineering and Mechanics
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• v.71 no.1
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• pp.99-107
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• 2019

Wave propagation analysis of a porous graphene platelet reinforced (GPLR) nanocomposite shell is investigated for the first time. The homogenization of the utilized material is procured by extending the Halpin-Tsai relations for the porous nanocomposite. Both symmetric and asymmetric porosity distributions are regarded in this analysis. The equations of the shell's motion are derived according to Hamilton's principle coupled with the kinematic relations of the first-order shear deformation theory of the shells. The obtained governing equations are considered to be solved via an analytical solution which includes two longitudinal and circumferential wave numbers. The accuracy of the presented formulations is examined by comparing the results of this method with those reported by former authors. The simulations reveal a stiffness decrease in the cases which porosity influences are regarded. Also, one must pay attention to the effects of longitudinal wave number on the wave dispersion curves of the nanocomposite structure.

• Journal of the Korean Chemical Society
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• v.40 no.5
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• pp.317-326
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• 1996

The frequency dependent longitudinal polarizabilities ${\alpha}zz(\omega)$ and the second hyper-polarizabilities ${\gamma}zzzz(\omega)$ of the linear polyenes, $C_4H_6\;to\;C_{30}H_{32}$, have been evaluated using the ab initio time-dependent coupled perturbed Hartree-Fock (TDCPHF) theory with the 6-31G basis set. The ratios of the dynamic properties to the static values have been examined to illustrate the relative dispersion effect and extrapolated to the infinite polymer limit. Also the effect of interchain interaction for linear and nonlinear optical properties has been investigated for $C_4H_6$ and the theoretical discussion has been described to overcome the limitation of ab initio TDHF method in the resonance region.