Disorder, pre-stress and non-affinity in polymer 8-chain models

To assess the role of single-chain elasticity, non-affine strain fields and pre-stressed reference states we present and discuss the results of numerical and analytical analyses of modified 8-chain Arruda-Boyce model for cross-linked polymer networks. This class of models has proved highly successful in modeling the finite-strain response of flexible rubbers. We extend it to include the effects of spatial disorder and the associated non-affinity, and use it to assess the validity of replacing the constituent chain's nonlinear elastic response with equivalent linear, Hookean springs. Surprisingly, we find that even in the regime of linear response, the full polymer model gives very different results from its linearized counterpart, even though none of the chains are stretched beyond their linear regime. We demonstrate that this effect is due to the fact that the polymer models are under considerable pre-stress in their ground state. We show that pre-stress strongly suppresses non-affinity in these unit cell models, resulting in a marked stiffening of the bulk response. The effects of pre-stress we discuss may explain why fully affine mechanical models, in many cases, predict the bulk mechanical response of disordered stiff polymer networks so well.Comment: 29 pages, 7 figures. Submitted to J. Mech. Phys. Solid

The specificity of European cosmopolitanism in light of European citizenship

In terms of cosmopolitan thought, the European integration adventure, and in particular European citizenship should be understood in a context derived from the very motto of the Union: that of building a United Europe, all the while safeguarding the specificities of the various European peoples. European cosmopolitanism isn't one in which national identities melt into a broader pan-European identity, but it implies a multiplicity of identities involving citizens, all of them coexisting in a multi-layered and composite political and legal space. The European answer to the cosmopolitan question should not be the creation of a European state but instead it should emphasize preserving and enriching the current federal structure of Europe

Lagrangian interactions within a special class of covariant mixed-symmetry type tensor gauge fields

Consistent nontrivial interactions within a special class of covariant mixed-symmetry type tensor gauge fields of degree three are constructed from the deformation of the solution to the master equation combined with specific cohomological techniques. In spacetime dimensions strictly greater than four, the only consistent interaction terms are those gauge invariant under the original symmetry. Only in four spacetime dimensions the gauge symmetry is found deformed.Comment: 24 pages; two equations corrected; matches the published versio

No interactions for a collection of Weyl gravitons intermediated by a scalar field

The cross-couplings among several Weyl gravitons (described in the free limit by a sum of linearized Weyl actions) in the presence of a scalar field are studied with the help of the deformation theory based on local BRST cohomology. Under the hypotheses of locality, smoothness of the interactions in the coupling constant, Poincare invariance, (background) Lorentz invariance, and the preservation of the number of derivatives on each field, together with the supplementary assumption that the internal metric defined by the sum of Weyl lagrangians is positively defined, we prove that there are no consistent cross-interactions among different Weyl gravitons in the presence of a scalar field. The couplings of a single Weyl graviton to a scalar field are also discussed.Comment: 53 page

Four-dimensional couplings among BF and matter theories from BRST cohomology

The local and manifestly covariant Lagrangian interactions in four spacetime dimensions that can be added to a ``free'' model that describes a generic matter theory and an abelian BF theory are constructed by means of deforming the solution to the master equation on behalf of specific cohomological techniques.Comment: 45 pages, no figure

Imaging of atomic orbitals with the Atomic Force Microscope - experiments and simulations

Atomic force microscopy (AFM) is a mechanical profiling technique that allows to image surfaces with atomic resolution. Recent progress in reducing the noise of this technique has led to a resolution level where previously undetectable symmetries of the images of single atoms are observed. These symmetries are related to the nature of the interatomic forces. The Si(111)-(7x7) surface is studied by AFM with various tips and AFM images are simulated with chemical and electrostatic model forces. The calculation of images from the tip-sample forces is explained in detail and the implications of the imaging parameters are discussed. Because the structure of the Si(111)-(7x7) surface is known very well, the shape of the adatom images is used to determine the tip structure. The observability of atomic orbitals by AFM and scanning tunneling microscopy is discussed.Comment: 21 pages, 17 figure