Defect-induced condensation and central peak at elastic phase transitions

Static and dynamical properties of elastic phase transitions under the influence of short--range defects, which locally increase the transition temperature, are investigated. Our approach is based on a Ginzburg--Landau theory for three--dimensional crystals with one--, two-- or three--dimensional soft sectors, respectively. Systems with a finite concentration $n_{\rm D}$ of quenched, randomly placed defects display a phase transition at a temperature $T_c(n_{\rm D})$, which can be considerably above the transition temperature $T_c^0$ of the pure system. The phonon correlation function is calculated in single--site approximation. For $T>T_c(n_{\rm D})$ a dynamical central peak appears; upon approaching $T_c(n_{\rm D})$, its height diverges and its width vanishes. Using an appropriate self--consistent method, we calculate the spatially inhomogeneous order parameter, the free energy and the specific heat, as well as the dynamical correlation function in the ordered phase. The dynamical central peak disappears again as the temperatur is lowered below $T_c(n_{\rm D})$. The inhomogeneous order parameter causes a static central peak in the scattering cross section, with a finite $k$ width depending on the orientation of the external wave vector ${\bf k}$ relative to the soft sector. The jump in the specific heat at the transition temperatur of the pure system is smeared out by the influence of the defects, leading to a distinct maximum instead. In addition, there emerges a tiny discontinuity of the specific heat at $T_c(n_{\rm D})$. We also discuss the range of validity of the mean--field approach, and provide a more realistic estimate for the transition temperature.Comment: 11 pages, 11 ps-figures, to appear in PR

Behandlung nichtlinearer Loesungspfade in der Statik mit Hybriden Krylov-Newton-Verfahren

This report is concerned with the application of inexact Newton methods to the computation of nonlinear solution paths. Using the Arnoldi method for solving the appearing sets of linear equations structures with various kinds of tangent stiffness matrices can be computed by one single pathfollowing concept. For a known finite element the described procedure accomplishes to compute axissymmetric shells in the postbuckling range for the first time. Furtheron three new variants of work controlled pathfollowing algorithms are derived, a generalized description of line search algorithms in structural mechanics is given and a new reliable method to control the load direction within a pathfollowing algorithm is presented. (orig.)Available from TIB Hannover: RR 275(1993,5)+a / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Experimental static and dynamic tests on a large-scale free-form Voronoi grid shell mock-up in comparison with finite-element method results

Grid shells supporting transparent or opaque panels are largely used to cover long-spanned spaces because of their lightness, the easy setup, and economy. This paper presents the results of experimental static and dynamic investigations carried out on a large-scale freeform grid shell mock-up, whose geometry descended from an innovative Voronoi polygonal pattern. Accompanying finite-element method (FEM) simulations followed. To these purposes, a four-step procedure was adopted: (1) a perfect FEM model was analyzed; (2) using the modal shapes scaled by measuring the mock-up, a deformed unloaded geometry was built, which took into account the defects caused by the assembly phase; (3) experimental static tests were executed by affixing weights to the mockup, and a simplified representative FEM model was calibrated, choosing the nodes stiffness and the material properties as parameters; and (4) modal identification was performed through operational modal analysis and impulsive tests, and then, a simplified FEM dynamical model was calibrated. Due to the high deformability of the mockup, only a symmetric load case configuration was adopted

When the line is crossed...: paths to control and sanction behaviour necessitating a state reaction

The article presents a special form of a European comparative synopsis. For this case examples have been chosen ranging from administrative or minor (criminal) offences to increasingly serious offences and offenders. In this way it can be comparatively demonstrated how the criminal justice systems studied handle specific cases and whether they do so in a similar or different way