We carry out Monte Carlo simulations of a colloidal fluid membrane with a free edge and composed of chiral rodlike viruses. The membrane is modeled by a triangular mesh of beads connected by bonds in which the bonds and beads are free to move at each Monte Carlo step. Since the constituent viruses are experimentally observed to twist only near the membrane edge, we use an effective energy that favors a particular sign of the geodesic torsion of the edge. The effective energy also includes the membrane bending stiffness, edge bending stiffness, and edge tension. We find three classes of membrane shapes resulting from the competition of the various terms in the free energy: branched shapes, chiral disks, and vesicles. Increasing the edge bending stiffness smooths the membrane edge, leading to correlations among the membrane normals at different points along the edge. The normalized power spectrum for edge displacements shows a peak with increasing preferred geodesic torsion. We also consider membrane shapes under an external force by fixing the distance between two ends of the membrane and finding the shape for increasing values of the distance between the two ends. As the distance increases, the membrane twists into a ribbon, with the force eventually reaching a plateau.

中文翻译：

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具有手性边缘的流体膜的形状

我们对具有自由边缘并由手性棒状病毒组成的胶体液膜进行了蒙特卡洛模拟。膜由通过连接的珠子组成的三角形网眼建模，在每个蒙特卡洛步骤中，键和珠子可以自由移动。由于实验观察到构成病毒仅在膜边缘附近扭曲，因此我们使用有效能量，该能量有利于边缘的短程线扭转的特定迹象。有效能量还包括膜的弯曲刚度，边缘弯曲刚度和边缘张力。我们发现，自由能中各种术语的竞争产生了三类膜形状：分支形状，手性圆盘和囊泡。增加边缘弯曲刚度可使膜边缘光滑，导致沿边缘不同点的膜法线之间的相关性。边缘位移的归一化功率谱显示出随着优选测地线扭转增加的峰值。我们还通过固定膜两端之间的距离并找到可增大两端之间距离值的形状来考虑外力作用下的膜形状。随着距离的增加，膜会扭曲成一条带，最终使力达到平稳状态。