Calderon Projector for the Hessian of the Perturbed Chern-Simons Function on a 3-Manifold with Boundary

The existence and continuity for the Calderón projectorof the perturbed odd signature operator on a 3-manifold is established.As an application we give a new proof of a result of Taubesrelating the modulo 2 spectral flow of a family of operatorson a homology 3-sphere with the difference in local intersectionnumbers of the character varieties coming from a Heegard decomposition.2000 Mathematics Subject Classification 57M27 (primary), 58J32(secondary).     

Theory and implementation of orthotropic materials in growing continua

Most biological tissues show a material behavior which is characterized through a pronounced anisotropy. In particular hard tissues such as bones or soft tissues as muscles are commonly modeled as either transversely isotropic or even orthotropic. In contrast to engineering materials, however, biological tissues possess the ability to adapt, e.g. their density, to the current loading situation. Based on a formulation for growth in isotropic continua, see for instance Kuhl, Menzel & Steinmann [3], and transversely isotropic continua as discussed e.g. in Himpel [2], we attend to a model for the functional adaption of orthotropic biomaterials. The material model has been implemented in a finite element code and is studied by means of a numerical example. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)