Powder compaction. Experiments,modeling and simulation

Field-assisted sintering technology (FAST) is a combined thermal and mechanical loading process to compact and sinter a powder material within one process step. In this short essay a constitutive model of thermo-viscoplasticity is proposed representing most of the phenomena observed in the experiments. The constitutive model is calibrated to the experimental data and some predicted experiments are compared with constitutive model showing appropriate results. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermo-mechanical modelling of cellular hybrid refractories

Refractory materials are subjected to both quasi-static and dynamic thermal loading (thermal shock) causing damage up to mechanical failure. Typical refractories are magnesia carbon bricks consisting of periclase (MgO) and carbon inclusions. Recently, a significant improvement of the thermo-mechanical behaviour could be achieved by cellular hybrid composites made of periclase-filled carbon foams. The present contribution focuses on MgO-filled carbon foams and the investigation and optimisation of the structure-property relationship with respect to a reduction of thermally induced stresses and damage. It is a transient as well as static, fully coupled thermo-mechanical problem. According to the fact that, in general, refractories are brittle materials a linear elastic model, with a damage criterion was used. To optimise the structural morphology of the cellular refractories, the effect of micro structural changes has been determined. For the investigation of the thermal shock! behaviour, the results correlate very well with the experimentally motivated Hasselman relation. There is a significant size effect depending on the pore size. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An adaptive moving mesh approach for hyperbolic conservation laws on time-dependent domains

The general idea of moving mesh approaches is to improve the approximation quality and the numerical performance by redistributing a fixed number of discretization points. This is called rrefinement. The classical approaches are applied to partial differential equations on fixed domains. An extension to time-dependent (expanding) domains is presented. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Higher Order Continuum Modelling for Predicting the Mechanical Behaviour of Solid Foams

A higher order continuum model is presented, which is able to capture size effects and regularize softening in rotational, shearing and especially compressive settings. It is shown that with a minimal setting of 3 additional constitutive parameters the model has all desired properties. For parameter identification an example system of a honeycomb structure is investigated. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A note on the growth of Betti numbers and ranks of 3-manifold groups

Let N   be an irreducible, compact 3-manifold with empty or toroidal boundary which is not a closed graph manifold. We show that it follows from the work of Agol, Kahn–Markovic and Przytycki–Wise that _π1(N)${\pi }_1(N)$ admits a cofinal filtration with ‘fast’ growth of Betti numbers as well as a cofinal filtration of _π1(N)${\pi }_1(N)$ with ‘slow’ growth of ranks.     

Comparison of software for computing the action of the matrix exponential

The implementation of exponential integrators requires the action of the matrix exponential and related functions of a possibly large matrix. There are various methods in the literature for carrying out this task. In this paper we describe a new implementation of a method based on interpolation at Leja points. We numerically compare this method with other codes from the literature. As we are interested in applications to exponential integrators we choose the test examples from spatial discretization of time dependent partial differential equations in two and three space dimensions. The test matrices thus have large eigenvalues and can be nonnormal.     

Efficient adaptive regression spline algorithms based on mapping approach with a case study on finance

Multivariate adaptive regression splines (MARS) has become a popular data mining (DM) tool due to its flexible model building strategy for high dimensional data. Compared to well-known others, it performs better in many areas such as finance, informatics, technology and science. Many studies have been conducted on improving its performance. For this purpose, an alternative backward stepwise algorithm is proposed through Conic-MARS (CMARS) method which uses a penalized residual sum of squares for MARS as a Tikhonov regularization problem. Additionally, by modifying the forward step of MARS via mapping approach, a time efficient procedure has been introduced by S-FMARS. Inspiring from the advantages of MARS, CMARS and S-FMARS, two hybrid methods are proposed in this study, aiming to produce time efficient DM tools without degrading their performances especially for large datasets. The resulting methods, called SMARS and SCMARS, are tested in terms of several performance criteria such as accuracy, complexity, stability and robustness via simulated and real life datasets. As a DM application, the hybrid methods are also applied to an important field of finance for predicting interest rates offered by a Turkish bank to its customers. The results show that the proposed hybrid methods, being the most time efficient with competing performances, can be considered as powerful choices particularly for large datasets.     

An improved algorithm to test copositivity

Copositivity plays a role in combinatorial and nonconvex quadratic optimization. However, testing copositivity of a given matrix is a co-NP-complete problem. We improve a previously given branch-and-bound type algorithm for testing copositivity and discuss its behavior in particular for the maximum clique problem. Numerical experiments indicate that the speedup is considerable.