Spontaneous rotational inversion in Phycomyces

The filamentary fungus Phycomyces blakesleeanus undergoes a series of remarkable transitions during aerial growth. During what is known as the Stage IV growth phase, the fungus extends while rotating in a counterclockwise manner when viewed from above (Stage IVa) and then, while continuing to grow, spontaneously reverses to a clockwise rotation (Stage IVb). This phase lasts for 24 - 48 hours and is sometimes followed by yet another reversal (Stage IVc) before the overall growth ends. Here, we propose a continuum mechanical model of this entire process using nonlinear, anisotropic, elasticity and show how helical anisotropy associated with the cell wall structure can induce spontaneous rotation and, under appropriate circumstances, the observed reversal of rotational handedness

Rotation, inversion, and perversion in anisotropic elastic cylindrical tubes and membranes

Cylindrical tubes and membranes are universal structural elements found in biology and engineering over a wide range of scales. Working in the framework of nonlinear elasticity we consider the possible deformations of elastic cylindrical shells reinforced by one or two families of anisotropic fibers. We consider both small and large deformations and the reduction from thick cylindrical shells (tubes) to thin shells (cylindrical membranes). In particular, a number of universal regimes can be identified including the possibility of inversion and perversion of rotation

Nonlinear Morphoelastic Plates I: Genesis of Residual Stress

Volumetric growth of an elastic body may give rise to residual stress. Here a rigorous analysis of the residual strains and stresses generated by growth in the axisymmetric Kirchhoff plate is given. Balance equations are derived via the global constraint principle, growth is incorporated via a multiplicative decomposition of the deformation gradient, and the system is closed by a response function. The particular case of a compressible neo-Hookean material is analyzed and the existence of residually stressed states is established

Nonlinear morphoelastic plates II: exodus to buckled states

Morphoelasticity is the theory of growing elastic materials. This theory is based on the multiple decomposition of the deformation gradient and provides a formulation of the deformation and stresses induced by growth. Following a companion paper, a general theory of growing nonlinear elastic Kirchhoff plate is described. First, a complete geometric description of incompatibility with simple examples is given. Second, the stability of growing Kirchhoff plates is analyzed

A local Gaussian filter and adaptive morphology as tools for completing partially discontinuous curves

This paper presents a method for extraction and analysis of curve--type structures which consist of disconnected components. Such structures are found in electron--microscopy (EM) images of metal nanograins, which are widely used in the field of nanosensor technology. The topography of metal nanograins in compound nanomaterials is crucial to nanosensor characteristics. The method of completing such templates consists of three steps. In the first step, a local Gaussian filter is used with different weights for each neighborhood. In the second step, an adaptive morphology operation is applied to detect the endpoints of curve segments and connect them. In the last step, pruning is employed to extract a curve which optimally fits the template

Transport in Almost Integrable Models: Perturbed Heisenberg Chains

The heat conductivity kappa(T) of integrable models, like the one-dimensional spin-1/2 nearest-neighbor Heisenberg model, is infinite even at finite temperatures as a consequence of the conservation laws associated with integrability. Small perturbations lead to finite but large transport coefficients which we calculate perturbatively using exact diagonalization and moment expansions. We show that there are two different classes of perturbations. While an interchain coupling of strength J_perp leads to kappa(T) propto 1/J_perp^2 as expected from simple golden-rule arguments, we obtain a much larger kappa(T) propto 1/J'^4 for a weak next-nearest neighbor interaction J'. This can be explained by a new approximate conservation law of the J-J' Heisenberg chain.Comment: 4 pages, several minor modifications, title change