Stochastic homogenization of plasticity equations

In the context of infinitesimal strain plasticity with hardening, we derive a stochastic homogenization result. We assume that the coefficients of the equation are random functions: elasticity tensor, hardening parameter and flow-rule function are given through a dynamical system on a probability space. A parameter \epsilon > 0 denotes the typical length scale of oscillations. We derive effective equations that describe the behavior of solutions in the limit \epsion -> 0. The homogenization procedure is based on the fact that stochastic coefficients “allow averaging”: For one representative volume element, a strain evolution [0; T] \ni t \mapsto\xi(t) \in Rd^dxd _s induces a stress evolution [0; T] \ni t \mapsto\Sigma(\xi)(t) \in Rd^dxd _s . Once the hysteretic evolution law \Sigma is justified for averages, we obtain that the macroscopic limit equation is given by -\triangledown\cdot\Sigma(\triangledown^s u) = f

Transient Run-Up Simulations of Rotors in Journal Bearings Considering Mass-Conserving Cavitation Approaches

The influence of mass-conserving cavitation modeling approaches on the stability of rotors in journal bearings is investigated. The model consists of a rotor represented by a flexible multibody system and the bearings discretized with finite elements. An approach for the pressure-dependent mixture density and mixture viscosity is made. Due to this mass-conserving cavitation approach, the Reynolds equation becomes explicitly time-dependent. Both subsystems – the multibody system for the rotor and the finite element system for the bearings – are coupled by means of an explicit co-simulation approach. Two different axial boundary conditions for the bearings are considered, namely a bearing submerged in an oil bath and an oil film free to air. The differences are studied in a stationary simulation. Then, the results of transient run-up simulations of a Jeffcott rotor and a turbocharger are discussed

A note on drastic product logic

The drastic product $*_D$ is known to be the smallest $t$-norm, since $x *_D y = 0$ whenever $x, y < 1$. This $t$-norm is not left-continuous, and hence it does not admit a residuum. So, there are no drastic product $t$-norm based many-valued logics, in the sense of [EG01]. However, if we renounce standard completeness, we can study the logic whose semantics is provided by those MTL chains whose monoidal operation is the drastic product. This logic is called ${\rm S}_{3}{\rm MTL}$ in [NOG06]. In this note we justify the study of this logic, which we rechristen DP (for drastic product), by means of some interesting properties relating DP and its algebraic semantics to a weakened law of excluded middle, to the $\Delta$ projection operator and to discriminator varieties. We shall show that the category of finite DP-algebras is dually equivalent to a category whose objects are multisets of finite chains. This duality allows us to classify all axiomatic extensions of DP, and to compute the free finitely generated DP-algebras.Comment: 11 pages, 3 figure

CMOS-compatible metal-stabilized nanostructured Si as anodes for lithium-ion microbatteries

The properties of fully complementary metal-oxide semiconductor (CMOS)-compatible metal-coated nanostructured silicon anodes for Li-ion microbatteries have been studied. The one-dimensional nanowires on black silicon (nb-Si) were prepared by inductively coupled plasma (ICP) etching and the metal (Au and Cu) coatings by successive magnetron sputtering technique. The Cu-coated nb-Si show the most promising electrochemical performance enhancements for the initial specific capacity as well as their cyclability compared to pristine nb-Si. The electrochemical and microstructural properties before and after cycling of the metal-coated nb-Si compared to their pristine counterparts are discussed in detail

Numerical stability of explicit and implicit co-simulation methods

Within a co-simulation approach, the subsystems are integrated by specific solvers; data exchange is accomplished only at certain user-defined macro-time points. Due to the approximation of the coupling variables by polynomials and as a result of the data exchange between the subsystems, errors are introduced, which may entail severe stability problems. Hence, the development of stabilized coupling techniques is of special interest. To analyze the stability of co-simulation approaches, we consider two coupled Dahlquist’s equations so that the conventional linear stability analysis can be applied. Consequently, the stability of the cosimulation method can be determined by calculating the spectral radius of the governing system of recurrence equations. The numerical stability of classical explicit and implicit co-simulation techniques is investigated here. Also, modified coupling approaches are discussed, which show an improved stability behavior

Entwicklung von Populationen bei Mais (Zea mays L.) Selektionseffizienz und Leistungsfähigkeit

Maize is one of the most important crops around the world. Global players in seed production offer more than hundreds of different varieties. All of them are hybrids whereas open pollinated varieties (OPVs) are rare or extinct. In Germany (and many other European countries) no new OPVs are registered; efforts to do so failed in the past. The main advantage of OPVs is their phenotypic and genetic heterogeneity and thus their ability to adapt to different environmental conditions. This could be of utmost interest facing the complex challenge of climate change. Populations based on new breeding material were developed and tested in comparison to actual hybrids and landraces. While the new populations achieved about 80 % of the hybrid yield, landraces failed with only 65 %. The efficiency of selection methods needs to be improved