On the necessity of the constant rank condition for LpL^p estimates

We consider a generalization of the elliptic $L^p$-estimate suited for linear operators with non-trivial kernels. A classical result of Schulenberger and Wilcox (Ann. Mat. Pura Appl. (4) 88: 229-305, 1971) shows that if the operator has constant rank then the estimate holds. We prove necessity of the constant rank condition for such an estimate.Comment: 5 pages; weaker versions of the results here had previously appeared in arXiv:1909.0392

Quasiconvexity, null Lagrangians, and Hardy space integrability under constant rank constraints

We present a systematic treatment of the theory of Compensated Compactness under Murat's constant rank assumption. We give a short proof of a sharp weak lower semicontinuity result for signed integrands, extending the results of Fonseca--M\"uller. The null Lagrangians are an important class of signed integrands, since they are the weakly continuous functions. We show that they are precisely the compensated compactness quantities with Hardy space integrability, thus proposing an answer to a question raised by Coifman-Lions-Meyer-Semmes. Finally we provide an effective way of computing the null Lagrangians associated with a given operator.Comment: Corrected typos and added an example in Section

Go with the Flow - Design of Cloud Logistics Service Blueprints

By adopting principles of cloud computing to the \ logistics domain the paradigm of Cloud Logistics is derived. It \ appears to be a promising paradigm in order to evolve logistics \ into being more flexible and collaborative. Yet, appropriate \ concepts that enable the cloud logistics paradigm are missing. \ In the paper, existing body of literature is reviewed and a \ definition and a framework of cloud logistics is given. Further, \ service blueprinting is combined with domain engineering and \ general morphological analysis in order to create a suitable \ method for designing cloud oriented service blueprints. Those \ are focusing on domain-specific flows and transformations \ enabling cloud oriented business collaboration. The method \ is applied to the logistics domain and a cloud logistics service \ blueprint is designed. Finally, the concept is evaluated with \ real use cases from logistics service providers

Compensation phenomena for concentration effects via nonlinear elliptic estimates

We study compensation phenomena for fields satisfying both a pointwise and a linear differential constraint. This effect takes the form of nonlinear elliptic estimates, where constraining the values of the field to lie in a cone compensates for the lack of ellipticity of the differential operator. We give a series of new examples of this phenomenon for a geometric class of cones and operators such as the divergence or the curl. One of our main findings is that the maximal gain of integrability is tied to both the differential operator and the cone, contradicting in particular a recent conjecture from arXiv:2106.03077. This extends the recent theory of compensated integrability due to D. Serre. In particular, we find a new family of integrands that are Div-quasiconcave under convex constraints

Gate-tunable Hall sensors on large area CVD graphene protected by h-BN with 1D edge contacts

Graphene is an excellent material for Hall sensors due to its atomically thin structure, high carrier mobility and low carrier density. However, graphene devices need to be protected from the environment for reliable and durable performance in different environmental conditions. Here we present magnetic Hall sensors fabricated on large area commercially available CVD graphene protected by exfoliated hexagonal boron nitride (h-BN). To connect the graphene active regions of Hall samples to the outputs the 1D edge contacts were utilized which show reliable and stable electrical properties. The operation of the Hall sensors shows the current-related sensitivity up to 345 V/(AT). By changing the carrier concentration and type in graphene by the application of gate voltage we are able to tune the Hall sensitivity

Compensated compactness: continuity in optimal weak topologies

For $l$-homogeneous linear differential operators $\mathcal{A}$ of constant rank, we study the implication $v_j\rightharpoonup v$ in $X$ and $\mathcal{A} v_j\rightarrow \mathcal{A} v$ in $W^{-l}Y$ implies $F(v_j)\rightsquigarrow F(v)$ in $Z$, where $F$ is an $\mathcal{A}$-quasiaffine function and $\rightsquigarrow$ denotes an appropriate type of weak convergence. Here $Z$ is a local $L^1$-type space, either the space $\mathscr{M}$ of measures, or $L^1$, or the Hardy space $\mathscr{H}^1$; $X,\, Y$ are $L^p$-type spaces, by which we mean Lebesgue or Zygmund spaces. Our conditions for each choice of $X,\,Y,\,Z$ are sharp. Analogous statements are also given in the case when $F(v)$ is not a locally integrable function and it is instead defined as a distribution. In this case, we also prove $\mathscr{H}^p$-bounds for the sequence $(F(v_j))_j$, for appropriate $p<1$, and new convergence results in the dual of H\"older spaces when $(v_j)$ is $\mathcal{A}$-free and lies in a suitable negative order Sobolev space $W^{-\beta,s}$. Some of these results are new even for distributional Jacobians.Comment: 33 page

Origin and evolution of surface spin current in topological insulators

The Dirac surface states of topological insulators offer a unique possibility for creating spin polarized charge currents due to the spin-momentum locking. Here we demonstrate that the control over the bulk and surface contribution is crucial to maximize the charge-to-spin conversion efficiency. We observe an enhancement of the spin signal due to surface-dominated spin polarization while freezing out the bulk conductivity in semiconducting Bi1.5Sb0.5Te1.7Se1.3 below 100K. Detailed measurements up to room temperature exhibit a strong reduction of the magnetoresistance signal between 2 and 100K, which we attribute to the thermal excitation of bulk carriers and to the electron-phonon coupling in the surface states. The presence and dominance of this effect up to room temperature is promising for spintronic science and technology

Modellgetriebene ad-hoc Integration von Logistikdienstleistern – Integrationsansatz und Prototyp

Der Logistikdienstleistungssektor ist durch arbeitsteilige sowie kurz-, mittel- und langfristige Zusammenarbeit gekennzeichnet. Insbesondere Fourth Party Logistics (4PL) stehen permanent vor der Aufgabe unterschiedliche Logistikdienstleister und damit auch deren Informationssysteme ad-hoc und medienbruchfrei in unternehmensübergreifende Informationsflüsse zu integrieren. Dieser Beitrag stellt verschiedene logistikspezifische Integrationsvarianten, einen modellgetriebenen Integrationsansatz sowie ein Lösungs-konzept auf Basis der Logistik Service Engineering & Management (LSEM)-Plattform vor. Die Umsetzung eines hierfür entwickelten Prototyps veranschaulicht das Lösungskonzept