• Title/Summary/Keyword: Nonlinear diffusion

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Analytical Solutions for Predicting Movement Rate of Submerged Mound (수중둔덕의 이동율 예측을 위한 해석해)

    • Journal of Korean Society of Coastal and Ocean Engineers
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    • v.10 no.4
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    • pp.165-173
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    • 1998
  • Analytical solutions to predict the movement rate of submerged mound are derived using the convection coefficient and the joint distribution function of wave heights and periods. Assuming that the sediment is moved onshore due to the velocity asymmetry of Stokes' second order nonlinear wave theory, the micro-scale bedload transport equation is applied to the sediment conservation. The nonlinear convection-diffusion equation can then be obtained which governs the migration of submerged mound. The movement rate decreases exponentially with increasing the water depth, but the movement rate tends to increase as the spectral width parameter, $ u$ increases. In comparison of the analytical solution with the measured data, it is found that the analytical solution overestimates the movement rate. However, the agreement between the analytical solution and the measured data is encouraging since this over-estimation may be due to the inaccuracy of input data and the limitation of sediment transport model. In particular, the movement rates with respect to the water depth predicted by the analytical solution are in very good agreement with the estimated result using the discritization technique with the hindcast wave data.

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Domestic Automotive Exterior Lamp-LEDs Demand and Forecasting using BASS Diffusion Model (BASS 확산 모형을 이용한 국내 자동차 외장 램프 LED 수요예측 분석)

  • Lee, Jae-Heun
    • Journal of Korean Society for Quality Management
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    • v.50 no.3
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    • pp.349-371
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    • 2022
  • Purpose: Compared to the rapid growth rate of the domestic automotive LED industry so far, the predictive analysis method for demand forecasting or market outlook was insufficient. Accordingly, product characteristics are analyzed through the life trend of LEDs for automotive exterior lamps and the relative strengths of p and q using the Bass model. Also, future demands are predicted. Methods: We used sales data of a leading company in domestic market of automotive LEDs. Considering the autocorrelation error term of this data, parameters m, p, and q were estimated through the modified estimation method of OLS and the NLS(Nonlinear Least Squares) method, and the optimal method was selected by comparing prediction error performance such as RMSE. Future annual demands and cumulative demands were predicted through the growth curve obtained from Bass-NLS model. In addition, various nonlinear growth curve models were applied to the data to compare the Bass-NLS model with potential market demand, and an optimal model was derived. Results: From the analysis, the parameter estimation results by Bass-NLS obtained m=1338.13, p=0.0026, q=0.3003. If the current trend continues, domestic automotive LED market is predicted to reach its maximum peak in 2021 and the maximum demand is $102.23M. Potential market demand was $1338.13M. In the nonlinear growth curve model analysis, the Gompertz model was selected as the optimal model, and the potential market size was $2864.018M. Conclusion: It is expected that the Bass-NLS method will be applied to LED sales data for automotive to find out the characteristics of the relative strength of q/p of products and to be used to predict current demand and future cumulative demand.

Non-Fickian Diffusion of Organic Solvents in Fluoropolymeys (불소고분자내 유기용매의 비-픽 확산)

  • 이상화
    • Polymer(Korea)
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    • v.28 no.1
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    • pp.24-34
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    • 2004
  • Transient sorption experiments were conducted among several combinations of fluoropolymers and various organic solvents. Fully fluorinated polymer tended to exhibit ideal sorption behavior, while partially fluorinated polymers showed anomalous sorption behaviors with a drastic acceleration at the final stage of uptake. Minimization of least-squares of the measured and predicted fractional uptake, which indicated the increasing degree of deviation from Fickian diffusion, gave values of 3.0${\times}$10$\^$-4/, 1.75${\times}$10$\^$-3/, 8.68${\times}$10/sup-3/, 1.75${\times}$10$\^$-2/, respectively, for perfluoroalkoxy copolymer, poly(ethylene-co-tetrafluoroethylene), poly(vinylidene fluoride), poly(ethylene-co-chlorotrifluoroethylene). From stress-strain tests, it was confirmed that non-Fickian diffusion is closely related to the significant variation of mechanical properties (such as modulus and tensile strength) of swollen polymer. Anomalous sorption behavior stemmed from non-Fickian diffusion caused by nonlinear disruption of polar inter-segmental bonds due to solvent-induced plasticization. Thus, it is imperative to investigate the diffusion behavior of swelling solvents in partially fluorinated polymers, especially for the application to barrier materials or perm-selective membranes.

NUMERICAL STUDIES OF COSMIC RAY ACCELERATION AT COSMIC SHOCKS

  • KANG HYESUNG
    • Journal of The Korean Astronomical Society
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    • v.37 no.4
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    • pp.225-232
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    • 2004
  • Shocks are ubiquitous in astrophysical environments and cosmic-rays (CRs) are known to be accelerated at collisionless shocks via diffusive shock acceleration. It is believed that the CR pressure is important in the evolution of the interstellar medium of our galaxy and most of galactic CRs with energies up to ${\~}\;10^{15}$ eV are accelerated by supernova remnant shocks. In this contribution we have studied the CR acceleration at shocks through numerical simulation of 1D, quasi-parallel shocks for a wide range of shock Mach numbers and shock speeds. We show that CR modified shocks evolve to time-asymptotic states by the time injected particles are accelerated to moderately relativistic energies, and that two shocks with the same Mach number, but with different shock speeds, evolve qualitatively similarly when the results are presented in terms of a characteristic diffusion length and diffusion time. We find that $10^{-4} - 10^{-3}$ of the particles passed through the shock are accelerated to form the CR population, and the injection rate is higher for shocks with higher Mach number. The time asymptotic value for the CR acceleration efficiency is controlled mainly by shock Mach number, and high Mach number shocks all evolve towards efficiencies ${\~}50\%$, regardless of the injection rate and upstream CR pressure. We conclude that the injection rates in strong quasi-parallel shocks are sufficient to lead to significant nonlinear modifications to the shock structures, implying the importance of the CR acceleration at astrophysical shocks.

A Study of Non-staggered Grid Approach for Incompressible Heat and Fluid Flow Analysis (비압축성 열유동 해석을 위한 비엇갈림 격자법에 대한 연구)

  • Kim Jongtae;Kim Sang-Baik;Kim Hee-Dong;Maeng Joo-sung
    • Journal of computational fluids engineering
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    • v.7 no.1
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    • pp.10-19
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    • 2002
  • The non-staggered(collocated) grid approach in which all the solution variables are located at the centers of control volumes is very popular for incompressible flow analyses because of its numerical efficiency on the curvilinear or unstructured grids. Rhie and Chow's paper is the first in using non-staggered grid method for SIMPLE algorithm, where pressure weighted interpolation was used to prevent decoupling of pressure and velocity. But it has been known that this non-staggered grid method has stability problems when pressure fields are nonlinear like in natural convection flows. Also Rhie-Chow scheme generates large numerical diffusion near curved walls. The cause of these unwanted problems is too large pressure damping term compared to the magnitude of face velocity. In this study the magnitude of pressure damping term of Rhie-Chow's method is limited to 1∼10% of face velocity to prevent physically unreasonable solutions. The wall pressure extrapolation which is necessary for cell-centered FVM is another source of numerical errors. Some methods are applied in a unstructured FV solver and analyzed in view of numerical accuracy. Here, two natural convection problems are solved to check the effect of the Rhie-Chow's method on numerical stability. And numerical diffusion from Rhie-Chow's method is studied by solving the inviscid flow around a circular cylinder.

Evaluation of Moisture Sorption Characteristics in Polymer Material (고분자 소재에서 흡습 특성의 평가)

  • Park, Hee-Jin
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.36 no.11
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    • pp.1297-1303
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    • 2012
  • In this paper, the standard procedures for measuring the moisture sorption properties of thin polymeric materials such as polyethylene terephthalate (PET) by using the thermo-gravimetric method to characterize the moisture diffusion in the polymer are presented, and the sorption properties are quantified. The moisture diffusivity and solubility are characterized to investigate the effect of temperature and humidity on the moisture sorption properties according to the Arrhenius equation. The validation of the obtained sorption properties using thermogravimetry is discussed with the measured permeability based on Fickian diffusion. The nonlinear behavior of the concentration dependent moisture diffusion is investigated experimentally, and the nonlinearity is characterized numerically for the case of having an interface with an inorganic material such as a metal. The Fickian/Non-Fickian model based on the obtained moisture sorption properties is compared and discussed.

A Numerical Analysis of Acoustic-Pressure Response of H2-Air Diffusion Flames with Application of Time-Lag Model (시간지연 모델의 적용을 통한 수소/공기 확산화염의 음향파 응답 분석)

  • Sohn, Chae-Hoon;Lim, Jun-Seok
    • Journal of the Korean Society of Propulsion Engineers
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    • v.16 no.1
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    • pp.1-8
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    • 2012
  • Acoustic-pressure response of diluted hydrogen-air diffusion flames is investigated numerically by adopting a fully unsteady analysis of flame structures in low and high pressure regimes. As acoustic frequency increases, finite-rate chemistry is enhanced through a nonlinear accumulation of heat release rate for any pressure regime, leading to a high amplification index. Same numerical results are analyzed with application of a pressure-sensitive time lag model, and thereby, interaction index and time lag are calculated for each pressure regime. The interaction index has the largest value in each pressure regime at an acoustic frequency near 1000 Hz. In a high-pressure regime, flames are more unstable than in a low-pressure regime. The interaction index shows a good agreement with the amplification index.

Negative Turbulent Magnetic 𝛽 Diffusivity effect in a Magnetically Forced System

  • Park, Kiwan;Cheoun, Myung-Ki
    • The Bulletin of The Korean Astronomical Society
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    • v.46 no.2
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    • pp.47.3-48
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    • 2021
  • We studied the large scale dynamo process in a system forced by helical magnetic field. The dynamo process is basically nonlinear, but can be linearized with 𝛼&𝛽 coefficients and large scale magnetic field $\bar{B}$. This is very useful to the investigation of solar (stellar) dynamo. A coupled semi-analytic equations based on statistical mechanics are used to investigate the exact evolution of 𝛼&𝛽. This equation set needs only magnetic helicity ${\bar{H}}_M({\equiv}{\langle}{\bar{A}}{\cdot}{\bar{B}}{\rangle},\;{\bar{B}}={\nabla}{\times}{\bar{A}})$ and magnetic energy ${\bar{E}}_M({\equiv}{\langle}{\bar{B}}^2{\rangle}/2)$. They are fundamental physics quantities that can be obtained from the dynamo simulation or observation without any artificial modification or assumption. 𝛼 effect is thought to be related to magnetic field amplification. However, in reality the averaged 𝛼 effect decreases very quickly without a significant contribution to ${\bar{B}}$ field amplification. Conversely, 𝛽 effect contributing to the magnetic diffusion maintains a negative value, which plays a key role in the amplification with Laplacian ∇2(= - k2) for the large scale regime. In addition, negative magnetic diffusion accounts for the attenuation of plasma kinetic energy EV(= 〈 U2 〉/2) (U: plasma velocity) when the system is saturated. The negative magnetic diffusion is from the interaction of advective term - U • ∇ B from magnetic induction equation and the helical velocity field. In more detail, when 'U' is divided into the poloidal component Upol and toroidal one Utor in the absence of reflection symmetry, they interact with - B • ∇ U and - U • ∇ B from ∇ × 〈 U × B 〉 leading to 𝛼 effect and (negative) 𝛽 effect, respectively. We discussed this process using the theoretical method and intuitive field structure model supported by the simulation result.

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Propagation Neural Networks based on vision techniques for detecting of Faulty Insulator (불량애자 검출을 위한 비젼 기반 전파 신경망)

  • Kim, Jong-Man;Kim, Young-Min;Hwang, Jong-Sun;Park, Hyun-Chul;Lim, Sung-Ho;Kim, Hyun-Chul
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2002.07b
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    • pp.1097-1102
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    • 2002
  • For detecting of Faulty Insulator, a new Lateral Information Propagation Networks (LIPN) has been proposed. Energized insulator is reduced the rate of insulation extremely, and taken the results dirty and injured. It is necessary to be actions that detect the faulty insulator and exchange the new one. And thus, we have designed the LIPN to be detected that insulators by the real time computation method through the inter-node diffusion. In the network, a node corresponds to a state in the quantized input space. Each node is composed of a processing unit and fixed weights from its neighbor nodes as well as its input terminal. Information propagates among neighbor nodes laterally and inter-node interpolation is achieved. Through several simulation experiments,real time reconstruction of the nonlinear image information is processed.

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A Dynamic Programming Neural Network to find the Safety Distance of Industrial Field (산업 현장의 안전거리 계측을 위한 동적 계획 신경회로망)

  • Kim, Jong-Man;Kim, Won-Sub;Kim, Yeong-Min;Hwang, Jong-Sun;Park, Hyun-Chul
    • Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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    • 2001.09a
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    • pp.23-27
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    • 2001
  • Making the safety situation from the various work system is very important in the industrial fields. The proposed neural network technique is the real titre computation method based theory of inter-node diffusion for searching the safety distances from the sudden appearance-objests during the work driving. The main steps of the distance computation using the theory of stereo vision like the eyes of man is following steps. One is the processing for finding the corresponding points of stereo images and the other is the interpolation processing of full image data from nonlinear image data of obejects. All of them request much memory space and titre. Therefore the most reliable neural-network algorithm is drived for real time recognition of obejects, which is composed of a dynamic programming algorithm based on sequence matching techniques. And the real time reconstruction of nonlinear image information is processed through several simulations. I-D LIPN hardware has been composed, and the real time reconstruction is verified through the various experiments.

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