The global dimensions of crossed products and crossed coproducts

In this paper, we show that if H is a finite-dimensional Hopf algebra such that H and H^＊ are semisimple, then gl.dim（A#σH）=gl.dim（A）, where a is a convolution invertible cocycle. We also discuss the relationship of global dimensions between the crossed product A^#σH and the algebra A, where A is coacted by H. Dually, we give a sufficient condition for a finite dimensional coalgebra C and a finite dimensional semisimple Hopf algebra H such that gl.dim（C α H）=gl.dim（C）.     

Micromechanical modeling of twinning

There exist material models that incorporate mechanical twinning in a homogenized sense, or consider specific aspects, like grain refinement or texture evolution. However, since the RVE-technique became a standard method, it is possible to obtain more detailed predictions based on micromechanical models. In this work, an approach based on a nonconvex elastic potential and the corresponding results of FE calculations are presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The complexity of crossed products

Let H be a finite-dimensional Hopf algebra, let A be a finite-dimensional algebra measured by H, and let A # _σ H be a crossed product. In this paper, we first show that if H is semisimple as well as its dual H*, then the complexity of A # _σ H is equal to that of A. Furthermore, we prove that the complexity of a finite-dimensional Hopf algebra H is equal to the complexity of the trivial module _H k. As an application, we prove that the complexity of Sweedler’s 4-dimensional Hopf algebra H ₄ is equal to 1.     

Geometry of a crossed product

We introduce a continuous dimension function on the Grothendieck group over the crossed product -algebra . The function has an elegant geometry: on every minimal flow it takes the value of the ``rotation number" of ; such a problem was posed in 1936 by A. Weil.

     

Micromechanical modeling of bainitic phase transformation

We develop a micromechanical material model for phase transformation from austenite to bainite for a polycrystalline low alloys steel. In this material (e.g. 51CrV4) the phase changes from austenite to perlite-ferrite, bainite or martensite, respectively. This work is concerned with phase transformation between austenite and n-bainite variants in differently orientated grains. The characteristic features of bainite formation are the combination of time-dependent transformation kinetics and lattice shearing in the microstructure. These effects are considered on the microscale and transferred to the polycrystalline macroscale by means of homogenisation of stochastically orientated grains. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On deformations of crossed products

Let A∗Γ be a crossed product algebra, where A is semisimple, finitely generated over its center and Γ is a finite group. We give a necessary and sufficient condition in terms of the outer action of Γ on A for the existence of a multi-parametric semisimple deformation of the form A((t₁,…,t_n))∗Γ (with the induced outer action). The main tool in the proof is the solution of the so-called twisting problem. We also give an example which shows that the condition is not sufficient if one drops the condition on the finite generation of A over its center.     

Branch and bound crossed with GA to solve hybrid flowshops

This article deals with an optimal methods for solving a k-stage hybrid flowshop scheduling problem. This problem is known to be NP-hard. In 1991, Brah and Hunsucker proposed a branch and bound algorithm to solve this problem. However, for some medium size problems, the computation time is not acceptable. The aim of this article is to present an improvement of this algorithm. As a matter of fact, we prove that the value of their lower bound (LB) may decrease along a path of the search tree. First of all, we present an improvement of their LB. Then, we introduce several heuristics at the beginning of the search in order to compute an initial upper bound and genetic algorithm (GA) to improve during the search the value of the upper bound. More precisely, our GA takes into account the set of partial decisions made by the branch and bound and builds a series of populations of complete solutions with the aim of improving the upper bound (the best found criterion value corresponding to a complete solution). Experimentation show that the optimality of branch and bound is more often reached and the value of criterion is improved when our improvements are taken into account.     

Invariant ideals of twisted crossed products

We will prove a result concerning the inclusion of non-trivial invariant ideals inside non-trivial ideals of a twisted crossed product. We will also give results concerning the primeness and simplicity of crossed products of twisted actions of locally compact groups on -algebras. Received: 25 January 2002; in final form: 22 May 2002/Published online: 2 December 2002 This work is partially supported by Hong Kong RGC Direct Grant.     

Cyclic homology of Hopf crossed products

We obtain a mixed complex, simpler than the canonical one, given the Hochschild, cyclic, negative and periodic homology of a crossed product E=A#fH, where H is an arbitrary Hopf algebra and f is a convolution invertible cocycle with values in A. We actually work in the more general context of relative cyclic homology. Specifically, we consider a subalgebra K of A which is stable under the action of H, and we find a mixed complex computing the Hochschild, cyclic, negative and periodic homology of E relative to K. As an application we obtain two spectral sequences converging to the cyclic homology of E relative to K. The first one works in the general setting and the second one (which generalizes those previously found by several authors) works when f takes its values in K.     

Micromechanical strength analysis of fiber reinforced plastics

Strength of an unidirectional lamina is computed with a representative volume element. An approximative “voxel” meshing method is used in conjunction with continuum damage mechanics to simulate crack growth in the RVE. Two material models for the nonlinear material behaviour of the epoxy resin are compared. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simplicity of crossed products by endomorphisms

Conditions are given for simplicity of the crossed product of a unital C^*-algebra by an endomorphism.     

Micromechanical modeling of talc particle reinforced thermoplastic polymers

The present work aims at investigating the mechanical behavior of talc particle reinforced thermoplastic polymers. Therefore, micromechanical analyses are performed utilizing detailed finite element models of the explicitely resolved microstructure. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Micromechanical Approach of Martensitic Transformation Problem in Steels

To determine the mechanical behavior of material involving the martensitic phase transformation (for example, steels like 100Cr6), a representative volume element (RVE) model including phase transformation criterion is desireable at micromechanical approach. A framework combining the Eshelby's inclusion theory as well as continuum mechanics with phase-transformation (PT) critical condition at RVE model is presented briefly. And application of this model to estimate the critical aspect ratio of martensitic plate or lath inside homogeneneous stress field is also included, where the RVE can be under uniaxial tension/compression or pure shear loading case. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Micromechanical Generalization of the Mises-Hill Anisotropy Yield Criterion

This paper proposes a new micromechanically motivated yield criterion expressed in terms of the leading tensorial texture coefficient of the crystallite orientation distribution function. The central finding is that although only a 4th–order anisotropy tensor occurs in the expression for the yield locus, the ansatz provides significantly better results in comparison to the quadratic Hill condition. The improvement is due to cubic and quartic tensorial contributions in terms of the stress direction. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An Approach for Micromechanical Modelling of Damage Mechanisms

In the framework of numerical simulation of damaged materials, softening behaviour represents an important topic. Thereby, the decrease of stiffness is mainly caused by the evolution of microvoids. In contrast to the established phenomenological damage approaches, the explicit consideration of effects on the micro scale can lead to an improved approximation quality. In this work, we discuss an approach to describe microstructural evolution. Based on a two phase micro model representing the macroscopical material behaviour, the structural evolution on the micro scale will be modelled based on configurational forces. Besides some theoretical basics on configurational forces at two phase systems and the definition of suitable evolution laws, we present an application of this approach on void growth process in rubberlike material. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Micromechanical modeling of Common yew and Norway spruce

In this contribution, a micromechanical modeling approach in the framework of poromechanics is adopted to study structure-stiffness relations of two quite different species, namely spruce and yew, in detail. In particular, microstructural specialties of yew and spruce are assessed. A dominant influence of the cellulose content and its orientation on the stiffness of the cell wall is revealed, while on the macroscopic scale, density is found to be the governing microstructural characteristic for elastic properties. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)