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41.
ABSTRACTA striking feature of lyotropic chromonic liquid crystals confined in cylinder model exhibit double-twist director configurations. Evidence suggests that saddle-splay deformation is among the most important factors for the distortions of director. Previous researches limit the director to distort at a fixed plane (r-? plane) by using specific boundary conditions such as degenerate planar anchoring condition. In this work, we consider lyotropic chromonic liquid crystals confined between two coaxial cylinders with free-surface boundary conditions and Rapini-Papoular-type anchoring conditions. By using finite-difference iterative method to solve the numerical solution of Euler equation, we find that saddle-splay deformation leads to double-twist director configurations under free-surface boundary conditions, which consist of the result under degenerate planar anchoring conditions. Furthermore, at Rapini-Papoular-type anchoring conditions, saddle-splay deformation has a great influence on the director in the radial direction (r direction) and the director distorts in three-dimensional space. Remarkably, our method provides a more accurate theory basis for the measured values of saddle-splay elastic constant K24。 相似文献
42.
目前,悬链线在竖向集中力和均布荷载共同作用下的构形分析和受力计算的理论仍不完善。针对这一问题,通过引入悬链线的几何约束方程、力平衡方程和超越方程,建立了竖向集中力与均布荷载共同作用下的非线性方程组。采用牛顿迭代法求解方程组,得到了悬链线的构形和受力情况。为了验证理论计算的正确性,进行了算例和试验验证。结果表明,算例的计算结果与文献结论保持一致,试验测得的构形和水平张力大小与理论计算的构形和水平张力大小吻合较好。本文的理论计算可以更加简单精确地计算出悬链线在竖向集中力和均布荷载共同作用下的构形和受力情况,为实际工程提供重要的理论指导。 相似文献
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The flow behavior in non-parallel walls is an important factor of any physical model including cavity flow and canals, which is applicable for diverging/converging channel. The present communication explains that the flow of the hybrid nanomaterial subjected to the convergent/divergent channel has non-parallel walls. It is assumed that the hybrid nanomaterial movement is in the porous region. A Darcy-Forchheimer medium of porosity is considered to interpret the porosity features. A useful similarity function is adopted to get the strong ordinary coupled equations. Numerical solutions are achieved through the Runge-Kutta-Fehlberg(RKF) fourth-fifth order method, and they are validated with the existing results. Physical nature of the involving constraints is reported with the help of plots. It is explored that the velocity of divergent channel decreases, and convergent channel enhances for the higher solid volume faction. Further, the presence of inertia coefficient and porosity parameter amplifies the velocity at the wall. 相似文献
45.
利用同余式、平方剩余、Pell方程的解的性质、递归序列证明了:不定方程x3-1=749y2仅有整数解(x,y)=(1,0). 相似文献
46.
We consider the chemotaxis‐Navier–Stokes system 1.1-1.4 (Keller–Segel system) in the whole space, which describes the motion of oxygen‐driven bacteria, eukaryotes, in a fluid. We proved the global existence and time decay estimate of solutions to the Cauchy problem 1.1-1.2 in with the small initial data. Moreover, when the fluid motion is described by the Stokes equations, we established the global weak solutions to 1.3-1.4 in with the potential function ? is small and the initial density n0(x) has finite mass. 相似文献
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This research is made to visualize the boundary layer flow by a curved stretching sheet embedded in porous medium. The geometry is bended(curved), therefore the curvilinear coordinates are used to model the present problem.Fluid is electrically conducting with the presence of uniform magnetic field. The governing non-linear partial differential equation reduces to non-linear ordinary differential equations by using the dimensionless suitable transformations. The numerical solutions are obtained by using the method bvp4c from MATLAB. The effects of curvature parameter, nondimensional magnetic parameter, and porosity parameter on the velocity field and skin friction coefficient are examined.The skin friction profile enhances with enhancing the values of porosity and magnetic parameter. Comparison of the present results with the existing results in the literature for the flat surface is also given. 相似文献
50.
We describe the indecomposable involutive non-degenerate set-theoretic solutions of the Yang–Baxter equation as dynamical extensions of non-degenerate left cycle sets. Moreover we characterize the indecomposable dynamical extensions and we produce several examples. As an application we construct a family of finite indecomposable solutions whose structure groups have not the unique product property. 相似文献