Closed form solution of the return mapping algorithm in elastoplasticity

In the present work a return mapping algorithm is discussed for small strain elastoplasticity boundary value problems with an exact closed form solution of the local constitutive equations. Nonlinear kinematic hardening rules are adopted in modelling kinematic hardening behavior of ductile materials. The local solution of the constitutive equations is expressed by only one nonlinear scalar equation which is subsequently reduced to a single variable algebraic equation. Due to the straightforward form of the nonlinear scalar equation the analytical solution of the algebraic equation is found in exact closed form. A remarkable advantage of the present approach is that no iterative solution method is used to solve the local constitutive equations in three-dimensional elastoplasticity. Numerical applications and computational results are reported in order to illustrate the robustness and effectiveness of the proposed algorithmic procedure

Worst-case convergence analysis of inexact gradient and Newton methods through semidefinite programming performance estimation

We provide new tools for worst-case performance analysis of the gradient (or steepest descent) method of Cauchy for smooth strongly convex functions, and Newton's method for self-concordant functions, including the case of inexact search directions. The analysis uses semidefinite programming performance estimation, as pioneered by Drori and Teboulle [Mathematical Programming, 145(1-2):451-482, 2014], and extends recent performance estimation results for the method of Cauchy by the authors [Optimization Letters, 11(7), 1185-1199, 2017]. To illustrate the applicability of the tools, we demonstrate a novel complexity analysis of short step interior point methods using inexact search directions. As an example in this framework, we sketch how to give a rigorous worst-case complexity analysis of a recent interior point method by Abernethy and Hazan [PMLR, 48:2520-2528, 2016].Comment: 22 pages, 1 figure. Title of earlier version was "Worst-case convergence analysis of gradient and Newton methods through semidefinite programming performance estimation

Addressing the Global Tragedy of Needless Pain: Rethinking the United Nations Single Convention on Narcotic Drugs

The lack of medical availability of effective pain medication is an enduring and expanding global health calamity. Despite important medical advances, pain remains severely under-treated worldwide, particularly in developing countries. This article contributes to the discussion of this global health crisis by considering international legal and institutional mechanisms to promote wider accessibility to critical narcotic drugs for pain relief

Spontaneous Breaking of N=2 Global Supersymmetry

We study spontaneous supersymmetry breaking in N=2 globally supersymmetric theories describing a system of abelian vector multiplets. We find that the most general form of the action admits, in addition to the usual Fayet-Iliopoulos term, a magnetic Fayet-Iliopoulos term for the auxiliary components of dual vector multiplets. In a generic case, N=2 supersymmetry is broken down spontaneously to N=1. In some cases however, the scalar potential can drive the theory towards a N=2 supersymmetric ground state where massless dyons condense in the vacuum.Comment: 12 pages, LaTe

A perturbative analysis of tachyon condensation

Tachyon condensation in the open bosonic string is analyzed using a perturbative expansion of the tachyon potential around the unstable D25-brane vacuum. Using the leading terms in the tachyon potential, Pad\'e approximants can apparently give the energy of the stable vacuum to arbitrarily good accuracy. Level-truncation approximations up to level 10 for the coefficients in the tachyon potential are extrapolated to higher levels and used to find approximants for the full potential. At level 14 and above, the resulting approximants give an energy less than -1 in units of the D25-brane tension, in agreement with recent level-truncation results by Gaiotto and Rastelli. The extrapolated energy continues to decrease below -1 until reaching a minimum near level 26, after which the energy turns around and begins to approach -1 from below. Within the accuracy of this method, these results are completely consistent with an energy which approaches -1 as the level of truncation is taken to be arbitrarily large.Comment: 8 pages, 3 eps figures, Latex; v2: typo correcte