Interaction of martensitic microstructures in adjacent grains

It is often observed that martensitic microstructures in adjacent polycrystal grains are related. For example, micrographs of Arlt exhibit propagation of layered structures across grain boundaries in the cubic-to-tetragonal phase transformation in $\rm BaTiO_3$. Such observations are related to requirements of compatibility of the deformation at the grain boundary. Using a generalization of the Hadamard jump condition, this is explored in the nonlinear elasticity model of martensitic transformations for the case of a bicrystal with suitably oriented columnar geometry, in which the microstructure in both grains is assumed to involve just two martensitic variants, with a planar or non-planar interface between the grains.Comment: 6 pages, 1 figure, submitted to ICOMAT 2017 Proceeding

Recent advances in understanding and managing chronic pelvic pain in women with special consideration to endometriosis

Chronic pelvic pain (CPP) in women is defined variably, but for clinical use it is cyclical or non-cyclical pain of at least 3-6 months' duration. It has major impacts on individuals and society. There are both structural and idiopathic causes. Whereas CPP is not curable in many cases, it is treatable. The most promising approach is multidisciplinary patient-centered care including cause-directed therapy, lifestyle changes, talking therapies, meditation, acupuncture, and physiotherapy (this is not a complete list). One of the most common structural causes for CPP is endometriosis. This review investigates current scientific concepts and recent innovations in this field as well as for CPP in general

Incompatible sets of gradients and metastability

We give a mathematical analysis of a concept of metastability induced by incompatibility. The physical setting is a single parent phase, just about to undergo transformation to a product phase of lower energy density. Under certain conditions of incompatibility of the energy wells of this energy density, we show that the parent phase is metastable in a strong sense, namely it is a local minimizer of the free energy in an $L^1$ neighbourhood of its deformation. The reason behind this result is that, due to the incompatibility of the energy wells, a small nucleus of the product phase is necessarily accompanied by a stressed transition layer whose energetic cost exceeds the energy lowering capacity of the nucleus. We define and characterize incompatible sets of matrices, in terms of which the transition layer estimate at the heart of the proof of metastability is expressed. Finally we discuss connections with experiment and place this concept of metastability in the wider context of recent theoretical and experimental research on metastability and hysteresis.Comment: Archive for Rational Mechanics and Analysis, to appea

Heavy Quark Production at High Energy

We report on QCD radiative corrections to heavy quark production valid at high energy. The formulae presented will allow a matched calculation of the total cross section which is correct at O(\as^3) and includes resummation of all terms of order \as^3 [\as \ln (s/m^2)]^n. We also include asymptotic estimates of the effect of the high energy resummation. A complete description of the calculation of the heavy quark impact factor is included in an appendix.Comment: 32 pages (LaTeX) with three figures. Resubmission to agree with published version, which contains a new note added in proof and modifications of text of appendix

Scale Setting for αs\alpha_s Beyond Leading Order

We present a general procedure for applying the scale-setting prescription of Brodsky, Lepage and Mackenzie to higher orders in the strong coupling constant \alphas. In particular, we show how to apply this prescription when the leading coefficient or coefficients in a series in \alphas are anomalously small. We give a general method for computing an optimum scale numerically, within dimensional regularization, and in cases when the coefficients of a series are known. We find significant corrections to the scales for $R_{e^+ e^-}$, $\Gamma(B \to X_u e \bar{\nu})$, $\Gamma(t \to b W)$, and the ratios of the quark pole to \MSbar and lattice bare masses.Comment: Lattice 2000 (Perturbation Theory), 5 pages, 7 figures, LaTe

Heavy baryon--light vector meson couplings in QCD

The strong coupling constants of heavy baryons with light vector mesons are calculated in the framework of the light cone QCD sum rules using the most general form of the interpolating currents for the heavy baryons. It is shown that the sextet--sextet, sextet--antitriplet and antitriplet--antitriplet transitions are described by one invariant function for each class of transitions. The values of the electric and magnetic coupling constants for these transitions are obtained.Comment: 16 Pages, 4 Figures and 7 Table

Curvature estimates for Weingarten hypersurfaces in Riemannian manifolds

We prove curvature estimates for general curvature functions. As an application we show the existence of closed, strictly convex hypersurfaces with prescribed curvature $F$, where the defining cone of $F$ is \C_+. $F$ is only assumed to be monotone, symmetric, homogeneous of degree 1, concave and of class C^{m,\al}, $m\ge4$.Comment: 9 pages, v2:final version, to be publishe