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One of the main statistical features of near-neutral atmospheric boundary layer (ABL) turbulence is the positive vertical velocity skewness $Sk_w$ above the roughness sublayer or the buffer region in smooth-walls. The $Sk_w$ variations are receiving renewed interest in many climate-related parameterizations of the ABL given their significance to cloud formation and to testing sub-grid schemes for Large Eddy Simulations (LES). The vertical variations of $Sk_w$ are explored here using high Reynolds number wind tunnel and flume experiments collected above smooth, rough, and permeable-walls in the absence of buoyancy and Coriolis effects. These laboratory experiments form a necessary starting point to probe the canonical structure of $Sk_w$ as they deal with a key limiting case (i.e. near-neutral conditions) that has received much less attention compared to its convective counterpart in atmospheric turbulence studies. Diagnostic models based on cumulant expansions, realizability constraints, and the now-popular constant mass flux approach routinely employed in the convective boundary layer as well as prognostic models based on third-order budgets are used to explain variations in $Sk_w$ for the idealized laboratory conditions. The failure of flux-gradient relations to model $Sk_w$ from the gradients of the vertical velocity variance $\sigma_w^2$ are explained and corrections based on models of energy transport offered. Novel links between the diagnostic and prognostic models are also featured, especially for the inertial term in the third order budget of the vertical velocity fluctuation. The co-spectral properties of $w'/\sigma_w$ versus $w'^2/\sigma_w^2$ are also presented for the first time to assess the dominant scales governing $Sk_w$ in the inner and outer layers, where $w'$ is the fluctuating vertical velocity and $\sigma_w$ is the vertical velocity standard deviation.

We provide empirical evidence that within the inertial sub layer of adiabatic turbulent flows over smooth walls, the skewness of the vertical velocity component $Sk_w$ displays universal behaviour, being constant and constrained within the range $Sk_w \approx 0.1-0.16$, regardless of flow configuration and Reynolds number. A theoretical model is proposed to explain the observed behaviour, including the observed range of variations of $Sk_w$. The model clarifies why $Sk_w$ cannot be predicted from down-gradient closure approximations routinely employed in meteorological and climate models whereby $Sk_w$ impacts cloud formation and dispersion processes. The model also offers an alternative and implementable approach.

The statistical properties of Uniform Momentum Zones (UMZs) are extracted from laboratory and field measurements in rough wall turbulent boundary layers to formulate a set of stochastic models for the simulation of instantaneous velocity profiles. A spatio-temporally resolved velocity dataset, covering a field of view of $8 \times 9$ m$^2$, was obtained in the atmospheric surface layer using super-large-scale particle image velocimetry (SLPIV), as part of the Grand-scale Atmospheric Imaging Apparatus (GAIA). Wind tunnel data from a previous study are included for comparison \citep{heisel2020mixing}. The probability density function of UMZ attributes such as their thickness, modal velocity, and averaged vertical velocity are built at varying elevations and modeled using log-normal and Gaussian distributions. Inverse transform sampling of the distributions is used to generate synthetic step-like velocity profiles that are spatially and temporally uncorrelated. Results show that in the wide range of wall-normal distances and $Re_\tau$ up to $ \sim O(10^6)$ investigated here, shear velocity scaling is manifested in the velocity jump across shear interfaces between adjacent UMZs, and attached eddy behavior is observed in the linear proportionality between UMZ thickness and their wall normal location. These very same characteristics are recovered in the generated instantaneous profiles, using both a fully stochastic and a data-driven hybrid stochastic models, which address, in different ways, the coupling between modal velocities and UMZ thickness. Our method provides a stochastic approach for generating an ensemble of instantaneous velocity profiles, consistent with the structural organization of UMZs, where the ensemble reproduces the logarithmic mean velocity profile and recovers significant portions of the Reynolds stresses and thus of the streamwise and vertical velocity variability.

Valuable insights, such as frequently visited environments in the wake of the COVID-19 pandemic, can oftentimes only be gained by analyzing sensitive data spread across edge-devices like smartphones. To facilitate such an analysis, we present a toolchain called PrivAgE for a distributed, privacy-preserving aggregation of local data by taking the limited resources of edge-devices into account. The distributed aggregation is based on secure summation and simultaneously satisfies the notion of differential privacy. In this way, other parties can neither learn the sensitive data of single clients nor a single client's influence on the final result. We perform an evaluation of the power consumption, the running time and the bandwidth overhead on real as well as simulated devices and demonstrate the flexibility of our toolchain by presenting an extension of the summation of histograms to distributed clustering.

Large-eddy simulations are used to evaluate mean profile similarity in the convective boundary layer (CBL). Particular care is taken regarding the grid sensitivity of the profiles and the mitigation of inertial oscillations in the simulation spin-up. The nondimensional gradients $\phi$ for wind speed and air temperature generally align with Monin-Obukhov similarity across cases but have a steeper slope than predicted within each profile. The same trend has been noted in several other recent studies. The Businger-Dyer relations are modified here with an exponential cutoff term to account for the decay in $\phi$ to first-order approximation, yielding improved similarity from approximately 0.05$z_i$ to above 0.3$z_i$, where $z_i$ is the CBL depth. The necessity for the exponential correction is attributed to an extended transition from surface scaling to zero gradient in the mixed layer, where the departure from Monin-Obukhov similarity may be negligible at the surface but becomes substantial well below the conventional surface layer height of 0.1$z_i$., Comment: 31 pages, 10 figures

A new mixed scaling parameter $Z=z/\sqrt{Lh}$ is proposed for similarity in the stable atmospheric surface layer, where $z$ is the height, $L$ is the Obukhov length, and $h$ is the boundary layer depth. Compared to the parameter $\zeta = z/L$ from Monin-Obukhov similarity theory (MOST), the new parameter $Z$ leads to improved mean profile similarity for wind speed and air temperature in large-eddy simulations. It also yields the same linear similarity relation for CASES-99 field measurements, including in the strongly stable (but still turbulent) regime where large deviations from MOST are observed. Results further suggest that similarity for turbulent energy dissipation rate depends on both $Z$ and $\zeta$. The proposed mixed scaling of $Z$ and relevance of $h$ can be explained by physical arguments related to the limit of z-less stratification that is reached asymptotically above the surface layer. While the presented evidence and fitted similarity relations are promising, the results and arguments are limited to a small sample of idealized stationary stable boundary layers. Corroboration is needed from independent datasets and analyses, including for complex and transient conditions not tested here., Comment: Submitted to Journal of the Atmospheric Sciences for peer review. Version 2 corrects typos in the references and online abstract. Version 3 includes peer review changes

Online self-disclosure is perhaps one of the last decade's most studied communication processes, thanks to the introduction of Online Social Networks (OSNs) like Facebook. Self-disclosure research has contributed significantly to the design of preventative nudges seeking to support and guide users when revealing private information in OSNs. Still, assessing the effectiveness of these solutions is often challenging since changing or modifying the choice architecture of OSN platforms is practically unfeasible. In turn, the effectiveness of numerous nudging designs is supported primarily by self-reported data instead of actual behavioral information. This work presents ENAGRAM, an app for evaluating preventative nudges, and reports the first results of an empirical study conducted with it. Such a study aims to showcase how the app (and the data collected with it) can be leveraged to assess the effectiveness of a particular nudging approach. We used ENAGRAM as a vehicle to test a risk-based strategy for nudging the self-disclosure decisions of Instagram users. For this, we created two variations of the same nudge and tested it in a between-subjects experimental setting. Study participants (N=22) were recruited via Prolific and asked to use the app regularly for 7 days. An online survey was distributed at the end of the experiment to measure some privacy-related constructs. From the data collected with ENAGRAM, we observed lower (though non-significant) self-disclosure levels when applying risk-based interventions. The constructs measured with the survey were not significant either, except for participants' External Information Privacy Concerns. Our results suggest that (i) ENAGRAM is a suitable alternative for conducting longitudinal experiments in a privacy-friendly way, and (ii) it provides a flexible framework for the evaluation of a broad spectrum of nudging solutions., Comment: Accepted at the 2022 European Symposium on Usable Security (EuroUSEC 2022)

A persistent spatial organization of eddies is identified in the lowest portion of the stably-stratified planetary boundary layer. The analysis uses flow realizations from published large-eddy simulations (Sullivan et al., J Atmos Sci 73(4):1815-1840, 2016) ranging in stability from neutral to nearly z-less stratification. The coherent turbulent structure is well approximated as a series of uniform momentum zones (UMZs) and uniform temperature zones (UTZs) separated by thin layers of intense gradients that are significantly greater than the mean. This pattern yields stairstep-like instantaneous flow profiles whose shape is distinct from the mean profiles that emerge from long-term averaging. However, the scaling of the stairstep organization is closely related to the resulting mean profiles. The differences in velocity and temperature across the thin gradient layers remain proportional to the surface momentum and heat flux conditions regardless of stratification. The vertical thickness of UMZs and UTZs is proportional to height above the surface for neutral and weak stratification, but becomes thinner and less dependent on height as the stability increases. Deviations from the logarithmic mean profiles for velocity and temperature observed under neutral conditions are therefore predominately due to the reduction in zone size with increasing stratification, which is empirically captured by existing Monin-Obukhov similarity relations for momentum and heat. The zone properties are additionally used to explain trends in the turbulent Prandtl number, thus providing a connection between the eddy organization, mean profiles, and turbulent diffusivity in stably stratified conditions., Comment: 35 pages, 12 figures

Stack Overflow (SO) is a popular platform among developers seeking advice on various software-related topics, including privacy and security. As for many knowledge-sharing websites, the value of SO depends largely on users' engagement, namely their willingness to answer, comment or post technical questions. Still, many of these questions (including cybersecurity-related ones) remain unanswered, putting the site's relevance and reputation into question. Hence, it is important to understand users' participation in privacy and security discussions to promote engagement and foster the exchange of such expertise. Objective: Based on prior findings on online social networks, this work elaborates on the interplay between users' engagement and their privacy practices in SO. Particularly, it analyses developers' self-disclosure behaviour regarding profile visibility and their involvement in discussions related to privacy and security. Method: We followed a mixed-methods approach by (i) analysing SO data from 1239 cybersecurity-tagged questions along with 7048 user profiles, and (ii) conducting an anonymous online survey (N=64). Results: About 33% of the questions we retrieved had no answer, whereas more than 50% had no accepted answer. We observed that "proactive" users tend to disclose significantly less information in their profiles than "reactive" and "unengaged" ones. However, no correlations were found between these engagement categories and privacy-related constructs such as Perceived Control or General Privacy Concerns. Implications: These findings contribute to (i) a better understanding of developers' engagement towards privacy and security topics, and (ii) to shape strategies promoting the exchange of cybersecurity expertise in SO., Comment: Submitted for publication

The inertial subrange of turbulent scales is commonly reflected by a power law signature in ensemble statistics such as the energy spectrum and structure functions - both in theory and from observations. Despite promising findings on the topic of fractal geometries in turbulence, there is no accepted image for the physical flow features corresponding to this statistical signature in the inertial subrange. The present study uses boundary layer turbulence measurements to evaluate the self-similar geometric properties of velocity isosurfaces and investigate their influence on statistics for the velocity signal. The fractal dimension of streamwise velocity isosurfaces, indicating statistical self-similarity in the size of "wrinkles" along each isosurface, is shown to be constant only within the inertial subrange of scales. For the transition between the inertial subrange and production range, it is inferred that the largest wrinkles become increasingly confined by the overall size of large-scale coherent velocity regions such as uniform momentum zones. The self-similarity of isosurfaces yields power law trends in subsequent one-dimensional statistics. For instance, the theoretical 2/3 power law exponent for the structure function can be recovered by considering the collective behavior of numerous isosurface level sets. The results suggest that the physical presence of inertial subrange eddies is manifested in the self-similar wrinkles of isosurfaces., Comment: 30 pages, 11 figures

Stochastic simulations are used to create synthetic one-dimensional telegraph approximation (TA) signals based on turbulent zero crossings, where the interval between crossings is governed by a power law probability distribution with exponent $\alpha$. The power law exponent is determined for statistics of simulated TA signals, namely the box-counting fractal dimension $D_1$, energy spectrum exponent $\beta_{TA}$, and an intermittency exponent $\mu_{TA}$. For the binary TA signal with no variability in amplitude, the parameters are related linearly as $D_1 = 2 - \beta_{TA} = 1 - \mu_{TA}$. The relations are unchanged if the crossing interval distribution has a finite power law region (i.e. inertial subrange) representing a flow with finite Reynolds number. However, the finite distribution yields statistics that are not truly scale-invariant, and distorts the linear relation between the statistic exponents and $\alpha$. The behavior is due to finite-size effects apparent from the survival function, or the complementary cumulative distribution, which for finite Reynolds number is only approximately self-similar and has an effective exponent differing from $\alpha$. An expression presented for the effective exponent recovers the expected relations between $\alpha$ and the TA statistics. The findings demonstrate how a finite Reynolds number can affect indicators of self-similarity, fractality, and intermittency observed from single-point measurements., Comment: New version (including updated title) to be published in Physical Review Fluids. No changes were made to the results or key conclusions from the original version

Access-Control Lists (ACLs) (a.k.a. friend lists) are one of the most important privacy features of Online Social Networks (OSNs) as they allow users to restrict the audience of their publications. Nevertheless, creating and maintaining custom ACLs can introduce a high cognitive burden on average OSNs users since it normally requires assessing the trustworthiness of a large number of contacts. In principle, community detection algorithms can be leveraged to support the generation of ACLs by mapping a set of examples (i.e. contacts labelled as untrusted) to the emerging communities inside the user's ego-network. However, unlike users' access-control preferences, traditional community-detection algorithms do not take the homophily characteristics of such communities into account (i.e. attributes shared among members). Consequently, this strategy may lead to inaccurate ACL configurations and privacy breaches under certain homophily scenarios. This work investigates the use of community-detection algorithms for the automatic generation of ACLs in OSNs. Particularly, it analyses the performance of the aforementioned approach under different homophily conditions through a simulation model. Furthermore, since private information may reach the scope of untrusted recipients through the re-sharing affordances of OSNs, information diffusion processes are also modelled and taken explicitly into account. Altogether, the removal of gatekeeper nodes is further explored as a strategy to counteract unwanted data dissemination., Comment: This work has been submitted to the IEEE for possible publication

Privacy in Social Network Sites (SNSs) like Facebook or Instagram is closely related to people's self-disclosure decisions and their ability to foresee the consequences of sharing personal information with large and diverse audiences. Nonetheless, online privacy decisions are often based on spurious risk judgements that make people liable to reveal sensitive data to untrusted recipients and become victims of social engineering attacks. Artificial Intelligence (AI) in combination with persuasive mechanisms like nudging is a promising approach for promoting preventative privacy behaviour among the users of SNSs. Nevertheless, combining behavioural interventions with high levels of personalization can be a potential threat to people's agency and autonomy even when applied to the design of social engineering countermeasures. This paper elaborates on the ethical challenges that nudging mechanisms can introduce to the development of AI-based countermeasures, particularly to those addressing unsafe self-disclosure practices in SNSs. Overall, it endorses the elaboration of personalized risk awareness solutions as i) an ethical approach to counteract social engineering, and ii) as an effective means for promoting reflective privacy decisions., Comment: Accepted for publication at IC3K 2020

Social Network Sites (SNSs) like Facebook or Instagram are spaces where people expose their lives to wide and diverse audiences. This practice can lead to unwanted incidents such as reputation damage, job loss or harassment when pieces of private information reach unintended recipients. As a consequence, users often regret to have posted private information in these platforms and proceed to delete such content after having a negative experience. Risk awareness is a strategy that can be used to persuade users towards safer privacy decisions. However, many risk awareness technologies for SNSs assume that information about risks is retrieved and measured by an expert in the field. Consequently, risk estimation is an activity that is often passed over despite its importance. In this work we introduce an approach that employs deleted posts as risk information vehicles to measure the frequency and consequence level of self-disclosure patterns in SNSs. In this method, consequence is reported by the users through an ordinal scale and used later on to compute a risk criticality index. We thereupon show how this index can serve in the design of adaptive privacy nudges for SNSs.

The effect of turbulence on snow precipitation is not incorporated into present weather forecasting models. Here we show evidence that turbulence is in fact a key influence on both fall speed and spatial distribution of settling snow. We consider three snowfall events under vastly different levels of atmospheric turbulence. We characterize the size and morphology of the snow particles, and we simultaneously image their velocity, acceleration, and relative concentration over vertical planes about 30 m2 in area. We find that turbulence-driven settling enhancement explains otherwise contradictory trends between the particle size and velocity. The estimates of the Stokes number and the correlation between vertical velocity and local concentration indicate that the enhanced settling is rooted in the preferential sweeping mechanism. When the snow vertical velocity is large compared to the characteristic turbulence velocity, the crossing trajectories effect results in strong accelerations. When the conditions of preferential sweeping are met, the concentration field is highly non-uniform and clustering appears over a wide range of scales. These clusters, identified for the first time in a naturally occurring flow, display the signature features seen in canonical settings: power-law size distribution, fractal-like shape, vertical elongation, and large fall speed that increases with the cluster size. These findings demonstrate that the fundamental phenomenology of particle-laden turbulence can be leveraged towards a better predictive understanding of snow precipitation and ground snow accumulation. They also demonstrate how environmental flows can be used to investigate dispersed multiphase flows at Reynolds numbers not accessible in laboratory experiments or numerical simulations., Comment: 22 pages, 13 figures

Since the introduction of the logarithmic law of the wall more than 80 years ago, the equation for the mean velocity profile in turbulent boundary layers has been widely applied to model near-surface processes and parameterise surface drag. Yet the hypothetical turbulent eddies proposed in the original logarithmic law derivation and mixing length theory of Prandtl have never been conclusively linked to physical features in the flow. Here, we present evidence that suggests these eddies correspond to regions of coherent streamwise momentum known as uniform momentum zones (UMZs). The arrangement of UMZs results in a step-like shape for the instantaneous velocity profile, and the smooth mean profile results from the average UMZ properties, which are shown to scale with the friction velocity and wall-normal distance in the logarithmic region. These findings are confirmed across a wide range of Reynolds number and surface roughness conditions from the laboratory scale to the atmospheric surface layer., Comment: Version 2 includes a new title and minor edits for clarification based on peer review. No changes were made to the primary results and conclusions. Version 3 corrected two important typos in the text related to the results

A discovery that neutrinos are not the usual Dirac but Majorana fermions, i.e. identical to their antiparticles, would be a manifestation of new physics with profound implications for particle physics and cosmology. Majorana neutrinos would generate neutrinoless double-$\beta$ ($0\nu\beta\beta$) decay, a matter-creating process without the balancing emission of antimatter. So far, 0$\nu\beta\beta$ decay has eluded detection. The GERDA collaboration searches for the $0\nu\beta\beta$ decay of $^{76}$Ge by operating bare germanium detectors in an active liquid argon shield. With a total exposure of 82.4 kg$\cdot$yr, we observe no signal and derive a lower half-life limit of T$_{1/2}$ > 0.9$\cdot$10$^{26}$ yr (90% C.L.). Our T$_{1/2}$ sensitivity assuming no signal is 1.1$\cdot$10$^{26}$ yr. Combining the latter with those from other $0{\nu}\beta\beta$ decay searches yields a sensitivity to the effective Majorana neutrino mass of 0.07 - 0.16 eV, with corresponding sensitivities to the absolute mass scale in $\beta$ decay of 0.15 - 0.44 eV, and to the cosmological relevant sum of neutrino masses of 0.46 - 1.3 eV., Comment: Authors' main+supplementary text: 13+28 pages, 3+12 figures, 1+7 tables. Definite version to be published in Science

The GERmanium Detector Array (GERDA) is a low background experiment located at the Laboratori Nazionali del Gran Sasso in Italy, which searches for neutrinoless double beta decay of $^{76}$Ge into $^{76}$Se+2e$^-$. GERDA has been conceived in two phases. Phase II, which started in December 2015, features several novelties including 30 new Ge detectors. These were manufactured according to the Broad Energy Germanium (BEGe) detector design that has a better background discrimination capability and energy resolution compared to formerly widely-used types. Prior to their installation, the new BEGe detectors were mounted in vacuum cryostats and characterized in detail in the HADES underground laboratory in Belgium. This paper describes the properties and the overall performance of these detectors during operation in vacuum. The characterization campaign provided not only direct input for GERDA Phase II data collection and analyses, but also allowed to study detector phenomena, detector correlations as well as to test the strength of pulse shape simulation codes., Comment: 29 pages, 18 figures

The GERDA experiment searches for the lepton number violating neutrinoless double beta decay of $^{76}$Ge ($^{76}$Ge $\rightarrow$ $^{76}$Se + 2e$^-$) operating bare Ge diodes with an enriched $^{76}$Ge fraction in liquid argon. The exposure for BEGe-type detectors is increased threefold with respect to our previous data release. The BEGe detectors feature an excellent background suppression from the analysis of the time profile of the detector signals. In the analysis window a background level of $1.0_{-0.4}^{+0.6}\cdot10^{-3}$ cts/(keV$\cdot$kg$\cdot$yr) has been achieved; if normalized to the energy resolution this is the lowest ever achieved in any 0$\nu\beta\beta$ experiment. No signal is observed and a new 90 \% C.L. lower limit for the half-life of $8.0\cdot10^{25}$ yr is placed when combining with our previous data. The median expected sensitivity assuming no signal is $5.8\cdot10^{25}$ yr., Comment: 5 pages, 2 figures

The GERDA collaboration is performing a sensitive search for neutrinoless double beta decay of $^{76}$Ge at the INFN Laboratori Nazionali del Gran Sasso, Italy. The upgrade of the GERDA experiment from Phase I to Phase II has been concluded in December 2015. The first Phase II data release shows that the goal to suppress the background by one order of magnitude compared to Phase I has been achieved. GERDA is thus the first experiment that will remain background-free up to its design exposure (100 kg yr). It will reach thereby a half-life sensitivity of more than 10$^{26}$ yr within 3 years of data collection. This paper describes in detail the modifications and improvements of the experimental setup for Phase II and discusses the performance of individual detector components., Comment: 31 pages, 34 figures

The GERmanium Detector Array (GERDA) experiment located at the INFN Gran Sasso Laboratory (Italy), is looking for the neutrinoless double beta decay of Ge76, by using high-purity germanium detectors made from isotopically enriched material. The combination of the novel experimental design, the careful material selection for radio-purity and the active/passive shielding techniques result in a very low residual background at the Q-value of the decay, about 1e-3 counts/(keV kg yr). This makes GERDA the first experiment in the field to be background-free for the complete design exposure of 100 kg yr. A search for neutrinoless double beta decay was performed with a total exposure of 47.7 kg yr: 23.2 kg yr come from the second phase (Phase II) of the experiment, in which the background is reduced by about a factor of ten with respect to the previous phase. The analysis presented in this paper includes 12.4 kg yr of new Phase II data. No evidence for a possible signal is found: the lower limit for the half-life of Ge76 is 8.0e25 yr at 90% CL. The experimental median sensitivity is 5.8e25 yr. The experiment is currently taking data. As it is running in a background-free regime, its sensitivity grows linearly with exposure and it is expected to surpass 1e26 yr within 2018., Comment: 8 pages, to appear in the proceedings of TAUP2017

Background coming from the $^{42}$Ar decay chain is considered to be one of the most relevant for the GERDA experiment, which aims to search of the neutrinoless double beta decay of $^{76}$Ge. The sensitivity strongly relies on the absence of background around the Q-value of the decay. Background coming from $^{42}$K, a progeny of $^{42}$Ar, can contribute to that background via electrons from the continuous spectrum with an endpoint of 3.5 MeV. Research and development on the suppression methods targeting this source of background were performed at the low-background test facility LArGe. It was demonstrated that by reducing $^{42}$K ion collection on the surfaces of the broad energy germanium detectors in combination with pulse shape discrimination techniques and an argon scintillation veto, it is possible to suppress the $^{42}$K background by three orders of magnitude. This is sufficient for Phase II of the GERDA experiment.

The Standard Model of particle physics cannot explain the dominance of matter over anti-matter in our Universe. In many model extensions this is a very natural consequence of neutrinos being their own anti-particles (Majorana particles) which implies that a lepton number violating radioactive decay named neutrinoless double beta ($0\nu\beta\beta$) decay should exist. The detection of this extremely rare hypothetical process requires utmost suppression of any kind of backgrounds. The GERDA collaboration searches for $0\nu\beta\beta$ decay of $^{76}$Ge ($^{76}\rm{Ge} \rightarrow\,^{76}\rm{Se} + 2e^-$) by operating bare detectors made from germanium with enriched $^{76}$Ge fraction in liquid argon. Here, we report on first data of GERDA Phase II. A background level of $\approx10^{-3}$ cts/(keV$\cdot$kg$\cdot$yr) has been achieved which is the world-best if weighted by the narrow energy-signal region of germanium detectors. Combining Phase I and II data we find no signal and deduce a new lower limit for the half-life of $5.3\cdot10^{25}$ yr at 90 % C.L. Our sensitivity of $4.0\cdot10^{25}$ yr is competitive with the one of experiments with significantly larger isotope mass. GERDA is the first $0\nu\beta\beta$ experiment that will be background-free up to its design exposure. This progress relies on a novel active veto system, the superior germanium detector energy resolution and the improved background recognition of our new detectors. The unique discovery potential of an essentially background-free search for $0\nu\beta\beta$ decay motivates a larger germanium experiment with higher sensitivity., Comment: 14 pages, 9 figures, 1 table; ; data, figures and images available at http://www.mpi-hd.mpg/gerda/public