Monte Carlo simulations of fluid vesicles with in plane orientational ordering

We present a method for simulating fluid vesicles with in-plane orientational ordering. The method involves computation of local curvature tensor and parallel transport of the orientational field on a randomly triangulated surface. It is shown that the model reproduces the known equilibrium conformation of fluid membranes and work well for a large range of bending rigidities. Introduction of nematic ordering leads to stiffening of the membrane. Nematic ordering can also result in anisotropic rigidity on the surface leading to formation of membrane tubes.Comment: 11 Pages, 12 Figures, To appear in Phys. Rev.

Application of the Fisher-Rao metric to ellipse detection

The parameter space for the ellipses in a two dimensional image is a five dimensional manifold, where each point of the manifold corresponds to an ellipse in the image. The parameter space becomes a Riemannian manifold under a Fisher-Rao metric, which is derived from a Gaussian model for the blurring of ellipses in the image. Two points in the parameter space are close together under the Fisher-Rao metric if the corresponding ellipses are close together in the image. The Fisher-Rao metric is accurately approximated by a simpler metric under the assumption that the blurring is small compared with the sizes of the ellipses under consideration. It is shown that the parameter space for the ellipses in the image has a finite volume under the approximation to the Fisher-Rao metric. As a consequence the parameter space can be replaced, for the purpose of ellipse detection, by a finite set of points sampled from it. An efficient algorithm for sampling the parameter space is described. The algorithm uses the fact that the approximating metric is flat, and therefore locally Euclidean, on each three dimensional family of ellipses with a fixed orientation and a fixed eccentricity. Once the sample points have been obtained, ellipses are detected in a given image by checking each sample point in turn to see if the corresponding ellipse is supported by the nearby image pixel values. The resulting algorithm for ellipse detection is implemented. A multiresolution version of the algorithm is also implemented. The experimental results suggest that ellipses can be reliably detected in a given low resolution image and that the number of false detections can be reduced using the multiresolution algorithm

The importance of parameter choice in modelling dynamics of the eye lens

The lens provides refractive power to the eye and is capable of altering ocular focus in response to visual demand. This capacity diminishes with age. Current biomedical technologies, which seek to design an implant lens capable of replicating the function of the biological lens, are unable as yet to provide such an implant with the requisite optical quality or ability to change the focussing power of the eye. This is because the mechanism of altering focus, termed accommodation, is not fully understood and seemingly conflicting theories require experimental support which is difficult to obtain from the living eye. This investigation presents finite element models of the eye lens based on data from human lenses aged 16 and 35 years that consider the influence of various modelling parameters, including material properties, a wide range of angles of force application and capsular thickness. Results from axisymmetric models show that the anterior and posterior zonules may have a greater impact on shape change than the equatorial zonule and that choice of capsular thickness values can influence the results from modelled simulations