Hierarchical Fractal Weyl Laws for Chaotic Resonance States in Open Mixed Systems

In open chaotic systems the number of long-lived resonance states obeys a fractal Weyl law, which depends on the fractal dimension of the chaotic saddle. We study the generic case of a mixed phase space with regular and chaotic dynamics. We find a hierarchy of fractal Weyl laws, one for each region of the hierarchical decomposition of the chaotic phase-space component. This is based on our observation of hierarchical resonance states localizing on these regions. Numerically this is verified for the standard map and a hierarchical model system.Comment: 5 pages, 3 figure

Analysis and numerical treatment of bulk-surface reaction-diffusion models of Gierer-Meinhardt type

We consider a Gierer-Meinhardt system on a surface coupled with aparabolic PDE in the bulk, the domain confined by this surface. Such a model was recently proposed and analyzed for two-dimensional bulk domains by Gomez, Ward and Wei (SIAM J. Appl. Dyn. Syst. 18, 2019).We prove the well-posedness of the bulk-surface system in arbitrary space dimensions and show that solutions remain uniformly bounded in parabolic Hölder spaces for all times. The proof uses Schauders fixed point theorem and a splitting in a surface and a bulk part. We also solve a reduced system, corresponding to the assumption of a well mixed bulk solution, numerically. We use operator-splitting methods which combine a finite element discretization of the Laplace-Beltrami operator with a positivity-preserving treatment of the source and sink terms. The proposed methodology is based on the flux-corrected transport (FCT) paradigm. It constrains the space and time discretization of the reduced problem in a manner which provides positivity preservation, conservation of mass, and second-order accuracy in smooth regions. The results of numerical studies for the system on a two-dimensional sphere demonstrate the occurrence of localized steady-state multispike pattern that have also been observed in one-dimensional models

App-based rehabilitation program after total knee arthroplasty: a randomized controlled trial

Introduction: New app-based programs for postoperative rehabilitation have been developed, but no long-term study has been published to date. Thus, a prospective randomized control trial with 2-year follow-up was performed to evaluate the effectiveness of app-based rehabilitation (GenuSport) compared to a control group after total knee arthroplasty (TKA). Methods: Between April and October 2016, 60 patients were enrolled in the study. Twenty-five patients were lost to follow-up, leaving 35 patients undergoing TKA for inclusion. In this group, twenty patients received app-based exercise program and 15 were randomized to the control group. The mean age was 64.37 +/- 9.32 years with a mean follow-up of 23.51 +/- 1.63 months. Patients in the app group underwent an app-based knee training starting on the day of surgery; whereas, patients in the control group underwent regular physiotherapy. Functional outcome scores using the Knee Injury and Osteoarthritis Outcome Score (KOOS), Knee Society Score (KSS) and VAS of pain were analyzed. Results: In the short term, significant differences between the app group and control group in time of 10-m walk (19.66 +/- 7.80 vs. 27.08 +/- 15.46 s; p = 0.029), VAS pain at rest and activity (2.65 +/- 0.82 vs. 3.57 +/- 1.58, respectively 4.03 +/- 1.26 vs. 5.05 +/- 1.21; p < 0.05) were observed. In the long term, a variety of different tendencies was found, highest in KSS Function with 76.32 +/- 16.49 (app group) vs. 67.67 +/- 16.57 (control group) (p = 0.130). Additionally, patients in the app group required less painkillers (10.0% vs. 26.7%) and more likely to participate in sports (65.0% vs. 53.3%). Conclusions: An app-based knee trainer is a promising tool in improving functional outcomes such as KSS function score and VAS after TKA

Bericht der Regierungskommission zur Überprüfung der Sicherheitsgesetzgebung in Deutschland vom 28. August 2013

Der Bericht der Kommission enthält konkrete Vorschläge zur Verbesserung der rechtsstaatlichen Ausrichtung der Sicherheitsgesetzgebung, sowie einen Maßnahmenkatalog für die Reform der Sicherheitsarchitektur

Pair distribution function analysis of ZrO2 nanocrystals and insights in the formation of ZrO2-YBa2Cu3O7 nanocomposites

The formation of superconducting nanocomposites from preformed nanocrystals is still not well understood. Here, we examine the case of ZrO2 nanocrystals in a YBa2Cu3O7-x matrix. First we analyzed the preformed ZrO2 nanocrystals via atomic pair distribution function analysis and found that the nanocrystals have a distorted tetragonal crystal structure. Second, we investigated the influence of various surface ligands attached to the ZrO2 nanocrystals on the distribution of metal ions in the pyrolyzed matrix via secondary ion mass spectroscopy technique. The choice of stabilizing ligand is crucial in order to obtain good superconducting nanocomposite films with vortex pinning. Short, carboxylate based ligands lead to poor superconducting properties due to the inhomogeneity of metal content in the pyrolyzed matrix. Counter-intuitively, a phosphonate ligand with long chains does not disturb the growth of YBa2Cu3O7-x. Even more surprisingly, bisphosphonate polymeric ligands provide good colloidal stability in solution but do not prevent coagulation in the final film, resulting in poor pinning. These results thus shed light on the various stages of the superconducting nanocomposite formation

Digitalisierung und Demokratie

Die Digitalisierung spielt bei den Prozessen und Entwicklungen in einer Demokratie eine immer größere Rolle. Denn Digitalisierung erweitert die Möglichkeiten der Information, Kommunikation und Partizipation. Gleichzeitig können digitale Technologien zu einer schnellen Verbreitung von Falschinformationen beitragen und bergen ein Potenzial für Meinungsmanipulation, zum Beispiel vor Wahlen. Dieses Spannungsfeld ist Thema der Stellungnahme "Digitalisierung und Demokratie". Darin analysieren die Autorinnen und Autoren Aspekte des Zusammenspiels von Digitalisierung und Demokratie. Darauf aufbauend formulieren sie Handlungsempfehlungen zur Gestaltung künftiger Entwicklungen durch Politik, Recht und Zivilgesellschaft

GRUNDRECHTLICHER INFORMATIONSSCHUTZ GEGEN PRIVATE

Gegenstand des Beitrags sind die dogmatischen Grundlagen des grundrechtlichen Schutzes gegen den Umgang Privater mit personenbezogenen Informationen. Quelle dieses Informationsschutzes sind spezifische Vertraulichkeitsgarantien sowie das unspezifische und übergreifende Recht auf informationelle Selbstbestimmung. Dieses Grundrecht erfüllt eine Doppelfunktion als objektiv-rechtlicher Ausgestaltungsauftrag für das private Datenschutzrecht und als subsidiärer punktueller Schutzanspruch des Einzelnen vor Übergriffen Privater. Hieraus ergeben sich Anforderungen an die rechtliche Würdigung einzelner Informationshandlungen wie auch an die einzelfallübergreifende rechtliche Strukturierung privater Datenverarbeitungen. Die entwickelten grundrechtsdogmatischen Aussagen werden anhand von Beispielen aus der Rechtsprechung des Bundesverfassungsgerichts und aus der aktuellen Diskussion zum Datenschutzrecht illustriert und getestet