Localised bifurcation in soft cylindrical tubes under axial stretching and surface tension

圆柱形纳米孔中自回避链的压缩和拉伸

Compression and stretching of a self-avoiding chain in cylindrical nanopores

利用分子动力学模拟、标度分析和解析计算，研究了直径为$D$的圆柱形空腔内自回避链的力致变形.我们得到并确认一个简单的标度关系$-f \cdot D \sim R^{-9/4}$在强压缩制度，而对于弱变形，我们发现$f \cdot D = -A(R/R_0) + B (R/R_0)^{-2}$，其中$A$和$B$是常数，$f$的外力，和$R$的链延伸（与$R_0$其未扰动值）。对于一个强的拉伸，我们提出了一个普遍的，分析力的延伸关系。我们的研究结果可用于分析生物分子在约束条件下的行为。

From cylindrical to stretching ridges and wrinkles in twisted ribbons

Twisted ribbons subjected to a tension exhibit a remarkably rich morphology, from smooth and wrinkled helicoids, to cylindrical or faceted patterns. These shapes are intimately related to the instability of the natural, helicoidal symmetry of the system, which generates both longitudinal and transverse stresses, thereby leading to buckling of the ribbon. In this paper, we focus on the tessellation patterns made of triangular facets. Our experimental observations are described within an "asymptotic isometry" approach that brings together geometry and elasticity. The geometry consists of paramet…

Elasto-capillary circumferential buckling of soft tubes under axial loading: existence and competition with localised beading and periodic axial modes

We provide an extension to previous analysis of the localised beading instability of soft slender tubes under surface tension and axial stretching. The primary questions pondered here are: under what loading conditions, if any, can bifurcation into circumferential buckling modes occur, and do such solutions dominate localisation and periodic axial modes? Three distinct boundary conditions are considered; in case 1 the tube's curved surfaces are traction free and under surface tension, whilst in cases 2 and 3 the inner and outer surfaces (respectively) are fixed to prevent radial displacement a…

Non-affine bending mode of thin cylindrical tubes

We discuss the response of thin cylindrical tubes to small indentations. The stretching-free embedding of these surfaces is completely determined by the embedding of one edge curve, thus reducing their bending response to an effectively one dimensional problem. We obtain that in general thin cylindrical tubes will bend non-uniformly in response to an indentation normal to their surface. As a consequence, their local bending stiffness, as measured by indenting at various locations along their axis, is predicted to peak at the center and decrease by a universal factor of 4 at either end of the t…

平面、球形和管状膜中的力和波动

Forces and fluctuations in planar, spherical and tubular membranes

脂质膜构成非常特殊的材料：一方面，它们在显微镜拉伸下非常容易破裂;另一方面，它们非常柔韧，即使在小尺度下也会变形。因此，一片膜具有相对于其光学可分辨面积（也称为投影面积）过量的面积。从力学的角度来看，我们可以确定三种与脂膜相关的张力：机械有效张力$τ$，与投影面积的增加和波动的平坦化相关;张力$σ$，与膜的显微镜面积相关，因此不可测量，但通常用于理论预测;而其宏观对应物通过波动谱$r$测量。到目前为止，在分析实验数据时，这些量之间的相等是理所当然的。在本论文中，我们利用投影应力张量研究了是否以及在什么条件下假定$τ= σ$是合理的。我们研究了三种几何形状（平面，球形和圆柱形），并获得了关系$τ\approx σ- σ_0$，其中$σ_0$是一个常数，仅取决于膜的高频截止和温度。因此，我们的结论是，忽略$τ$和$σ$之间的差异是合理的，只有在大张力下的膜：在小张力的情况下，必须考虑到校正。我们已经研究了这一结果的解释涉及膜纳米管的实验的影响。关于$r$，我们质疑了以前关于它与$τ$平等的示威。最后，首次定量了平面膜和膜纳米管的力波动。