Stelitano D, Rothman DH
Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Nov;62(5 Pt A):6667-80. doi: 10.1103/physreve.62.6667.
We study the dynamics of elastic interfaces-membranes-immersed in thermally excited fluids. The work contains three components: the development of a numerical method, a purely theoretical approach, and numerical simulation. In developing a numerical method, we first discuss the dynamical coupling between the interface and the surrounding fluids. An argument is then presented that generalizes the single-relaxation-time lattice-Boltzmann method for the simulation of hydrodynamic interfaces to include the elastic properties of the boundary. The implementation of this method is outlined and it is tested by simulating the static behavior of spherical bubbles and the dynamics of bending waves. By means of the fluctuation-dissipation theorem we recover analytically the equilibrium frequency power spectrum of thermally fluctuating membranes and the correlation function of the excitations. Also, the nonequilibrium scaling properties of the membrane roughening are deduced, leading us to formulate a scaling law describing the interface growth, W2(L,t)=L(3) g(t/L(5/2)), where W, L, and t are the width of the interface, the linear size of the system, and the time, respectively, and g is a scaling function. Finally, the phenomenology of thermally fluctuating membranes is simulated and the frequency power spectrum is recovered, confirming the decay of the correlation function of the fluctuations. As a further numerical study of fluctuating elastic interfaces, the nonequilibrium regime is reproduced by initializing the system as an interface immersed in thermally preexcited fluids.
我们研究了浸没在热激发流体中的弹性界面（膜）的动力学。这项工作包含三个部分：一种数值方法的开发、一种纯理论方法以及数值模拟。在开发数值方法时，我们首先讨论界面与周围流体之间的动力学耦合。然后提出了一个论点，将用于模拟流体动力学界面的单弛豫时间格子玻尔兹曼方法进行推广，以纳入边界的弹性特性。概述了该方法的实现过程，并通过模拟球形气泡的静态行为和弯曲波的动力学对其进行了测试。借助涨落耗散定理，我们通过解析得到了热涨落膜的平衡频率功率谱以及激发的相关函数。此外，推导了膜粗糙化的非平衡标度性质，从而使我们能够制定一个描述界面生长的标度律，即(W^2(L,t)=L^3 g(t/L^{5/2}))，其中(W)、(L)和(t)分别是界面宽度、系统的线性尺寸和时间，(g)是一个标度函数。最后，对热涨落膜的现象学进行了模拟，并恢复了频率功率谱，证实了涨落相关函数的衰减。作为对涨落弹性界面的进一步数值研究，通过将系统初始化为浸没在热预激发流体中的界面来再现非平衡态。
