Effects of fiber and interfacial layer architectures on the thermoplastic response of metal matrix composites

Examined here is the effect of fiber and interfacial layer morphologies on thermal fields in metal matrix composites (MMCs). A micromechanics model based on an arbitrarily layered concentric cylinder configuration is used to calculate thermal stress fields in MMCs subjected to spatially uniform temperature changes. The fiber is modelled as a layered material with isotropic or orthotropic elastic layers, whereas the surrounding matrix, including interfacial layers, is treated as a strain-hardening, elastoplastic, von Mises solid with temperature-dependent parameters. The solution to the boundary-value problem of an arbitrarily layered concentric cylinder under the prescribed thermal loading is obtained using the local/global stiffness matrix formulation originally developed for stress analysis of multilayered elastic media. Examples are provided that illustrate how the morphology of the SCS6 silicon carbide fiber and the use of multiple compliant layers at the fiber/matrix interface affect the evolution of residual stresses in SiC/Ti composites during fabrication cool-down

Dynamics of Diblock Copolymers in Dilute Solutions

We consider the dynamics of freely translating and rotating diblock (A-B), Gaussian copolymers, in dilute solutions. Using the multiple scattering technique, we have computed the diffusion and the friction coefficients D_AB and Zeta_AB, and the change Eta_AB in the viscosity of the solution as functions of x = N_A/N and t = l_B/l_A, where N_A, N are the number of segments of the A block and of the whole copolymer, respectively, and l_A, l_B are the Kuhn lengths of the A and B blocks. Specific regimes that maximize the efficiency of separation of copolymers with distinct "t" values, have been identified.Comment: 20 pages Revtex, 7 eps figures, needs epsf.tex and amssymb.sty, submitted to Macromolecule

T-duality and Differential K-Theory

We give a precise formulation of T-duality for Ramond-Ramond fields. This gives a canonical isomorphism between the "geometrically invariant" subgroups of the twisted differential K-theory of certain principal torus bundles. Our result combines topological T-duality with the Buscher rules found in physics.Comment: 23 pages, typos corrected, submitted to Comm.Math.Phy

D3 branes in a Melvin universe: a new realm for gravitational holography

The decoupling limit of a certain configuration of D3 branes in a Melvin universe defines a sector of string theory known as Puff Field Theory (PFT) - a theory with non-local dynamics but without gravity. In this work, we present a systematic analysis of the non-local states of strongly coupled PFT using gravitational holography. And we are led to a remarkable new holographic dictionary. We show that the theory admits states that may be viewed as brane protrusions from the D3 brane worldvolume. The footprint of a protrusion has finite size - the scale of non-locality in the PFT - and corresponds to an operator insertion in the PFT. We compute correlators of these states, and we demonstrate that only part of the holographic bulk is explored by this computation. We then show that the remaining space holographically encodes the dynamics of the D3 brane tentacles. The two sectors are coupled: in this holographic description, this is realized via quantum entanglement across a holographic screen - a throat in the geometry - that splits the bulk into the two regions in question. We then propose a description of PFT through a direct product of two Fock spaces - akin to other non-local settings that employ quantum group structures.Comment: 44 pages, 13 figures; v2: minor corrections, citations added; v3: typos corrected in section on local operators, some asymptotic expansions improved and made more consistent with rest of paper in section on non-local operator

Using short-term postseismic displacements to infer the ambient deformation conditions of the upper mantle

Author Posting. © American Geophysical Union, 2012. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophyscial Research 117 (2012): B01409, doi:10.1029/2011JB008562.To interpret short-term postseismic surface displacements in the context of key ambient conditions (e.g., temperature, pressure, background strain rate, water content, creep mechanism), we combined steady state and transient flow into a single constitutive relation that can explain the response of a viscoelastic material to a change in stress. The flow law is then used to investigate mantle deformation beneath the Eastern California Shear Zone following the 1999 M7.1 Hector Mine earthquake. The flow law parameters are determined using finite element models of relaxation processes, constrained by surface displacement time series recorded by 55 continuous GPS stations for 7 years following the earthquake. Results suggest that postseismic flow following the Hector Mine earthquake occurs below a depth of ~50 km and is controlled by dislocation creep of wet olivine. Diffusion creep models can also explain the data, but require a grain size (3.5 mm) that is smaller than the inferred grain size (10–20 mm) based on the mantle conditions at these depths. In addition, laboratory flow laws predict dislocation creep would dominate at the stress/grain size conditions that provide the best fit to diffusion creep models. Model results suggest a transient creep phase that lasts ~1 year and has a viscosity ~10 times lower than subsequent steady state flow, in general agreement with laboratory observations. The postseismic response is best explained as occurring within a relatively hot upper mantle (e.g., 1200–1300°C at 50 km depth) with a long-term background mantle strain rate of 0.1–0.2 μstrain/yr, consistent with the observed surface strain rate. Long-term background shear stresses at the top of the mantle are ~4 MPa, then decrease with depth to a minimum of 0.1–0.2 MPa at 70 km depth before increasing slowly with depth due to the pressure dependence of viscosity. These conditions correspond to a background viscosity of 1021 Pa s within a thin mantle lid that decreases to ~5 × 1019 Pa s within the underlying asthenosphere. This study shows the utility of using short-term postseismic observations to infer long-term mantle conditions that are not readily observable by other means.This work was supported by the National Science Foundation grants EAR-0952234 (A.M.F.), EAR-0810188 (G.H.), and EAR-0854673 (M.D.B.).2012-07-3

A holographic computation of the central charges of d=4, N=2 SCFTs

We use the AdS/CFT correspondence to compute the central charges of the d=4, N=2 superconformal field theories arising from N D3-branes at singularities in F-theory. These include the conformal theories with E_n global symmetries. We compute the central charges a and c related to the conformal anomaly, and also the central charges k associated to the global symmetry in these theories. All of these are related to the coefficients of Chern-Simons terms in the dual string theory on AdS_5. Our computation is exact for all values of N, enabling several tests of the dualities recently proposed by Argyres and Seiberg for the E_6 and E_7 theories with N=1.Comment: 16 pages; v4: one reference adde

Non-Abelian Chern-Simons models with discrete gauge groups on a lattice

We construct the local Hamiltonian description of the Chern-Simons theory with discrete non-Abelian gauge group on a lattice. We show that the theory is fully determined by the phase factors associated with gauge transformations and classify all possible non-equivalent phase factors. We also construct the gauge invariant electric field operators that move fluxons around and create/anihilate them. We compute the resulting braiding properties of the fluxons. We apply our general results to the simplest class of non-Abelian groups, dihedral groups D_n.Comment: 16 pages, 7 figure

Holomorphic Supercurves and Supersymmetric Sigma Models

We introduce a natural generalisation of holomorphic curves to morphisms of supermanifolds, referred to as holomorphic supercurves. More precisely, supercurves are morphisms from a Riemann surface, endowed with the structure of a supermanifold which is induced by a holomorphic line bundle, to an ordinary almost complex manifold. They are called holomorphic if a generalised Cauchy-Riemann condition is satisfied. We show, by means of an action identity, that holomorphic supercurves are special extrema of a supersymmetric action functional.Comment: 30 page