The Amplitude of Non-Equilibrium Quantum Interference in Metallic Mesoscopic Systems

We study the influence of a DC bias voltage V on quantum interference corrections to the measured differential conductance in metallic mesoscopic wires and rings. The amplitude of both universal conductance fluctuations (UCF) and Aharonov-Bohm effect (ABE) is enhanced several times for voltages larger than the Thouless energy. The enhancement persists even in the presence of inelastic electron-electron scattering up to V ~ 1 mV. For larger voltages electron-phonon collisions lead to the amplitude decaying as a power law for the UCF and exponentially for the ABE. We obtain good agreement of the experimental data with a model which takes into account the decrease of the electron phase-coherence length due to electron-electron and electron-phonon scattering.Comment: New title, refined analysis. 7 pages, 3 figures, to be published in Europhysics Letter

Women’s Perspectives on Human Security: Violence, Environment, and Sustainability

Violent conflict, climate change, and poverty present distinct threats to women worldwide. Importantly, women are leading the way creating and sharing sustainable solutions. Women’s security is a valuable analytical tool as well as a political agenda insofar as it addresses the specific problems affecting women’s ability to live dignified, free, and secure lives. First, this collection focuses on how conflict impacts women’s lives and well-being, including rape and gendered constructions of ethnicity, race, and religion. The book’s second section looks beyond the scope of large-scale violence to examine human security in terms of environmental policy, food, water, health, and economics. Multidisciplinary in scope, these essays from new and established contributors draw from gender studies, international relations, criminology, political science, economics, sociology, biological and ecological sciences, and planning.https://ohioopen.library.ohio.edu/oupress/1012/thumbnail.jp

Degradation and healing in a generalized neo-Hookean solid due to infusion of a fluid

The mechanical response and load bearing capacity of high performance polymer composites changes due to diffusion of a fluid, temperature, oxidation or the extent of the deformation. Hence, there is a need to study the response of bodies under such degradation mechanisms. In this paper, we study the effect of degradation and healing due to the diffusion of a fluid on the response of a solid which prior to the diffusion can be described by the generalized neo-Hookean model. We show that a generalized neo-Hookean solid - which behaves like an elastic body (i.e., it does not produce entropy) within a purely mechanical context - creeps and stress relaxes when infused with a fluid and behaves like a body whose material properties are time dependent. We specifically investigate the torsion of a generalized neo-Hookean circular cylindrical annulus infused with a fluid. The equations of equilibrium for a generalized neo-Hookean solid are solved together with the convection-diffusion equation for the fluid concentration. Different boundary conditions for the fluid concentration are also considered. We also solve the problem for the case when the diffusivity of the fluid depends on the deformation of the generalized neo-Hookean solid.Comment: 24 pages, 10 figures, submitted to Mechanics of Time-dependent Material

Doubly connected minimal surfaces and extremal harmonic mappings

The concept of a conformal deformation has two natural extensions: quasiconformal and harmonic mappings. Both classes do not preserve the conformal type of the domain, however they cannot change it in an arbitrary way. Doubly connected domains are where one first observes nontrivial conformal invariants. Herbert Groetzsch and Johannes C. C. Nitsche addressed this issue for quasiconformal and harmonic mappings, respectively. Combining these concepts we obtain sharp estimates for quasiconformal harmonic mappings between doubly connected domains. We then apply our results to the Cauchy problem for minimal surfaces, also known as the Bjorling problem. Specifically, we obtain a sharp estimate of the modulus of a doubly connected minimal surface that evolves from its inner boundary with a given initial slope.Comment: 35 pages, 2 figures. Minor edits, references adde

Mappings of least Dirichlet energy and their Hopf differentials

The paper is concerned with mappings between planar domains having least Dirichlet energy. The existence and uniqueness (up to a conformal change of variables in the domain) of the energy-minimal mappings is established within the class $\bar{\mathscr H}_2(X, Y)$ of strong limits of homeomorphisms in the Sobolev space $W^{1,2}(X, Y)$, a result of considerable interest in the mathematical models of Nonlinear Elasticity. The inner variation leads to the Hopf differential $h_z \bar{h_{\bar{z}}} dz \otimes dz$ and its trajectories. For a pair of doubly connected domains, in which $X$ has finite conformal modulus, we establish the following principle: A mapping $h \in \bar{\mathscr H}_2(X, Y)$ is energy-minimal if and only if its Hopf-differential is analytic in $X$ and real along the boundary of $X$. In general, the energy-minimal mappings may not be injective, in which case one observes the occurrence of cracks in $X$. Nevertheless, cracks are triggered only by the points in the boundary of $Y$ where $Y$ fails to be convex. The general law of formation of cracks reads as follows: Cracks propagate along vertical trajectories of the Hopf differential from the boundary of $X$ toward the interior of $X$ where they eventually terminate before making a crosscut.Comment: 51 pages, 4 figure

On Non-Abelian Symplectic Cutting

We discuss symplectic cutting for Hamiltonian actions of non-Abelian compact groups. By using a degeneration based on the Vinberg monoid we give, in good cases, a global quotient description of a surgery construction introduced by Woodward and Meinrenken, and show it can be interpreted in algebro-geometric terms. A key ingredient is the `universal cut' of the cotangent bundle of the group itself, which is identified with a moduli space of framed bundles on chains of projective lines recently introduced by the authors.Comment: Various edits made, to appear in Transformation Groups. 28 pages, 8 figure

Measures on Banach Manifolds and Supersymmetric Quantum Field Theory

We show how to construct measures on Banach manifolds associated to supersymmetric quantum field theories. These measures are mathematically well-defined objects inspired by the formal path integrals appearing in the physics literature on quantum field theory. We give three concrete examples of our construction. The first example is a family $\mu_P^{s,t}$ of measures on a space of functions on the two-torus, parametrized by a polynomial $P$ (the Wess-Zumino-Landau-Ginzburg model). The second is a family \mu_\cG^{s,t} of measures on a space \cG of maps from $\P^1$ to a Lie group (the Wess-Zumino-Novikov-Witten model). Finally we study a family $\mu_{M,G}^{s,t}$ of measures on the product of a space of connection s on the trivial principal bundle with structure group $G$ on a three-dimensional manifold $M$ with a space of \fg-valued three-forms on $M.$ We show that these measures are positive, and that the measures \mu_\cG^{s,t} are Borel probability measures. As an application we show that formulas arising from expectations in the measures \mu_\cG^{s,1} reproduce formulas discovered by Frenkel and Zhu in the theory of vertex operator algebras. We conjecture that a similar computation for the measures $\mu_{M,SU(2)}^{s,t},$ where $M$ is a homology three-sphere, will yield the Casson invariant of $M.$Comment: Minor correction

Effects of Long-term Exposure on E-glass Composite Material Subjected to Stress Corrosion in a Saline Medium

[EN] This work provides an insight on very long-term degradation of polyester-fiber glass composites immersed more than 30,000 h in saline medium under service stresses. Samples were loaded under bending conditions with stresses both in the elastic and plastic fields, with the result that characteristics in a flexural mode were able to be determined and the ensuing decrease in characteristics was fitted to an exponential model. The degree of losses ranged from 25 to 31% for the bending modulus, from 28 to 35% for the flexural strength, and from 40 to 51% for the specific fracture energy. The most notable losses were for specimens immersed in artificial sea water under a continuous stress of 140 MPa, corresponding to the plastic behavior of the material. Although the existence of matrix plasticization is doubtful, the osmotic effects of the diffusion on the matrix and the junction to the fibers, the presence of microcracks, and the effects of chemical ions in the medium on the surface fiber composition became evident in the strength degradation of the material.Segovia López, EF.; Salvador Moya, MD.; Sahuquillo Navarro, O.; Vicente Escuder, Á. (2007). Effects of Long-term Exposure on E-glass Composite Material Subjected to Stress Corrosion in a Saline Medium. Journal of Composite Materials. 41(17):2119-2128. doi:10.1177/0021998307074134S21192128411