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首页> 外文会议>The Role of Mechanics in the Study of Lipid Bilayers >The Geometry of Fluid Membranes: Variational Principles, Symmetries and Conservation Laws
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The Geometry of Fluid Membranes: Variational Principles, Symmetries and Conservation Laws

机译：流体膜的几何：变分原理，对称性和守恒律

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摘要

The behavior of a lipid membrane on mesoscopic scales is captured unusually accurately by its geometrical degrees of freedom. Indeed, the membrane geometry is, very often, a direct reflection of the physical state of the membrane. In this chapter we will examine the intimate connection between the geometry and the physics of fluid membranes from a number of points of view. We begin with a review of the description of the surface geometry in terms of the metric and the extrinsic curvature, examining surface deformations in terms of the behavior of these two tensors. The shape equation describing membrane equilibrium is derived and the qualitative behavior of solutions described. We next look at the conservation laws implied by the Euclidean invariance of the energy, describing the remarkably simple relationship between the stress distributed in the membrane and its geometry. This relationship is used to examine membrane-mediated interactions. We show how this geometrical framework can be extended to accommodate constraints-both global and local-as well as additional material degrees of freedom coupling to the geometry. The conservation laws are applied to examine the response of an axially symmetric membrane to localized external forces and to characterize topologically nontrivial states. We wrap up by looking at the conformal invariance of the symmetric two-dimensional bending energy, and examine some of its consequences.
机译：脂质膜在介观尺度上的行为通过其几何自由度被异常精确地捕获。实际上，膜的几何形状经常是膜的物理状态的直接反映。在本章中，我们将从多个角度研究流体膜的几何形状与物理之间的紧密联系。我们先从度量和外在曲率的角度对表面几何形状的描述进行回顾，然后根据这两个张量的行为来检查表面变形。得出描述膜平衡的形状方程，并描述溶液的定性行为。接下来，我们看一下能量的欧几里得不变所隐含的守恒律，描述了膜中分布的应力与其几何形状之间非常简单的关系。该关系用于检查膜介导的相互作用。我们展示了如何扩展此几何框架以适应全局和局部约束以及耦合到几何的其他材料自由度。守恒律适用于检查轴对称膜对局部外力的响应并表征拓扑上的非平凡状态。我们通过观察对称二维弯曲能量的共形不变性来总结一下，并研究其一些后果。

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  • 会议地点 Udine(IT)
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    Jemal Guven; Pablo Vazquez-Montejo;

  • 作者单位

    Institute de Ciencias Nucleares, Universidad Nacional Aut6noma de Mexico, Apdo. Postal 70-543, 04510 Mexico City, Mexico;

    Facultad de Matemfiticas, Universidad Aut6noma de Yucatan, Perifenco Norte, Tablaje 13615, 97110 M6rida, Yucatan, Mexico;

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