Scale invariant Green-Kubo relation for time averaged diffusivity

In recent years it was shown both theoretically and experimentally that in certain systems exhibiting anomalous diffusion the time and ensemble average mean squared displacement are remarkably different. The ensemble average diffusivity is obtained from a scaling Green-Kubo relation, which connects the scale invariant non-stationary velocity correlation function with the transport coefficient. Here we obtain the relation between time averaged diffusivity, usually recorded in single particle tracking experiments, and the underlying scale invariant velocity correlation function. The time averaged mean squared displacement is given by $\overline{\delta^2} \sim 2 D_\nu t^{\beta}\Delta^{\nu-\beta}$ where $t$ is the total measurement time and $\Delta$ the lag time. Here $\nu>1$ is the anomalous diffusion exponent obtained from ensemble averaged measurements $\langle x^2 \rangle \sim t^\nu$ while $\beta\ge -1$ marks the growth or decline of the kinetic energy $\langle v^2 \rangle \sim t^\beta$. Thus we establish a connection between exponents which can be read off the asymptotic properties of the velocity correlation function and similarly for the transport constant $D_\nu$. We demonstrate our results with non-stationary scale invariant stochastic and deterministic models, thereby highlighting that systems with equivalent behavior in the ensemble average can differ strongly in their time average. This is the case, for example, if averaged kinetic energy is finite, i.e. $\beta=0$, where $\langle \overline{\delta^2}\rangle \neq \langle x^2\rangle$

Non-Markovian out-of-equilibrium dynamics: A general numerical procedure to construct time-dependent memory kernels for coarse-grained observables

We present a numerical method to compute non-equilibrium memory kernels based on experimental data or molecular dynamics simulations. The procedure uses a recasting of the non-stationary generalized Langevin equation, in which we expand the memory kernel in a series that can be reconstructed iteratively. Each term in the series can be computed based solely on knowledge of the two-time auto-correlation function of the observable of interest. As a proof of principle, we apply the method to crystallization from a super-cooled Lennard Jones melt. We analyze the nucleation and growth dynamics of crystallites and observe that the memory kernel has a time extent that is about one order of magnitude larger than the typical timescale needed for a particle to be attached to the crystallite in the growth regime

Anomalous statistical properties and fluctuations on multiple timescales

How can fluctuations in one-dimensional time series data be characterized and how can detected effects be decomposed into their dynamical origins or causes? In the context of these questions, a variety of problems are discussed and solutions are introduced. The first issue concerns the causes of anomalous diffusion. A previously proposed framework decomposes the Hurst exponent into the Joseph, Noah, and Moses effects. They represent violations of the three premises of the central limit theorem. Here the framework is applied to an intermittent deterministic system, which exhibits a rich combination of all three effects. Nevertheless, the results provide an intuitive interpretation of the dynamics. In addition, the framework is theoretically discussed and connected to a calculation that proves its validity for a large class of systems. Once the type of anomalous statistical behavior is classified, one might ask what the dynamical origin of the effects is. Especially the property of long range temporal correlations (the Joseph effect) is discussed in detail. In measurements, they might arise from different dynamical origins or can be explained as an emerging phenomenon. A collection of different routes to the observed behavior is established here. A popular tool for detecting long range correlations is detrended fluctuation analysis. Its advantages over traditional methods are stability and smoothness for timescales up to one fourth of the measurement time and the ability to neglect the slow dynamics and trends. Recently, a theory for an analytical understanding of this method was introduced. In this thesis, the method is further analyzed and developed. An approach is presented that enables scientists to use this method for short range correlated data, even if the dynamics is very complex. Fluctuations can be decomposed into a superposition of linear models that explain its features. Therefore, on the one hand, this thesis is about understanding the effects of anomalous diffusion. On the other hand, it is about widening the applicability of one of its detection methods such that it becomes useful for understanding normal or complex statistical behavior. A good example of a complex system, where the proposed stochastic methods are useful, is the atmosphere. Here it is shown how detrended fluctuation analysis can be used to uncover oscillatory modes and determine their periods. One of them is the El Ni\~no southern oscillation. A less well known and more challenging application is a 7--8 year mode in European temperature fluctuations. A power grid is a very different type of complex system. However, using the new method, it is possible to generate a data model that incorporates the important features of the grid frequency

Gerichtsdiplomatie des Bundesverfassungsgerichts: Bilaterale Gerichtstreffen als neuartige Datenquelle zur Beurteilung der transnationalen Kommunikation von Verfassungsgerichten

Judicial diplomacy describes the courts’ efforts to promote liberal democracy and protect their institutional authority. Bilateral court meetings are essential for judicial diplomacy, encompassing jurisprudential (e.g., discussion of case law) and aims of strategic (e.g., maximising influence). This study presents a novel approach to assess such meetings. It analyses the German Federal Constitutional Court meeting reports between 1998–2019, using content and semantic network analysis. The content analysis shows that court meetings focus on jurisprudential aspects; however, strategic considerations also play a role in discussions with interlocutors from emerging democracies. These findings are substantiated by the semantic network analysis, which discloses that recent case law, Europeanisation, and globalisation are the main issues discussed. Hence, this study presents an analysis of a novel data source. Further, it contributes to judicial politics research as transnational court meetings could be a missing link to understand legal citation networks.Verfassungsgerichte versuchen aktiv, mittels diplomatischer Bemühungen, liberale demokratische Strukturen zu fördern und gleichzeitig ihre institutionelle Autorität zu stärken. Ein wesentliches Element dieser Gerichtsdiplomatie sind bilaterale Treffen, mit welchen nationale Gerichte sowohl juristische (z. B. mittels Fachgespräche über nationale Rechtssprechungspraktiken) als auch strategische (z. B. Maximierung des eigenen innenpolitischen Einflusses) Aspekte diskutieren. Mittels einer Analyse von Pressemitteilungen bezüglich bilateraler Treffen des deutschen Bundesverfassungsgerichts zwischen 1998–2019, stellt diese Studie einen neuen Ansatz zur Untersuchung von bilateralen Treffen vor. Methodisch werden sowohl eine Inhalts- als auch eine semantische Netzwerkanalyse durchgeführt. Die Inhaltsanalyse zeigt, dass die bilateralen Treffen auf rechtswissenschaftliche Aspekte fokussiert sind, während strategische Überlegungen insbesondere bei Diskussionen mit Gesprächspartnern aus sich in Entwicklung befindlichen Demokratien eine Rolle spielen. Diese Ergebnisse werden durch die semantische Netzwerkanalyse bestätigt, die offenlegt, dass die Hauptthemen, die diskutiert werden, nationale Rechtssprechungspraktiken, Europäisierung und Globalisierung sind. Diese Studie präsentiert eine Analyse einer neuartigen Datenquelle. Darüber hinaus leistet die Studie einen Beitrag zur Gerichtsforschung, indem sie zeigt, dass transnationale Gerichtstreffen dabei helfen können juristische Zitationsnetzwerke und transnationale Entscheidungsverweise zu verstehen

Communicating judicial decisions : court press releases and their effect on the news media

Constitutional review courts construe constitutions in the light of legal, social, and political disputes. As such, constitutional review has become a key feature of modern-day democracies. However, the court’s authority depends on their reputation and support within the public, as they are unable to enforce their decisions and sanction noncompliance. Only if the public is aware of the courts and their actions and lends them their support, elected politicians will more likely comply with court decisions. To create awareness and to enable public scrutiny, courts have several tools. Among others, a proactive strategy to communicate and transmit information on court decisions and, thus, to increase transparency and openness is perceived to be an essential tool that courts have at their disposal. Through communication, court decisions become more accessible, potentially better understood, and the courts and their judges are held accountable to the public. In this dissertation, I study press releases by constitutional courts. Since the news media is the gatekeeper between the government and the public, I also assess how court communication shapes news media coverage of court decisions. I draw on the comparative judicial politics literature, the literature on policy agendas, and communication and journalism studies on the concepts of court reporting and news values. Throughout four empirical chapters, I ask which institutional structures influence the publication of court press releases, when and what kind of information courts communicate, and how these communication efforts shape the news media. I extend the existing literature in two regards. First, I argue that press releases are of central importance for a court’s agenda-setting power. Second, I argue that courts actively use the institutional tools at their disposal to create publicity and increase the chances of being reported on in the news. One such instrument is the publication of press releases, and this dissertation found that the strategic use of press releases enables courts to increase media coverage and, therefore, facilitate public scrutiny. I test these arguments empirically by combining inference methods such as logistic regressions with methods from the fields of machine learning and computational text analysis. Throughout all chapters, I test my arguments using data on court decisions and press releases of the German Federal Constitutional Court. The German court is a suitable case as it enjoys a sturdy and robust public support and has a comparatively long history of public relations and issuing press releases. The findings presented in the four chapters present a wide range of empirical evidence. In particular, I show that court decisions shape the policy issued discussed in the press releases through first-level agenda-setting dynamics. Additionally, I find evidence that press releases are published selectively and are more likely to occur when a decision declares a law unconstitutional. Concerning the news media, the results suggest that journalists rarely use court press releases when reporting on court decisions. However, if they use press releases for their reporting, they are more likely to use those that promote decisions that the public is already aware of. Finally, the likelihood of media coverage of FCC decisions is higher for those that were promoted with a press release and had high news value. The findings of my dissertation confirm that press releases help a court to communicate its policy agenda to the public. Moreover, my results suggest that court communication efforts partially serve the media logic, as I found first, that court decisions are more likely promoted with a press release if they entail newsworthy characteristics like conflict, relevance, and familiarity and second, that media coverage is more likely for decisions that entail these particular characteristics. Finally, since the likelihood of media coverage of court decisions is found to be higher when promoted with a press release, courts have considerable leverage to shape public opinion. Therefore, my results have implications for the research on strategic court behavior, court communication, and court reporting. Overall, since this dissertation offers novel perspectives on how courts communicate and how these efforts shape the media, it contributes to the growing discussion on open justice and the accountability of courts in times where judiciaries are under populist pressure. Hence, this dissertation has important implications for the sustainability of liberal democracy and the legitimacy of constitutional review in constitutional states