Comparing Nonsmooth Nonconvex Bundle Methods in Solving Hemivariational Inequalities

Hemivariational inequalities can be considered as a generalization of variational inequalities. Their origin is in nonsmooth mechanics of solid, especially in nonmonotone contact problems. The solution of a hemivariational inequality proves to be a substationary point of some functional, and thus can be found by the nonsmooth and nonconvex optimization methods. We consider two type of bundle methods in order to solve hemivariational inequalities numerically: proximal bundle and bundle-Newton methods. Proximal bundle method is based on first order polyhedral approximation of the locally Lipschitz continuous objective function. To obtain better convergence rate bundle-Newton method contains also some second order information of the objective function in the form of approximate Hessian. Since the optimization problem arising in the hemivariational inequalities has a dominated quadratic part the second order method should be a good choice. The main question in the functioning of the methods is how remarkable is the advantage of the possible better convergence rate of bundle-Newton method when compared to the increased calculation demand.     

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On a new finite element technology for electromagnetic metal forming processes

The increasing need for lightweight building components has led to the development of new methods to manufacture such components. A promising concept is the systematic application of high-speed metal forming methods. Electromagnetic forming is one such method. Here, the deformation of the workpiece is driven by the Lorentz force which results from the interaction of a current generated in the workpiece with a magnetic field generated by a coil adjacent to the workpiece. This force represents an additional volume- or body-force density contribution in the balance of linear momentum. The numerical treatment of the coupled set of partial differential equations for the mechanical and electromagnetic fields can be made more efficient from the computational point of view by using the finite element technology suggested here, which is based on reduced integration and hourglass stabilisation. The main idea behind this new technology is to expand the constitutive quantities in a Taylor expansion with respect to a point on the local coordinate axis in the thickness direction. The result is a weak system of equations which decomposes into a part to be evaluated in two Gauss points and in addition the so-called hourglass stabilisation to be computed analytically.     

Experimental and numerical investigation of a viscoplastic Carbopol gel injected into a prototype 3D mold cavity

A numerical model for free-surface flow of a viscoplastic liquid into a cavity is presented. This flow is regarded as a basic model of injection molding, which is a widely used processing technology. Model experiments of the injection process are performed with a water-based gel with shear-thinning behavior. The filling process is visualized by tracing the free surface of the gel within the cavity. Filling times of the cavity are deduced from the experimental observations. The filling process is also analyzed by means of numerical simulation.The flow equations are integrated according to the finite-volume method. The volume-of-fluid method is employed in order to describe the flow of two incompressible, immiscible phases, the phase interface is resolved by the method of geometric reconstruction or alternatively by the method of surface compression. The Herschel–Bulkley model is used in order to describe the shear-thinning behavior of the gel and the effects of a yielding point. The governing equations of the flow are solved by means of the commercial code Fluent as well as the Open Source code OpenFOAM.The results of the numerical simulations are analyzed in detail. They are compared with the experimental findings. Cavity filling times in the experiments and the simulations are in good agreement. Different patterns of the filling flow depending on the injection parameters are evident in the experiments and the simulations. They are characterized and arranged with respect to the similarity parameters of the flow configuration. Again, the results of the simulation are found to agree well with the experimental observations.     

A 3‐level discretisation strategy using substructuring

This contribution deals with a new three‐level discretisation strategy which enables to discretise a structure according to the required modelling accuracy. Correspondingly the structure is separated into a continuum, a structural and a black box model level. This note especially focuses on the transitions between continuum‐structure and structure‐substitute model. The first one is realised by means of a model adaptive concept based on the innovative finite element technology of the Q1SP family. The latter is carried out by an enhanced modal reduction method which is combined with a novel substructure technique. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A Highly K+‐Selective Phenylaza‐[18]crown‐6‐Lariat‐Ether‐Based Fluoroionophore and Its Application in the Sensing of K+ Ions with an Optical Sensor Film and in Cells

Herein, we report the synthesis of two phenylaza‐[18]crown‐6 lariat ethers with a coumarin fluorophore ( 1 and 2 ) and we reveal that compound 1 is an excellent probe for K⁺ ions under simulated physiological conditions. The presence of a 2‐methoxyethoxy lariat group at the ortho position of the anilino moiety is crucial to the substantially increased stability of compounds 1 and 2 over their lariat‐free phenylaza‐[18]crown‐6 ether analogues. Probe 1 shows a high K⁺/Na⁺ selectivity and a 2.5‐fold fluorescence enhancement was observed in the presence of 100 mM K⁺ ions. A fluorescent membrane sensor, which was prepared by incorporating probe 1 into a hydrogel, showed a fully reversible response, a response time of 150 s, and a signal change of 7.8 % per 1 mM K⁺ within the range 1–10 mM K⁺. The membrane was easily fabricated (only a single sensing layer on a solid polyester support), yet no leaching was observed. Moreover, compound 1 rapidly permeated into cells, was cytocompatible, and was suitable for the fluorescent imaging of K⁺ ions on both the extracellular and intracellular levels.     

Sulfido‐bridged rhenium–carbonyl complexes with planar and folded Re2S2 cores

The two sulfido‐bridged dirhenium complexes bis(μ‐4‐methoxy­phenyl­sulfido‐S)bis­(tetra­carbonyl­rhenium), [Re₂(C₇H₇­OS)₂­(CO)₈], and bis(μ‐naphthyl­sulfido‐S)bis[tricarbonyl(dicyclohexylphosphane)rhenium], [Re₂­(C₁₂­H₂₃P)₂(C₁₀H₇S)₂­(CO)₆], show different geometries of the common Re₂S₂ core. The 4‐methoxy­phenyl derivative has crystallographic symmetry and the naphthyl derivative has C² symmetry. This results from intramolecular repulsion due to different substitution patterns at the Re and S atoms.