The relaxed-polar mechanism of locally optimal Cosserat rotations for an idealized nanoindentation and comparison with 3D-EBSD experiments

The rotation ${\rm polar}(F) \in {\rm SO}(3)$ arises as the unique orthogonal factor of the right polar decomposition $F = {\rm polar}(F) \cdot U$ of a given invertible matrix $F \in {\rm GL}^+(3)$. In the context of nonlinear elasticity Grioli (1940) discovered a geometric variational characterization of ${\rm polar}(F)$ as a unique energy-minimizing rotation. In preceding works, we have analyzed a generalization of Grioli's variational approach with weights (material parameters) $\mu > 0$ and $\mu_c \geq 0$ (Grioli: $\mu = \mu_c$). The energy subject to minimization coincides with the Cosserat shear-stretch contribution arising in any geometrically nonlinear, isotropic and quadratic Cosserat continuum model formulated in the deformation gradient field $F := \nabla\varphi: \Omega \to {\rm GL}^+(3)$ and the microrotation field $R: \Omega \to {\rm SO}(3)$. The corresponding set of non-classical energy-minimizing rotations $${\rm rpolar}^\pm_{\mu,\mu_c}(F) := \substack{{\rm argmin}\\ R\,\in\,{\rm SO(3)}} \Big\{ W_{\mu, \mu_c}(R\,;F) := \mu\, || {\rm sym}(R^TF - 1)||^2 + \mu_c\, ||{\rm skew}(R^TF - 1)||^2 \Big\}$$ represents a new relaxed-polar mechanism. Our goal is to motivate this mechanism by presenting it in a relevant setting. To this end, we explicitly construct a deformation mapping $\varphi_{\rm nano}$ which models an idealized nanoindentation and compare the corresponding optimal rotation patterns ${\rm rpolar}^\pm_{1,0}(F_{\rm nano})$ with experimentally obtained 3D-EBSD measurements of the disorientation angle of lattice rotations due to a nanoindentation in solid copper. We observe that the non-classical relaxed-polar mechanism can produce interesting counter-rotations. A possible link between Cosserat theory and finite multiplicative plasticity theory on small scales is also explored.Comment: 28 pages, 11 figure

Regularity for a geometrically nonlinear flat Cosserat micropolar membrane shell with curvature

We consider the rigorously derived thin shell membrane $\Gamma$-limit of a three-dimensional isotropic geometrically nonlinear Cosserat micropolar model and deduce full interior regularity of both the midsurface deformation $m:\omega\subset{\mathbb R}^2\to{\mathbb R}^3$ and the orthogonal microrotation tensor field $R:\omega\subset{\mathbb R}^2\to SO(3)$. The only further structural assumption is that the curvature energy depends solely on the uni-constant isotropic Dirichlet type energy term $|DR|^2$. We use Rivi\`ere's regularity techniques of harmonic map type systems for our system which couples harmonic maps to $SO(3)$ with a linear equation for $m$. The additional coupling term in the harmonic map equation is of critical integrability and can only be handled because of its special structure

Jointly they edit: examining the impact of community identification on political interaction in Wikipedia

In their 2005 study, Adamic and Glance coined the memorable phrase "divided they blog", referring to a trend of cyberbalkanization in the political blogosphere, with liberal and conservative blogs tending to link to other blogs with a similar political slant, and not to one another. As political discussion and activity increasingly moves online, the power of framing political discourses is shifting from mass media to social media. Continued examination of political interactions online is critical, and we extend this line of research by examining the activities of political users within the Wikipedia community. First, we examined how users in Wikipedia choose to display (or not to display) their political affiliation. Next, we more closely examined the patterns of cross-party interaction and community participation among those users proclaiming a political affiliation. In contrast to previous analyses of other social media, we did not find strong trends indicating a preference to interact with members of the same political party within the Wikipedia community. Our results indicate that users who proclaim their political affiliation within the community tend to proclaim their identity as a "Wikipedian" even more loudly. It seems that the shared identity of "being Wikipedian" may be strong enough to triumph over other potentially divisive facets of personal identity, such as political affiliation.Comment: 33 pages, 5 figure

Novel H(symCurl)H(\mathrm{sym} \mathrm{Curl})-conforming finite elements for the relaxed micromorphic sequence

In this work we construct novel $H(\mathrm{sym} \mathrm{Curl})$-conforming finite elements for the recently introduced relaxed micromorphic sequence, which can be considered as the completion of the $\mathrm{div} \mathrm{Div}$-sequence with respect to the $H(\mathrm{sym} \mathrm{Curl})$-space. The elements respect $H(\mathrm{Curl})$-regularity and their lowest order versions converge optimally for $[H(\mathrm{sym} \mathrm{Curl}) \setminus H(\mathrm{Curl})]$-fields. This work introduces a detailed construction, proofs of linear independence and conformity of the basis, and numerical examples. Further, we demonstrate an application to the computation of metamaterials with the relaxed micromorphic model

Transitional cluster dynamics in a model for delay-coupled chemical oscillators

Cluster synchronization is a fundamental phenomenon in systems of coupled oscillators. Here, we investigate clustering patterns that emerge in a unidirectional ring of four delay-coupled electrochemical oscillators. A voltage parameter in the experimental set-up controls the onset of oscillations via a Hopf bifurcation. For a smaller voltage, the oscillators exhibit simple, so-called primary, clustering patterns, where all phase differences between each set of coupled oscillators are identical. However, upon increasing the voltage, additional secondary states, where phase differences differ, are detected. Previous work on this system saw the development of a mathematical model that explains how the existence, stability, and common frequency of the experimentally observed cluster states can be accurately controlled by the delay time of the coupling. In this study, we revisit the mathematical model of the electrochemical oscillators to address open questions by means of bifurcation analysis. Our analysis reveals how the stable cluster states, corresponding to experimental observations, lose their stability via an assortment of bifurcation types. The analysis further reveals a complex interconnectedness between branches of different cluster types; in particular, we find that each secondary state provides a continuous transition between certain primary states. These connections are explained by studying the phase space and parameter symmetries of the respective states. Furthermore, we show that it is only for a larger value of the voltage parameter that the branches of secondary states develop intervals of stability. Otherwise, for a smaller voltage, all the branches of secondary states are completely unstable and therefore hidden to experimentalists.Comment: 13 pages, 14 figure

The Role of Application Portfolio Management in Application Services Outsourcing: Explicating Variations in Application Portfolio Management among Outsourcing Gestalts

Prior research has identified different outsourcing strategy types most likely to succeed, described by the outsourcing extent, the contract type, and duration. Each of the strategy types serves a particular outsourcing outcome. Since application portfolio management pursues improvement and optimization in the application landscape, it supports and enables decisions in the field of application services outsourcing. The aim of our research is to investigate the varying role of application portfolio management (APM) for different application services outsourcing strategies. Therefore, we conducted case study research with eleven large German and Swiss companies. In order to identify the varying role of APM, we compared the behaviors of the companies successfully applying particular strategy types, analyzing the differences in APM capabilities, application portfolio structure, and the influence of application characteristics. The results reveal that the companies applying different strategies vary in the extent to which APM is implemented in an organization