Explicit computation of Galois representations occurring in families of curves

We extend our method to compute division polynomials of Jacobians of curves over Q to curves over Q(t), in view of computing mod ell Galois representations occurring in the \'etale cohomology of surfaces over Q. Although the division polynomials which we obtain are unfortunately too complicated to achieve this last goal, we still obtain explicit families of Galois representations over P^1_Q, and we study their degeneration at places of bad reduction of the corresponding curve.Comment: Comments welcom

Fracture Toughness of Electrospun Fibrous Mats

Fiber reinforced composite hydrogels have become a popular material used in tissue engineering in recent years due to their robust nature under tension and biocompatibility qualities [1]. However, little is known of the fracture mechanics of the fiber reinforcements themselves (which are typically created of Electrospun materials, a process in which a high voltage differential is applied to a polymer solution, creating a jet of nanofibers that collect into a mat- like material) [2]. This study provides ana analysis of the fracture toughness of two Electrospun materials: one created from a 100 bloom strength gelatin solution, and one created from a 300 bloom strength gelatin solution. It is found that the fracture toughness increases as the rate of extension increases during standard tear testing in both materials, and the fracture toughness of the 300 bloom strength material is greater than that of the 100 bloom strength material. Further experimentation is needed to confirm the results of this preliminary data

Mechanical Characterization of 3D Printed Hydrogel Lattices

White matter brain tissue is largely inaccessible and is therefore difficult to mechanically characterize although this would be useful in understanding injuries and injury prevention. Thus, soft gels and 3D bioprinted materials allow for the estimation of the mechanical properties of brain tissue through non-invasive means. Through previous studies, it is determined that brain tissue is inherently anisotropic. To properly model it, the use of anisotropic cubic, diamond, and vintile type lattice 10 x 10 x 10 cm cube structures were used in compression testing to determine the elastic modulus of each lattice type in each of its orientations. Each lattice was scaled by 2 times in its X-direction and remined the same in its Y and Z directions. It was found that anisotropy in the material produces greater overall stiffness in the lattice structure, although more testing is needed to verify the results of this original study