论文标题
半月板悬浮跃迁的关键效果和缩放
Critical effects and scaling at meniscus osculation transitions
论文作者
论文摘要
我们提出了一个简单的缩放理论，描述了圆形拟南期的关键效应，当液体液体液体液的宏观降低的拉普拉斯半径与局部曲率$ r_w $相吻合时，这种效果会发生。我们认为，指数$β_ {\ rm osc} $表征了界面高度$ \ ell_0 \ propto r_w^{β_{\ rm osc}} $的规模，以大型$ r_w $表示，代表大型$ r_w $，代表两个政策，表现出两种政策，属于上流和平均水平的行为。这两个方案由上临界维度隔开，在此明确确定，这取决于分子间力的范围。在以短距力力的系统类别的波动为主的制度中，指数与界面徘徊的指数$ζ$ x $β_ {\ rm osc} =3ζ/（4-ζ）$有关。相比之下，在尚未确定的平均野外策略中，对于具有较长范围的力（和较高维度）的系统而发生，指数$β_{\ rm osc} $具有与指数$β_S^{\ rm co} $完全由Intermolecular intermolecular serals确定的指数$β_S^{\ rm co} $相同的值。使用界面汉密尔顿模型确认了预测$β_ {\ rm osc} = 3/7 $ in $ d = 2 $（对应于$ζ= 1/2 $）的系统（对应于$ζ= 1/2 $），这确认了界面汉密尔顿模型，该模型确定了界面高度高概率分布功能的精确缩放形式。基于微观模型密度函数理论的$ d = 3 $的数值研究确定$β_ {\ rm osc} \ oftβ_s^{\ rm co} \ ofβ_s^{\ rm co} \大约0.326 $接近适合预测的$ 1/3 $，适用于平均型号的均值$ 1/3 $。
We propose a simple scaling theory describing critical effects at rounded meniscus osculation transitions which occur when the Laplace radius of a condensed macroscopic drop of liquid coincides with the local radius of curvature $R_w$ in a confining parabolic geometry. We argue that the exponent $β_{\rm osc}$ characterising the scale of the interfacial height $\ell_0 \propto R_w^{β_{\rm osc}}$ at osculation, for large $R_w$, falls into two regimes representing fluctuation-dominated and mean-field like behaviour, respectively. These two regimes are separated by an upper critical dimension, which is determined here explicitly and which depends on the range of the intermolecular forces. In the fluctuation-dominated regime, representing the universality class of systems with short-ranged forces, the exponent is related to the value of the interfacial wandering exponent $ζ$ by $β_{\rm osc}=3ζ/(4-ζ)$. In contrast, in the mean-field regime, which has not been previously identified, and which occurs for systems with longer ranged forces (and higher dimensions), the exponent $β_{\rm osc}$ takes the same value as the exponent $β_s^{\rm co}$ for complete wetting which is determined directly by the intermolecular forces. The prediction $β_{\rm osc}=3/7$ in $d=2$ for systems with short-ranged forces (corresponding to $ζ=1/2$) is confirmed using an interfacial Hamiltonian model which determines the exact scaling form for the decay of the interfacial height probability distribution function. A numerical study in $d=3$, based on a microscopic model Density Functional Theory, determines that $β_{\rm osc} \approx β_s^{\rm co}\approx 0.326$ close to the predicted value $1/3$ appropriate to the mean-field regime for dispersion forces.
