Topology optimization of dynamics problems with Padé approximants

An efficient procedure for topology optimization of dynamics problems is proposed. The method is based on frequency responses represented by Padé approximants and analytical sensitivity analysis derived using the adjoint method. This gives an accurate approximation of the frequency response over wide frequency ranges and a formulation that allows for design sensitivities to be computed at low computational cost also for a large number of design variables. Two examples that deal with optimization of forced vibrations are included. Copyright © 2007 John Wiley & Sons, Ltd.     

Reinforced masonry beams under shear load – Proposals for future designs / Bewehrte schubbeanspruchte Mauerwerksbalken – Vorschläge für zukünftige Bemessungen

This article is written against the backdrop of the work of the European standardisation committees on the amendment of EN 1996‐1‐1 [N 4] which will also exert an influence on the design of reinforced masonry in Germany. This paper focusses on the design approaches of DIN EN 1996‐1‐1 for untensioned reinforced masonry beams under shear load in the ultimate limit state (ULS). Proposals are made to discuss their revision. The contents of E DIN 1053‐3 [N 3] and of the final draft of the guideline ”Flat Lintels” [7] are taken into account.     

Designing experiments to understand the variability in biochemical reaction networks

Exploiting the information provided by the molecular noise of a biological process has proved to be valuable in extracting knowledge about the underlying kinetic parameters and sources of variability from single-cell measurements. However, quantifying this additional information a priori, to decide whether a single-cell experiment might be beneficial, is currently only possible in systems where either the chemical master equation is computationally tractable or a Gaussian approximation is appropriate. Here, we provide formulae for computing the information provided by measured means and variances from the first four moments and the parameter derivatives of the first two moments of the underlying process. For stochastic kinetic models for which these moments can be either computed exactly or approximated efficiently, the derived formulae can be used to approximate the information provided by single-cell distribution experiments. Based on this result, we propose an optimal experimental design framework which we employ to compare the utility of dual-reporter and perturbation experiments for quantifying the different noise sources in a simple model of gene expression. Subsequently, we compare the information content of a set of experiments which have been performed in an engineered light-switch gene expression system in yeast and show that well-chosen gene induction patterns may allow one to identify features of the system which remain hidden in unplanned experiments.     

Fully Symbolic Model Checking of Timed Systems using Difference Decision Diagrams

Current approaches for analyzing timed systems are based on an explicit enumeration of the discrete states and thus these techniques are only capable of analyzing systems with a handful of timers and a few thousand states. We address this limitation by describing how to analyze a timed system fully symbolically, i.e., by representing sets of discrete states and their associated timing information implicitly. We demonstrate the efficiency of the symbolic technique by computing the set of reachable states for a non-trivial timed system and compare the results with the state-of-the-art tools Kronos and Uppaal. With an implementation based on difference decision diagrams, the runtimes are several orders of magnitudes better. The key operation in obtaining these results is the ability to advance time symbolically. We show how to do this efficiently by essentially quantifying out a special variable z which is used to represent the constant zero. The symbolic manipulations given in this paper are sufficient to verify TCTL-formulae fully symbolically.     

Effects of rolling and hot pressing on mechanical properties of boron carbide-based ceramics

A study of hot pressed B₄C-based laminates, after rolling and without rolling, has been performed to elucidate the existence of fracture resistance/crack length anisotropy induced by this processing technique. While the crack lengths/fracture resistance was affected significantly by the presence of the residual stresses in B₄C/B₄C–ZrB₂ laminates, no differences in Vickers crack lengths were observed in B₄C/B₄C laminates prepared by rolling and hot pressing, as compared to the crack lengths seen in pure B₄C ceramics prepared by hot pressing without rolling. X-ray diffraction analysis confirmed that no texture has been formed during the rolling and hot pressing of B₄C ceramics.     

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