顺向列胶体中的相互作用能
Interaction energies in paranematic colloids
AI总结：
本文研究顺向列相中胶体粒子的远场相互作用，通过变分模型线性化的严格渐近分析及数值验证，证明非线性与线性问题衰减率相似，并利用蒙特卡洛模拟揭示系统统计性质。
摘要：
我们考虑一个嵌入在顺向列相中的胶体粒子系统——即高于向列-各向同性转变温度的向列介质中的各向同性相。在这种状态下，向列序由每个粒子周围狭窄区域内的边界条件诱导，并在体相中指数衰减。我们发展了相应变分模型线性化的严格渐近分析，从而能够描述二维顺向列悬浮液中胶体粒子之间的弱远场相互作用。我们解析地证明了完整非线性问题与线性问题解的衰减速率相似，并通过数值验证了这些问题中粒子间相互作用对粒子间距离的依赖关系相似。最后，我们对顺向列相中的胶体粒子系统进行了蒙特卡洛模拟，并描述了该系统的统计性质。
英文摘要：
We consider a system of colloidal particles embedded in a paranematic -- an isotropic phase of a nematogenic medium above the temperature of the nematic-to-isotropic transition. In this state, the nematic order is induced by the boundary conditions in a narrow band around each particle and it decays exponentially in the bulk. We develop rigorous asymptotics of the linearization of the appropriate variational model that allow us to describe weak far-field interactions between the colloidal particles in two dimensional paranematic suspensions. We demonstrate analytically that decay rates of solutions to the full nonlinear and linear problems are similar and verify numerically that the interactions between the particles in these problems have similar dependence on the distance between the particles. Finally, we perform Monte-Carlo simulations for a system of colloidal particles in a paranematic and describe the statistical properties of this system.
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