Mixed finite element methods for linear elasticity with weakly imposed symmetry

In this paper, we construct new finite element methods for the approximation of the equations of linear elasticity in three space dimensions that produce direct approximations to both stresses and displacements. The methods are based on a modified form of the Hellinger-Reissner variational principle that only weakly imposes the symmetry condition on the stresses. Although this approach has been previously used by a number of authors, a key new ingredient here is a constructive derivation of the elasticity complex starting from the de Rham complex. By mimicking this construction in the discrete case, we derive new mixed finite elements for elasticity in a systematic manner from known discretizations of the de Rham complex. These elements appear to be simpler than the ones previously derived. For example, we construct stable discretizations which use only piecewise linear elements to approximate the stress field and piecewise constant functions to approximate the displacement field.

     

Finite elements for symmetric tensors in three dimensions

We construct finite element subspaces of the space of symmetric tensors with square-integrable divergence on a three-dimensional domain. These spaces can be used to approximate the stress field in the classical Hellinger-Reissner mixed formulation of the elasticty equations, when standard discontinuous finite element spaces are used to approximate the displacement field. These finite element spaces are defined with respect to an arbitrary simplicial triangulation of the domain, and there is one for each positive value of the polynomial degree used for the displacements. For each degree, these provide a stable finite element discretization. The construction of the spaces is closely tied to discretizations of the elasticity complex and can be viewed as the three-dimensional analogue of the triangular element family for plane elasticity previously proposed by Arnold and Winther.

     

Tuning the magnetic properties of Li(x)CrTi0.25Se2 (0.03 < or = x < or = 0.7) by directed deintercalation of lithium

X-ray diffraction (XRD), in situ energy-dispersive X-ray diffraction (EDXRD), X-ray absorption near-edge structure (XANES), extended X-ray absorption fine structure (EXAFS), and magnetic measurements were applied to investigate the effects of lithium deintercalation on pseudolayered Li(0.70)CrTi(0.25)Se(2). A detailed picture of structural changes during the deintercalation process was obtained by combining the results of EDXRD and EXAFS. Removal of Li from the host-guest complex leads to anisotropic contraction of the unit cell with stronger impact on the c axis, which is the stacking axis of the layers. The EDXRD experiments evidence that the shrinkage of the lattice parameters with decreasing x(Li) in Li(x)CrTi(0.25)Se(2) is nonlinear in the beginning and then becomes linear. Analysis of the EXAFS spectra clearly shows that the Cr/Ti-Se distances are affected in a different manner by Li removal. The Cr-Se bond lengths decrease, whereas the Ti-Se bonds lengthen when the Li content is reduced, which is consistent with XRD data. Magnetic measurements reveal a change from predominantly antiferromagnetic exchange (theta(p) = -300 K) interactions for the pristine material to ferromagnetic exchange interactions (theta = 25 K) for the fully intercalated material. Thus, the magnetic properties can be altered under ambient conditions by directed adjustment of the dominant magnetic exchange. The unusual magnetic behavior can be explained on the basis of the variation of the metal-metal distances and the Cr-Se-Cr angles with x, which were determined by Rietveld refinements. Owing to competing ferromagnetic and antiferromagnetic exchange interactions and disorder, the magnetic ground state of the intercalated materials is characterized by spin-glass or spin-glass-like behavior.     

Preconditioned Iterative Methods for Scattered Data Interpolation

The scattered data interpolation problem in two space dimensions is formulated as a partial differential equation with interpolating side conditions. The system is discretized by the Morley finite element space. The focus of this paper is to study preconditioned iterative methods for the corresponding discrete systems. We introduce block diagonal preconditioners, where a multigrid operator is used for the differential equation part of the system, while we propose an operator constructed from thin plate radial basis functions for the equations corresponding to the interpolation conditions. The effect of the preconditioners are documented by numerical experiments.     

Interior penalty preconditioners for mixed finite element approximations of elliptic problems

It is established that an interior penalty method applied to second-order elliptic problems gives rise to a local operator which is spectrally equivalent to the corresponding nonlocal operator arising from the mixed finite element method. This relation can be utilized in order to construct preconditioners for the discrete mixed system. As an example, a family of additive Schwarz preconditioners for these systems is constructed. Numerical examples which confirm the theoretical results are also presented.

     

Numerical simulation of glottal flow in surgically changed larynx

According to clinical experience the shape of the larynx seems to have a significant impact on the airflow degree and breathing pattern. In this study we perform a set of numerical experiments simulating the glottal flow in surgically changed larynx, where the vocal folds or false vocal are modified. We are aiming to find an optimal geometry of the larynx in terms of easiness for breathing. To this goal we numerically solve the system for weakly compressible Navier–Stokes equations using the finite element method and we compare the airflow resistance and the volumetric flow rate for the set of geometries for inspiration as well as expiration. We discuss the optimal geometry with respect to the quality of breathing. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Conformational properties of 1-methyl-1-germacyclohexane: low-temperature NMR and quantum chemical calculations

The conformational preference of the methyl group of 1-methyl-1-germacyclohexane was studied experimentally in solution (low-temperature ¹³C NMR) and by quantum chemical calculations (CCSD(T), MP2 and DFT methods). The NMR experiment resulted in an axial/equatorial ratio of 44/56 mol% at 114 K corresponding to an A value (A = G _ax ? G _eq) of 0.06 kcal mol^?1. An average value for ΔG _e→a ^#  = 5.0 ± 0.1 kcal mol^?1 was obtained for the temperature range 106–134 K. The experimental results are very well reproduced by the calculations. CCSD(T)/CBS calculations + thermal corrections resulted in an A value of 0.02 kcal mol^?1, whereas a ΔE value of ?0.01 kcal mol^?1 at 0 K was obtained.     

The Herschel-Quincke tube: the attenuation conditions and their sensitivity to mean flow

The classic Herschel-Quincke tube is a parallel connection of two ducts yielding multiple noise attenuation maxima via destructive interference. This problem has been discussed to different degrees by a number of authors over the years. This study returns to the basics of the system for the purpose of furthering the understanding of the conditions necessary for noise attenuation and especially their sensitivity to mean flow. First, the transmission loss for an N-duct system with mean flow and arbitrary conditions of state in the different ducts is derived. Next, the two types of conditions yielding the attenuation maxima are studied. In addition to a discussion of the underlying physics, generic expressions for frequencies at which maximum attenuation occur are presented. Experiments without mean flow generally show good agreement with theory based on straight duct elements. However, more detailed models may be required for accurate simulations in the presence of mean flow. A simple model compensating for the losses associated with bends is shown to improve the results significantly for the geometry studied.     

The effect of mineral fillers on impact and tensile properties of polypropylene

Impact and tensile properties of polypropylene filled with various minerals have been measured. The minerals investigated were dolomite, calcium carbonate, mica and wollastonite. The effect of particle shape, size, content and surface treatment on mechanical properties was studied. A special interest was devoted to the measuring of impact strength, since this is an important property in many applications.

The results show that, for stearic acid treated minerals, there is a marked relationship between decreasing particle size and increasing impact strength. This is especially distinct for the results from the staircase method of ASTM-D3029. Comparing the coarsest and finest fraction of particulate fillers studied, there is a 20-fold difference in impact strength at 50% filler content. The staircase method, compared to the instrumented falling weight impact test, shows a higher sensitivity to changes in impact strength, caused by, for example, variations in particle size or content.     

Mechanically interlocked mechanophores by living-radical polymerization from rotaxane initiators

Two [2]rotaxane initiators for single-electron-transfer living-radical-polymerization were synthesized and used for the controlled polymerization of methyl acrylate. The mechanically interlocked polymers exhibited distinct responses to mechanical activation by ultrasound. Monitoring the fate of the rotaxanes' charge transfer absorption bands provides evidence for preferential mechanical degradation of a midsection rotaxane unit as compared to a terminal rotaxane entity as a consequence of mechanical forces accumulating in the central region of the polymer chain.