Mass-velocity correlation in impact induced fragmentation of heterogeneous solids

We study the impact fragmentation of disordered solids by means of a discrete element model focusing on the velocity and mass-velocity correlation of fragments. Simulations are performed with plate-like objects varying the plate thickness and the impact velocity in broad ranges. Depending on the impact velocity the breakup process has two different outcomes: at low velocities the sample gets only damaged, to achieve fragmentation, where no large residues survive, the impact velocity has to surpass a critical value. In the fragmented phase the velocity components of fragments are power law distributed with a stretched exponential cutoff, where the impact velocity and plate thickness mainly control the standard deviation of the distributions. Mass velocity correlation is only pointed out for thin plates, while it disappears for three-dimensional bulk samples. In the damage phase of thin plates the mass and velocity of fragments proved to be strongly correlated, however, in the fragmented phase correlation occurs in the vicinity of the critical velocity and it is limited to the large fragments only. The correlation function decays as a power law with different exponents for small and large fragments in good agreement with recent experimental findings. We show that the mass-velocity correlation originates from the spatial dependence of the mass and velocity of pieces inside the fragmenting body.     

Comparison of type-based and alias-based component recognition for embedded systems software

Component-based software engineering has found broad acceptance within the embedded systems community over the last years. However, to fully exploit its potential in terms of reusability and cost-efficiency, existing code-bases have to be refactored in a component-based way. To support refactorization, static analysis techniques can be used to identify components within coarse-grained layered or even monolithic legacy software for embedded systems. We present an approach for semi-automatic extraction of components from automotive software and compare two different versions, one type-based component-recognition analysis of linear complexity with a more precise version based on a points-to analysis of almost linear algorithmic complexity. Both analyses are applied to an industrial implementation of an automotive communication stack. Each analysis is evaluated with two sets of additional manually created annotations of distinct size and precision. Thus, both analyses are fully evaluated in terms of execution-time, memory consumption and analysis precision, and its impact on the number of recognized components. We show that the analysis with higher precision allows the use of a smaller user-provided filter set and obtain a proper component recognition.     

Maps on density operators preserving quantum f-divergences

For an arbitrary strictly convex function $f$ defined on the non-negative real line we determine the structure of all transformations on the set of density operators which preserve the quantum $f$ -divergence.