CMES-Vol. 75, Nos. 3&4, 2011

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Darcy-Stokes Equations with Finite Difference and Natural Boundary Element Coupling Method
Peng Weihong¹, Cao Guohua², Dongzhengzhu¹, Li Shuncai³
CMES-Computer Modeling in Engineering & Sciences, Vol.75, No.3&4, pp. 173-188, 2011, DOI:10.3970/cmes.2011.075.173
Abstract Numerical method is applied to investigate the Darcy-Stokes equations, which is governing the steady incompressible Stokes flow past a circular cavity in a porous medium. The free fluid flow is modeled by the incompressible Stokes equations, and the flow in the porous medium is imposed by Darcy equations. Based on domain decomposition method with D-N alternating iteration algorithm, the coupling method of finite difference method and natural boundary element method is studied for the coupling Darcy-Stokes equations under a certain pressure difference. The numerical results indicate that the finite difference and natural boundary element coupling More >

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A Geometric Approach to Solve Fuzzy Linear Systems
Nizami Gasilov¹, Şahin Emrah Amrahov², Afet Golayoğlu Fatullayev¹, Halil İbrahim Karakaş¹, Ömer Akın³
CMES-Computer Modeling in Engineering & Sciences, Vol.75, No.3&4, pp. 189-204, 2011, DOI:10.3970/cmes.2011.075.189
Abstract In this paper, linear systems with a crisp real coefficient matrix and with a vector of fuzzy triangular numbers on the right-hand side are studied. A new method, which is based on the geometric representations of linear transformations, is proposed to find solutions. The method uses the fact that a vector of fuzzy triangular numbers forms a rectangular prism in n-dimensional space and that the image of a parallelepiped is also a parallelepiped under a linear transformation. The suggested method clarifies why in general case different approaches do not generate solutions as fuzzy numbers. It… More >

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Investigation on the Singularities of Some Singular Integrals
Zai You Yan¹, Qiang Zhang¹
CMES-Computer Modeling in Engineering & Sciences, Vol.75, No.3&4, pp. 205-222, 2011, DOI:10.3970/cmes.2011.075.205
Abstract In a boundary element method, the treatment of all the possible singular integrals is very important for the correctness and accuracy of the solutions. Generally, the directional derivative of a weakly singular integral is computed by an integral in the sense of Cauchy principal value if the directional derivative of the weakly singular integral kernel is strongly singular or in the sense of Hadamard finite part integral if it is hypersingular. In this paper, we try to discover how the strongly singular and hypersingular integrals are generated and propose an idea to avoid the appearance More >

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Applications of Parameter-Expanding Method to Nonlinear Oscillators in which the Restoring Force is Inversely Proportional to the Dependent Variable or in Form of Rational Function of Dependent Variable
Canan Köroğlu¹, Turgut Öziş²
CMES-Computer Modeling in Engineering & Sciences, Vol.75, No.3&4, pp. 223-234, 2011, DOI:10.3970/cmes.2011.075.223
Abstract He's parameter-expanding method with an adjustment of restoring forces in terms of Chebyshev's series is used to construct approximate frequency-amplitude relations for a conservative nonlinear singular oscillator in which the restoring force is inversely proportional to the dependent variable or in form of rational function of dependant variable. The procedure is used to solve the nonlinear differential equation approximately. The approximate frequency obtained using this procedure is more accurate than those obtained using other approximate methods and the discrepancy between the approximate frequency and the exact one negligible. More >

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Size-Dependent Behavior of Macromolecular Solids III: The Role of Entanglements
W. Wei, David CC LAM¹
CMES-Computer Modeling in Engineering & Sciences, Vol.75, No.3&4, pp. 235-246, 2011, DOI:10.3970/cmes.2011.075.235
Abstract Chain rotations in macromolecular solids are constrained by entanglements. The effects of constraints on strain deformation and strain gradient deformation were investigated using molecular dynamic (MD) simulation in this paper. The effects on the chains were examined by embedding the chains inside bent beams. For thick beams, the simulated elastic moduli for styrene butyl rubber (SBR), polyimide (PI) and polyethylene (PE) were in good agreement with elastic moduli reported in the literature. The elastic moduli varied linearly with entanglements and inversely with the molecular weight. For thin beams where strain gradients were non-negligible, the results More >

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A Hybrid Quantum-Classical Simulation Study on Stress-Dependence of Li Diffusivity in Graphite
N. Ohba^1,2, S. Ogata², T. Tamura², S. Yamakawa¹, R. Asahi¹
CMES-Computer Modeling in Engineering & Sciences, Vol.75, No.3&4, pp. 247-266, 2011, DOI:10.3970/cmes.2011.075.247
Abstract Understanding the stress dependence of Li diffusivity in the Li-graphite intercalation compound (Li-GIC) that has been used in the Li-ion rechargeable battery as a negative electrode, is important to search for better conditions to improve the power performance of the battery. In the Li-GIC, the Li ion creates a long-ranged stress field around itself by expanding the inter-layer distance of the graphite. To take into account such a long-ranged stress field in the first-principles simulation of the Li diffusion, we develop the hybrid quantum (QM)-classical (CL) simulation code. In the hybrid code, the QM region… More >

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