hp-dGFEM for Second-Order Elliptic Problems in Plyhedra I: Stability and Quasioptimality on Geometric Meshes

We introduce and analyze hp-version discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems in three-dimensional polyhedral domains. To resolve possible corner-, edge- and corner-edge singularities, we consider hexahedral meshes that are geometrically and anisotropically refined toward the corresponding neighborhoods. Similarly, the local polynomial degrees are increased linearly and possibly anisotropically away from singularities. We design interior penalty hp-dG methods and prove that they are well-defined for problems with singular solutions and stable under the proposed hp-refinements. We establish (abstract) error bounds that will allow us to prove exponential rates of convergence in the second part of this work.

hp-dGFEM for Second-Order Elliptic Problems in Plyhedra II: Exponential Convergence

The goal of this paper is to establish exponential convergence of $hp$-version interior penalty (IP) discontinuous Galerkin (dG) finite element methods for the numerical approximation of linear second-order elliptic boundary-value problems with homogeneous Dirichlet boundary conditions and piecewise analytic data in three-dimensional polyhedral domains. More precisely, we shall analyze the convergence of the $hp$-IP dG methods considered in [D. Schötzau, C. Schwab, T. P. Wihler, SIAM J. Numer. Anal., 51 (2013), pp. 1610--1633] based on axiparallel $\sigma$-geometric anisotropic meshes and $\bm{s}$-linear anisotropic polynomial degree distributions.

hp-DGFEM for second-order mixed elliptic problems polyhedra

We prove exponential rates of convergence of hp-version discontinuous Galerkin (dG) interior penalty finite element methods for second-order elliptic problems with mixed Dirichlet-Neumann boundary conditions in axiparallel polyhedra. The dG discretizations are based on axiparallel, σ-geometric anisotropic meshes of mapped hexahedra and anisotropic polynomial degree distributions of μ-bounded variation. We consider piecewise analytic solutions which belong to a larger analytic class than those for the pure Dirichlet problem considered in [11, 12]. For such solutions, we establish the exponential convergence of a nonconforming dG interpolant given by local L 2 -projections on elements away from corners and edges, and by suitable local low-order quasi-interpolants on elements at corners and edges. Due to the appearance of non-homogeneous, weighted norms in the analytic regularity class, new arguments are introduced to bound the dG consistency errors in elements abutting on Neumann edges. The non-homogeneous norms also entail some crucial modifications of the stability and quasi-optimality proofs, as well as of the analysis for the anisotropic interpolation operators. The exponential convergence bounds for the dG interpolant constructed in this paper generalize the results of [11, 12] for the pure Dirichlet case.

Relative Predicativity and dependent recursion in second-order set theory and higher-orders theories

This article reports that some robustness of the notions of predicativity and of autonomous progression is broken down if as the given infinite total entity we choose some mathematical entities other than the traditional ω. Namely, the equivalence between normal transfinite recursion scheme and new dependent transfinite recursion scheme, which does hold in the context of subsystems of second order number theory, does not hold in the context of subsystems of second order set theory where the universe V of sets is treated as the given totality (nor in the contexts of those of n+3-th order number or set theories, where the class of all n+2-th order objects is treated as the given totality).

Varying spin state composition by the choice of capping ligand in a family of molecular chains: detailed analysis of magnetic properties of chromium(III) horseshoes

We report a detailed physical analysis on a family of isolated, antiferro-magnetically (AF) coupled, chromium(III) finite chains, of general formula (Cr(RCO(2))(2)F)(n) where the chain length n = 6 or 7. Additionally, the chains are capped with a selection of possible terminating ligands, including hfac (= 1,1,1,5,5,5-hexafluoropentane-2,4-dionate(1-)), acac (= pentane-2,4-dionate(1-)) or (F)(3). Measurements by inelastic neutron scattering (INS), magnetometery and electron paramagnetic resonance (EPR) spectroscopy have been used to study how the electronic properties are affected by n and capping ligand type. These comparisons allowed the subtle electronic effects the choice of capping ligand makes for odd member spin 3/2 ground state and even membered spin 0 ground state chains to be investigated. For this investigation full characterisation of physical properties have been performed with spin Hamiltonian parameterisation, including the determination of Heisenberg exchange coupling constants and single ion axial and rhombic anisotropy. We reveal how the quantum spin energy levels of odd or even membered chains can be modified by the type of capping ligand terminating the chain. Choice of capping ligands enables Cr-Cr exchange coupling to be adjusted by 0, 4 or 24%, relative to Cr-Cr exchange coupling within the body of the chain, by the substitution of hfac, acac or (F)(3) capping ligands to the ends of the chain, respectively. The manipulation of quantum spin levels via ligands which play no role in super-exchange, is of general interest to the practise of spin Hamilton modelling, where such second order effects are generally not considered of relevance to magnetic properties.

The emotional power of music: How music enhances the feeling of affective pictures

Music is an intriguing stimulus widely used in movies to increase the emotional experience. However, no brain imaging study has to date examined this enhancement effect using emotional pictures (the modality mostly used in emotion research) and musical excerpts. Therefore, we designed this functional magnetic resonance imaging study to explore how musical stimuli enhance the feeling of affective pictures. In a classical block design carefully controlling for habituation and order effects, we presented fearful and sad pictures (mostly taken from the IAPS) either alone or combined with congruent emotional musical excerpts (classical pieces). Subjective ratings clearly indicated that the emotional experience was markedly increased in the combined relative to the picture condition. Furthermore, using a second-level analysis and regions of interest approach, we observed a clear functional and structural dissociation between the combined and the picture condition. Besides increased activation in brain areas known to be involved in auditory as well as in neutral and emotional visual-auditory integration processes, the combined condition showed increased activation in many structures known to be involved in emotion processing (including for example amygdala, hippocampus, parahippocampus, insula, striatum, medial ventral frontal cortex, cerebellum, fusiform gyrus). In contrast, the picture condition only showed an activation increase in the cognitive part of the prefrontal cortex, mainly in the right dorsolateral prefrontal cortex. Based on these findings, we suggest that emotional pictures evoke a more cognitive mode of emotion perception, whereas congruent presentations of emotional visual and musical stimuli rather automatically evoke strong emotional feelings and experiences.

(Non)-Dissipative Hydrodynamics on Embedded Surfaces

We construct the theory of dissipative hydrodynamics of uncharged fluids living on embedded space-time surfaces to first order in a derivative expansion in the case of codimension-1 surfaces (including fluid membranes) and the theory of non-dissipative hydrodynamics to second order in a derivative expansion in the case of codimension higher than one under the assumption of no angular momenta in transverse directions to the surface. This construction includes the elastic degrees of freedom, and hence the corresponding transport coefficients, that take into account transverse fluctuations of the geometry where the fluid lives. Requiring the second law of thermodynamics to be satisfied leads us to conclude that in the case of codimension-1 surfaces the stress-energy tensor is characterized by 2 hydrodynamic and 1 elastic independent transport coefficient to first order in the expansion while for codimension higher than one, and for non-dissipative flows, the stress-energy tensor is characterized by 7 hydrodynamic and 3 elastic independent transport coefficients to second order in the expansion. Furthermore, the constraints imposed between the stress-energy tensor, the bending moment and the entropy current of the fluid by these extra non-dissipative contributions are fully captured by equilibrium partition functions. This analysis constrains the Young modulus which can be measured from gravity by elastically perturbing black branes.

What does professionalisation mean? Perceptions of professionalisation in swiss sport federations

Introduction: Organisational changes in sports federations are often associated with a drift from a volunteer driven to an increasingly business-like phenomenon (Shilbury & Ferkins, 2011). This process of transfor-mation is be called as “professionalization”. Accordingly, professionalization seems to be an appropriate strategy for sport organisations in order to meet organizational pressure due to challenges of a more complex and dynamic changing environment adequately. Despite the increasing research interest and the attempts for systematization on the phenomenon of professionalization it still remains unclear what does the term professionalization exactly mean (Dowling et al., 2014). Thus, there is a lack of a consistent concept of professionalization that is needed in order to explore different facets and perspectives of this phenomenon more validly. Against this background following question emerged: What is the suitable concept of professionalization for analyzing the actual ongoing processes of change, adaption or transformation in sport federations? Methods: Dealing with this question, following two-step approach was choosen: (1) In a first step a scholar’s perspective at professionalisation of sport organisations will be displayed in order to explore both the common ground as well as divergences and inconsistencies in previous approaches. Therefore, a literature review is indicated. (2) In a second step, and in contrast to previous studies we will consider a practical point of view by a so called second-order observation of experts to gain valuable insights into current thinking and acting towards professionalization in sport federations. In doing so, a hermeneutical approach is used, which is about understanding the meaning of contexts by grasping the everyday world, and draw insight and meaning from it (Shilbury et al., 2013). Accordance with hermeneutics, the explorative interpretive knowledge of expert interviews was used. The interviews were conducted with a sample of six selected experts, who have both dedicated insider knowledge and the overall view of all Swiss sport federations. Results and discussion: The summaries of literature review could be categorized into two research currents. The one defines professionalization as a structural process towards professional status of occupations. The other defines it in a broader sense as an organisational change towards a business-like approach. Whereas the first perspective there is a broad scientific consensus that second isn’t that clear, however. Explorative analysis of interview data reveals different themes in relation to professionalization of sports federation. First theme deals with a changed philosophy as more strategic alignment towards for-profit, efficiency and quality orientation. Second theme refers to paid work associated with more competence orientation and balanced governance between paid and voluntary work. Third theme deals with acting shift towards more rationalization and efficiency by implementation of innovative management and communication tools. Based on findings of both our review of scholar`s perspective as well insights from experts we will provide – in the sense of synthesis – a more clear understanding of what does professionalization mean that can be useful in terms of further studies. References: Dowling, M., Edwards, J. & Washington, M. (2014). Understanding the concept of professionalisation in sport management research. Sport Management Review, 17 (4), 520–529. Shilbury, D., Ferkins, L. & Smythe, L. (2013). Sport governance encounters: Insights from lived experiences. Sport Management Review, 16,349–363. Shilbury, D., & Ferkins, L. (2011). Professionalisation, sport governance and strategic capability. Managing Leisure, 16, 108–127.