• Korea-Australia Rheology Journal
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• 제21권2호
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• pp.143-146
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• 2009

Breakthrough of high Weisenberg number problem is related with keeping the positive definiteness of the conformation tensor in numerical procedures. In this paper, we suggest a simple method to preserve the positive definiteness by use of vector decomposition of the conformation tensor which does not require eigenvalue problem. We also derive the constitutive equation of tensor-logarithmic transform in simpler way than that of Fattal and Kupferman and discuss the comparison between the vector decomposition and tensor-logarithmic transformation.

• Korea-Australia Rheology Journal
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• 제16권4호
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• pp.183-191
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• 2004

High Deborah or Weissenberg number problems in viscoelastic flow modeling have been known formidably difficult even in the inertialess limit. There exists almost no result that shows satisfactory accuracy and proper mesh convergence at the same time. However recently, quite a breakthrough seems to have been made in this field of computational rheology. So called matrix-logarithm (here we name it tensor-logarithm) formulation of the viscoelastic constitutive equations originally written in terms of the conformation tensor has been suggested by Fattal and Kupferman (2004) and its finite element implementation has been first presented by Hulsen (2004). Both the works have reported almost unbounded convergence limit in solving two benchmark problems. This new formulation incorporates proper polynomial interpolations of the log­arithm for the variables that exhibit steep exponential dependence near stagnation points, and it also strictly preserves the positive definiteness of the conformation tensor. In this study, we present an alternative pro­cedure for deriving the tensor-logarithmic representation of the differential constitutive equations and pro­vide a numerical example with the Leonov model in 4:1 planar contraction flows. Dramatic improvement of the computational algorithm with stable convergence has been demonstrated and it seems that there exists appropriate mesh convergence even though this conclusion requires further study. It is thought that this new formalism will work only for a few differential constitutive equations proven globally stable. Thus the math­ematical stability criteria perhaps play an important role on the choice and development of the suitable con­stitutive equations. In this respect, the Leonov viscoelastic model is quite feasible and becomes more essential since it has been proven globally stable and it offers the simplest form in the tensor-logarithmic formulation.

• 한국정보디스플레이학회:학술대회논문집
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• 한국정보디스플레이학회 2003년도 International Meeting on Information Display
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• pp.1112-1117
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• 2003

Polarized Fourier transform infrared (IR) absorption is used to probe molecular conformation in a ferroelectric liquid crystal (FLC) during the reorientation induced by the external field. Spectra of planar aligned cells of FLC W314 are measured as functions of IR polarizer orientation and electric field applied to the FLC. The time evolution of the dichroism of the absorbance due to biphenyl core and alkyl tail molecular vibration modes, is observed. Static IR dichroism experiments show a W314 dichroism structure in which the principal axis of dielectric tensor from molecular core vibration are tilted further from the smectic layer normal than those of the tail. This structure indicates the effective binding site in which the molecules are confined in the Sm-C phase has, on average, "zig-zag" shape and this zig-zag binding site structure is rigidly maintained while the molecular axis rotates about the layer normal during field-induced switching.

• 대한기계학회논문집B
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• 제41권7호
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• pp.455-462
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• 2017

외부자기장에 의한 타원형 야누스 자성입자 사이의 자성 상호작용을 직접수치해석을 사용하여 분석하였다. 유한요소법에 기초한 가상영역법을 사용하여 입자계 유동해석을 수행하였고, 자기장 문제에서는 자성 포텐셜에 대한 지배방정식을 입자와 유체를 포함하는 전체영역에 대하여 풀어 자기장을 구하였다. 이 때 구해진 자기장으로부터 구한 맥스웰 응력을 사용하여 개별 입자에 작용하는 자기력이 계산된다. 입자의 운동과 최종적인 조립구조는 입자의 형상비, 개별 입자의 배향, 입자의 초기 분포에 크게 영향을 받는 것이 확인되었다. 또한 입자의 배향은 입자 주위의 유체 유동에도 영향을 주었다. 외부자기장에 의한 타원형 야누스 입자의 최종 조립구조는 앞서 언급한 인자들에 의해서 영향을 받은 것을 수치해석을 통해 확인할 수 있었다.