Long-term aging of elastomers: Chemical stress relaxation of fluorosilicone rubber and other studies

Aerospace applications of elastomers are considered, including: propellant binders, bladder materials for liquid propellant expulsion systems, and fuel tank sealants for high-speed aircraft. A comprehensive molecular theory for mechanical properties of these materials has been developed but has only been tested experimentally in cases where chemical degradation processes are excluded. Hence, a study is being conducted to ascertain the nature, extent, and rate of chemical changes that take place in some elastomers of interest. Chemical changes that may take place in the fluorosilicone elastomer, LS 420, which is regarded as a fuel and high-temperature-resistant rubber are investigated. The kinetic analysis of the chemical stress relaxation and gel permeation chromatography studies comprise the major portion of the report

Lp-cohomology of negatively curved manifolds

We compute the $L^p$-cohomology spaces of some negatively curved manifolds. We deal with two cases: manifolds with finite volume and sufficiently pinched negative curvature, and conformally compact manifolds

On ``hyperboloidal'' Cauchy data for vacuum Einstein equations and obstructions to smoothness of ``null infinity''

Various works have suggested that the Bondi--Sachs--Penrose decay conditions on the gravitational field at null infinity are not generally representative of asymptotically flat space--times. We have made a detailed analysis of the constraint equations for ``asymptotically hyperboloidal'' initial data and find that log terms arise generically in asymptotic expansions. These terms are absent in the corresponding Bondi--Sachs--Penrose expansions, and can be related to explicit geometric quantities. We have nevertheless shown that there exists a large class of ``non--generic'' solutions of the constraint equations, the evolution of which leads to space--times satisfying the Bondi--Sachs--Penrose smoothness conditions.Comment: 8 pages, revtex styl

Self similar expanding solutions of the planar network flow

We prove the existence of self-similar expanding solutions of the curvature flow on planar networks where the initial configuration is any number of half-lines meeting at the origin. This generalizes recent work by Schn\"urer and Schulze which treats the case of three half-lines. There are multiple solutions, and these are parametrized by combinatorial objects, namely Steiner trees with respect to a complete negatively curved metric on the unit ball which span $k$ specified points on the boundary at infinity. We also provide a sharp formulation of the regularity of these solutions at $t=0$

Hodge theory on Cheeger spaces

We extend the study of the de Rham operator with ideal boundary conditions from the case of isolated conic singularities, as analyzed by Cheeger, to the case of arbitrary stratified pseudomanifolds. We introduce a class of ideal boundary operators and the notion of mezzoperversity, which intermediates between the standard lower and upper middle perversities in intersection theory, as interpreted in this de Rham setting, and show that the de Rham operator with these boundary conditions is Fredholm and has compact resolvent. We also prove an isomorphism between the resulting Hodge and L2 de Rham cohomology groups, and that these are independent of the choice of iterated edge metric. On spaces which admit ideal boundary conditions of this type which are also self-dual, which we call ‘Cheeger spaces’, we show that these Hodge/de Rham cohomology groups satisfy Poincare' Duality

Stability in Designer Gravity

We study the stability of designer gravity theories, in which one considers gravity coupled to a tachyonic scalar with anti-de Sitter boundary conditions defined by a smooth function W. We construct Hamiltonian generators of the asymptotic symmetries using the covariant phase space method of Wald et al.and find they differ from the spinor charges except when W=0. The positivity of the spinor charge is used to establish a lower bound on the conserved energy of any solution that satisfies boundary conditions for which $W$ has a global minimum. A large class of designer gravity theories therefore have a stable ground state, which the AdS/CFT correspondence indicates should be the lowest energy soliton. We make progress towards proving this, by showing that minimum energy solutions are static. The generalization of our results to designer gravity theories in higher dimensions involving several tachyonic scalars is discussed.Comment: 29 page

Asymptotic gluing of asymptotically hyperbolic solutions to the Einstein constraint equations

We show that asymptotically hyperbolic solutions of the Einstein constraint equations with constant mean curvature can be glued in such a way that their asymptotic regions are connected.Comment: 37 pages; 2 figure

Informed assessment of structural health conditions of bridges based on free-vibration tests

consolidated procedure for the evaluation of current structural health con-ditions in bridges consists in the comparison between estimated modal features from in-situ tests and numerical values. This strategy allows making informed decisions for existing bridge structures to ensure structural safety or serviceability. Free vibration tests are common in bridges monitoring since they allow a quick and cost-effective determination of dynamic infor-mation about the structure, using a sparse network of few sensors and avoid long-lasting monitoring campaigns. Exploiting an identification method based on a tuned version of Vari-ational Mode Decomposition and an area-ratio based approach, modal parameters are deter-mined from free vibration tests. This technique is applied to the dynamic identification of cables in a stay-cabled bridge assumed as case study: the obtained results prove reliability of the adopted method as a useful tool for objective dynamic identification purposes, with focus on the structural health conditions of bridges