• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.4
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• pp.299-304
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• 2011

In this paper, we investigate the properties of rough approximations defined by preordered sets. We study the relations among the lower and upper rough approximations, closure and interior systems, and closure and interior operators.

• Korean Journal of Mathematics
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• v.19 no.2
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• pp.219-232
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• 2011

We investigated the properties of rough approximations induced by two families of preordered sets and closure systems. We study the relations among the lower and upper rough approximations, closure and interior systems, preordered sets.

• Korea-Australia Rheology Journal
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• v.12 no.2
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• pp.125-133
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• 2000

The present work is aimed at performing injection molding filling simulation of fiber suspension in polymer based matrix. The numerical simulation incorporates the coupling effect between the flow field and the fiber orientation state together with in-plane velocity gradient effect with recently proposed closure approximations. Predicted orientation components are compared with available experimental data of a film-gated strip and a center-gated disk. Predictions with IBOF closure approximation show excellent behaviors with regard to accuracy and numerical efficiency. However, predicted results seem to have consistent errors in comparison with experimental data. Diffusivity term which accounts for fiber-fiber interaction might have to be modified.

• Korea-Australia Rheology Journal
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• v.21 no.4
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• pp.245-268
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• 2009

Recent developments in dilute polymer solution rheology are reviewed, and placed within the context of the general goals of predicting the complex flow of complex fluids. In particular, the interplay between the use of polymer kinetic theory and continuum mechanics to advance the microscopic and the macroscopic description, respectively, of dilute polymer solution rheology is delineated. The insight that can be gained into the origins of the high Weissenberg number problem through an analysis of the configurational changes undergone by a single molecule at various locations in the flow domain is discussed in the context of flow around a cylinder confined between flat plates. The significant role played by hydrodynamic interactions as the source of much of the richness of the observed rheological behaviour of dilute polymer solutions is highlighted, and the methods by which this phenomenon can be incorporated into a macroscopic description through the use of closure approximations and multi scale simulations is discussed.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.32A no.4
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• pp.15-23
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• 1995

In this paper, we evaluate the performance of a transient queueing approximation when it is applied to modeling computer communication networks. An operational computer network that uses the ISO IS-IS(Intermediate System-Intermediate System) routing protocol is modeled as a Jackson network. The primary goal of the approximation pursued in the study was to provide transient queue statistics comparable in accuracy to the results from conventional Monte Carlo simulations. A closure approximation of the M/M/1 queueing system was extended to the general Jackson network in order to obtain transient queue statistics. The performance of the approximation was compared to a discrete event simulation under nonstationary conditions. The transient results from the two simulations are compared on the basis of queue size and computer execution time. Under nonstationary conditions, the approximations for the mean and variance of the number of packets in the queue erer fairly close to the simulation values. The approximation offered substantial speed improvements over the discrete event simulation. The closure approximation provided a good alternative Monte Carlo simulation of the computer networks.

• Journal of the Korean Mathematical Society
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• v.37 no.6
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• pp.1031-1042
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• 2000

The equations prescribed in Ω⊂R(sup)n are called loaded, if they contain some operations of the traces of desired solution on manifolds (of dimension which is strongly less than n) from closure Ω. These equations result from approximations of nonlinear equations by linear ones, in the problems of optimal control when the control when the control actions depends on a part of independent variables, in investigations of the inverse problems and so on. In present work we study the nonlocal boundary value problems for first-order loaded differential operator equations. Criterion of unique solvability is established. We illustrate the obtained results by examples.

• The Korean Journal of Rheology
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• v.10 no.4
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• pp.202-216
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• 1998

Improved version of previous 'Orthotropic' closure approximation, termed 'ORW' has been numerically developed using new homogeneous flow data. Previous 'Orthotropic' closure approximation, i.e., ORF or ORL showed non-physical oscillation for interaction coefficient $C_1$<0.001 at simple shear flow. It also shows non-physcial oscillation and under-prediction compared with 'Distribution Function Calculation' at non-homogeneous flow of center-gated disk. These phenomena are mainly due to the flow data of 'Distribution Function Calculation' which were used for least-square optimization. ORW obtained by fitting flow data of low interaction coefficient does not show non-physical oscillation and results in reasonably good behaviors at non-homogeneous flows as well as homogeneous flows. Fitting function forms have not been found to improve overall behaviors. It has been found that considering all the eigenvalues of orientation tensor (including the third eigenvalues) might end up with a better closure approximation than just considering the first and second eigenvalues. It is, however, very important and yet difficult to select appropriate function forms of eigenvalues. Numerical simulation including coupling and in-plane velocity gradient effects were performed for injection mold filing process with a film-gated strip and a center-gated disk using ORW and various other closure approximations for comparisons. Although ORW is in excellent agreement with 'Distribution Function Calculation', the predicted results seem to have consistent error in comparison with experimental data. The diffusivity term with constant interaction coefficient might have to be further investigated in order to accurately describe orientation states.