Statistical mechanics of asymmetric tethered membranes: spiral and crumpled phases
Tirthankar Banerjee, Niladri Sarkar, John Toner, Abhik Basu
备注：
28 pages, 12 captioned figures. This is an accompanying longer version of our already submitted work, arXiv:1811.12440, containing all the technical details required for a thorough reading of arXiv:1811.12440
我们发展的弹性理论的反转非对称栓系膜，并使用它来识别和研究它们可能的阶段。系留膜中的不对称性导致自发曲率，这通常取决于系留网络的局部面内膨胀。这反过来又导致局部平均曲率和高斯曲率之间的长程相互作用，这在对称系留膜中不存在。这种不对称性和高斯曲率之间的相互作用导致了一种新的{ \em双螺旋}相，这种相在对称的栓系膜中没有发现。在温度$T=0$下，任意大尺寸的系留膜总是紧紧地卷起成一对相连的阿基米德螺线。在有限的$T$这个螺旋结构膨胀显着的代数螺旋的特点是普遍的指数，我们计算。这些螺旋具有长程取向顺序，并且是统计上平坦对称的系留膜的不对称类似物。我们还发现，足够强的不对称性可以触发结构的不稳定性，导致这些膜起皱。这为非对称系留膜的起皱提供了一条新的途径。我们计算了$L_c$的最大线性范围，超过该范围，膜起皱，并计算了$L_c$对膜参数的普遍依赖性。通过调节不对称参数，$L_c$可以连续变化，这意味着{ \em尺度依赖}起皱。我们的理论可以在具有血影蛋白丝的人工沉积物的脂质的对照实验、% \sout{artificial deposition of spectrin filaments on}红细胞膜提取物、% \sout{after %depletion of adenosine-tri-phosphate molecules}和一侧涂覆的石墨烯的体外实验上进行测试。
英文摘要：
We develop the elastic theory for inversion-asymmetric tethered membranes and use it to identify and study their possible phases. Asymmetry in a tethered membrane causes spontaneous curvature, which in general depends upon the local in-plane dilation of the tethered network. This in turn leads to long-ranged interactions between the local mean and Gaussian curvatures, which is not present in symmetric tethered membranes. This interplay between asymmetry and Gaussian curvature leads to a new {\em double-spiral} phase not found in symmetric tethered membranes. At temperature $T=0$, tethered membranes of arbitrarily large size are always rolled up tightly into a conjoined pair of Archimedes' spirals. At finite $T$ this spiral structure swells up significantly into algebraic spirals characterized by universal exponents which we calculate. These spirals have long range orientational order, and are the asymmetric analogs of statistically flat symmetric tethered membranes. We also find that sufficiently strong asymmetry can trigger a structural instability leading to crumpling of these membranes as well. This provides a new route to crumpling for asymmetric tethered membranes. We calculate the maximum linear extent $L_c$ beyond which the membrane crumples, and calculate the universal dependence of $L_c$ on the membrane parameters. By tuning the asymmetry parameter, $L_c$ can be continuously varied, implying a {\em scale-dependent} crumpling. Our theory can be tested on controlled experiments on lipids with artificial deposits of spectrin filaments, in-vitro experiments on %\sout{artificial deposition of spectrin filaments on} red blood cell membrane extracts, %\sout{after %depletion of adenosine-tri-phosphate molecules} and on graphene coated on one side.
Anisotropy can make a moving active fluid membrane rough or crumpled
Saha Institute of Nuclear Physics（萨哈核物理研究所）；Homi Bhabha National Institute（霍米·巴巴国立研究所）；Saarland University（萨尔兰大学）；Max-Planck-Institut für Physik komplexer Systeme（马克斯·普朗克复杂系统物理研究所）
