Limit analysis and inf-sup conditions on convex cones

This paper is focused on analysis and reliable computations of limit loads in perfect plasticity. We recapitulate our recent results arising from a continuous setting of the so-called limit analysis problem. This problem is interpreted as a convex optimization subject to conic constraints. A related inf-sup condition on a convex cone is introduced and its importance for theoretical and numerical purposes is explained. Further, we introduce a penalization method for solving the kinematic limit analysis problem. The penalized problem may be solved by standard finite elements due to available convergence analysis using a simple local mesh adaptivity. This solution concept improves the simplest incremental method of limit analysis based on a load parametrization of an elastic-perfectly plastic problem

Towards conformal invariance of 2D lattice models

Many 2D lattice models of physical phenomena are conjectured to have conformally invariant scaling limits: percolation, Ising model, self-avoiding polymers, ... This has led to numerous exact (but non-rigorous) predictions of their scaling exponents and dimensions. We will discuss how to prove the conformal invariance conjectures, especially in relation to Schramm-Loewner Evolution.Comment: ICM 2006 paper with a few typos correcte

HST/STIS observations of the RW Aurigae bipolar jet: mapping the physical parameters close to the source

We present the results of new spectral diagnostic investigations applied to high-resolution long-slit spectra of the RW Aur bipolar jet obtained with HST/STIS. The spectra include the forbidden doublets [O I] 6300,6363 \AA, [S II] 6716,6731 \AA, and [N II] 6548, 6583 \AA that we utilized to determine electron density, electron temperature, hydrogen ionisation fraction, total hydrogen density, radial velocity and the mass outflow rate. We were able to extract the parameters as far as 3".9 in the red- and 2".1 in the blueshifted beam. The RW Aur jet appears to be the second densest outflow from a T Tauri star studied so far, but its other properties are quite similar to those found in other jets from young stars. The overall trend of the physical parameters along the first few arcseconds of the RW Aur jet is similar to that of HH 30 and DG Tau and this can reflect analogies in the mechanisms operating in that region, suggesting the same engine is accelerating the jets in the T Tauri stars with outflows. Our study of the RW Aur jet indicates for the first time that, despite the detected marked asymmetries in physical and kinematic properties between the two lobes, the mass outflow rates in the two lobes are similar. This appears to indicate that the central engine has constraining symmetries on both sides of the system, and that the observed asymmetries are probably due to different environmental conditions.Comment: 24 pages, 10 figures, accepted for publication in the Astronomy and Astrophysic

Dynamical simulations of QCD at finite temperature with a truncated perfect action

The Hypercube operator determines a variant of the approximate, truncated perfect fermion action. In this pilot study we are going to report on first experiences in dynamical QCD simulations with the Hypercube fermions. We apply this formulation in an investigation of the finite temperature transition for two flavours. On lattices of size $8^3\times 4$ we explore the phase diagram. Physical scales are estimated from pseudoscalar and vector meson masses obtained on $8^3\times 16$ lattices. We observe the presence of a metastability region but do not find evidence for an Aoki phase. The Hypercube operator allows us to simulate at ratios of pseudoscalar to vector meson masses at least as small as 0.8 at the thermal crossover at $N_t=4$, which renders this formulation cheaper than the Wilson like fermions.Comment: 7 pages, 8 figures, talk presented at Lattice 2006 (High temperature and density

Numerical solution of perfect plastic problems with contact: part II - numerical realization

This contribution is a continuation of our contribution denoted as PART I, where the discretized contact problem for elasto-perfectly plastic bodies was studied and suitable numerical methods were introduced. In particular, frictionless contact boundary conditions and Hencky’s material model with the von Mises criterion are considered. Here we describe some implementation details and present several numerical examples