Complex bifurcation maps in electroelastic elastomeric plates

[EN] Stress-strain relationships for rubbery materials are highly non-linear. In this work, a particular configuration of electroactive material is considered: an isotropic, incompressible electroelastic squared plate is subjected to equal biaxial homogeneous deformation and a scalar electrical potential is applied on the sides of compliant electrodes. This case is analysed according to two methodologies: the Hessian approach and the use of incremental deformation together with increment in the electric displacement. First, an extended Mooney Rivlin model is considered for the material and then an Ogden model is also analysed. Results, show, that despite of available experimental results, some predictions can be made and the pertinent analysis show complex bifurcation maps. This can help in the future progress in the knowledge of the instabilities and bifurcation phenomena which should appear in these materials. The present paper has been mainly motivated by the work of Ogden and DorfmannDíaz Calleja, R.; Llovera Segovia, P.; Quijano Lopez, A. (2017). Complex bifurcation maps in electroelastic elastomeric plates. International Journal of Solids and Structures. 113:70-84. doi:10.1016/j.ijsolstr.2016.12.021S708411

Identification, Characterization, and Localization of a Novel Kidney Polycystin-1-Polycystin-2 Complex

The functions of the two proteins defective in autosomal dominant polycystic kidney disease, polycystin-1 and polycystin-2, have not been fully clarified, but it has been hypothesized that they may heterodimerize to form a "polycystin complex" involved in cell adhesion. In this paper, we demonstrate for the first time the existence of a native polycystin complex in mouse kidney tubular cells transgenic for PKD1, non-transgenic kidney cells, and normal adult human kidney. Polycystin-1 is heavily N-glycosylated, and several glycosylated forms of polycystin-1 differing in their sensitivity to endoglycosidase H (Endo H) were found; in contrast, native polycystin-2 was fully Endo H-sensitive. Using highly specific antibodies to both proteins, we show that polycystin-2 associates selectively with two species of full-length polycystin-1, one Endo H-sensitive and the other Endo H-resistant; importantly, the latter could be further enriched in plasma membrane fractions and co-immunoprecipitated with polycystin-2. Finally, a subpopulation of this complex co-localized to the lateral cell borders of PKD1 transgenic kidney cells. These results demonstrate that polycystin-1 and polycystin-2 interact in vivo to form a stable heterodimeric complex and suggest that disruption of this complex is likely to be of primary relevance to the pathogenesis of cyst formation in autosomal dominant polycystic kidney disease

A Presentation For The Automorphisms Of The 3-Sphere That Preserve A Genus Two Heegaard Splitting

Scharlemann constructed a connected simplicial 2-complex $\Gamma$ with an action by the group ${\mathcal H_{2}}$ of isotopy classes of orientation preserving homeomorphisms of $S^3$ that preserve the isotopy class of an unknotted genus 2 handlebody $V$. In this paper we prove that the 2-complex $\Gamma$ is contractible. Therefore we get a finite presentation of ${\mathcal H_{2}}$.Comment: Completely rewritten. 21 pages with 22 figure

Bubble divergences from cellular cohomology

We consider a class of lattice topological field theories, among which are the weak-coupling limit of 2d Yang-Mills theory, the Ponzano-Regge model of 3d quantum gravity and discrete BF theory, whose dynamical variables are flat discrete connections with compact structure group on a cell 2-complex. In these models, it is known that the path integral measure is ill-defined in general, because of a phenomenon called `bubble divergences'. A common expectation is that the degree of these divergences is given by the number of `bubbles' of the 2-complex. In this note, we show that this expectation, although not realistic in general, is met in some special cases: when the 2-complex is simply connected, or when the structure group is Abelian -- in both cases, the divergence degree is given by the second Betti number of the 2-complex.Comment: 5 page

The automorphism group of the free group of rank two is a CAT(0) group

We prove that the automorphism group of the braid group on four strands acts faithfully and geometrically on a CAT(0) 2-complex. This implies that the automorphism group of the free group of rank two acts faithfully and geometrically on a CAT(0) 2-complex, in contrast to the situation for rank three and above.Comment: 7 pages, 2 figures. The manuscript has been modified in minor ways in accordance with a referee's recommendations, and a misattribution of the result "Aut F_2 is biautomatic" has been correcte