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Dam breach models are commonly used to predict outflow hydrographs of potentially failing dams and are key ingredients for evaluating flood risk. In this paper a new dam breach modeling framework is introduced that shall improve the reliability of hydrograph predictions of homogeneous earthen embankment dams. Striving for a small number of parameters, the simplified physics-based model describes the processes of failing embankment dams by breach enlargement, driven by progressive surface erosion. Therein the erosion rate of dam material is modeled by empirical sediment transport formulations. Embedding the model into a Bayesian multilevel framework allows for quantitative analysis of different categories of uncertainties. To this end, data available in literature of observed peak discharge and final breach width of historical dam failures was used to perform model inversion by applying Markov Chain Monte Carlo simulation. Prior knowledge is mainly based on non-informative distribution functions. The resulting posterior distribution shows that the main source of uncertainty is a correlated subset of parameters, consisting of the residual error term and the epistemic term quantifying the breach erosion rate. The prediction intervals of peak discharge and final breach width are congruent with values known from literature. To finally predict the outflow hydrograph for real case applications, an alternative residual model was formulated that assumes perfect data and a perfect model. The fully probabilistic fashion of hydrograph prediction has the potential to improve the adequate risk management of downstream flooding.

Using an optimally coupled nanometer-scale superconducting quantum interference device, we measure the magnetic flux originating from an individual ferromagnetic Ni nanotube attached to a Si cantilever. At the same time, we detect the nanotube's volume magnetization using torque magnetometry. We observe both the predicted reversible and irreversible reversal processes. A detailed comparison with micromagnetic simulations suggests that vortex-like states are formed in different segments of the individual nanotube. Such stray-field free states are interesting for memory applications and non-invasive sensing., Comment: 12 pages, 4 figures

Nanoscale magnets might form the building blocks of next generation memories. To explore their functionality, magnetic sensing at the nanoscale is key. We present a multifunctional combination of a scanning nanometer-sized superconducting quantum interference device (nanoSQUID) and a Ni nanotube attached to an ultrasoft cantilever as a magnetic tip. We map out and analyze the magnetic coupling between the Ni tube and the Nb nanoSQUID, demonstrate imaging of an Abrikosov vortex trapped in the SQUID structure - which is important in ruling out spurious magnetic signals - and reveal the high potential of the nanoSQUID as an ultrasensitive displacement detector. Our results open a new avenue for fundamental studies of nanoscale magnetism and superconductivity., Comment: 7 pages, 5 figures

We have investigated asymmetrically shunted Nb/Al-AlO$_x$/Nb direct current (dc) superconducting quantum interference devices (SQUIDs). While keeping the total resistance $R$ identical to a comparable symmetric SQUID with $R^{-1} = R_1^{-1} + R_2^{-1}$, we shunted only one of the two Josephson junctions with $R = R_{1,2}/2$. Simulations predict that the optimum energy resolution $\epsilon$ and thus also the noise performance of such an asymmetric SQUID can be 3--4 times better than that of its symmetric counterpart. Experiments at a temperature of 4.2\,K yielded $\epsilon \approx 32\,\hbar$ for an asymmetric SQUID with an inductance of $22\,\rm{pH}$. For a comparable symmetric device $\epsilon = 110\,\hbar$ was achieved, confirming our simulation results., Comment: 5 pages, 4 figures

Even after 25 years of research the pairing mechanism and - at least for electron doped compounds - also the order parameter symmetry of the high transition temperature (high-Tc) cuprate superconductors is still under debate. One of the reasons is the complex crystal structure of most of these materials. An exception are the infinite layer (IL) compounds consisting essentially of CuO2 planes. Unfortunately, these materials are difficult to grow and, thus, there are only few experimental investigations. Recently, we succeeded in depositing high quality films of the electron doped IL compound Sr1-xLaxCuO2 (SLCO), with x approximately 0.15, and on the fabrication of well-defined grain boundary Josephson junctions (GBJs) based on such SLCO films. Here we report on a phase sensitive study of the superconducting order parameter based on GBJ SQUIDs from a SLCO film grown on a tetracrystal substrate. Our results show that also the parent structure of the high-Tc cuprates has dx2-y2-wave symmetry, which thus seems to be inherent to cuprate superconductivity., Comment: Submitted to PRL, 5 pages, 3 figures, supplementary information included (4 pages, 4 figures)

We investigated, at temperature $4.2\,\mathrm{K}$, electric transport, flux noise and resulting spin sensitivity of miniaturized Nb direct current superconducting quantum interference devices (SQUIDs) based on submicron Josephson junctions with HfTi barriers. The SQUIDs are either of the magnetometer-type or gradiometric in layout. In the white noise regime, for the best magnetometer we obtain a flux noise $S_{\Phi}^{1/2}=250\,\mathrm{n}\Phi_0/\mathrm{Hz}^{1/2}$, corresponding to a spin sensitivity $S^{1/2}_\mu\,\ge\,29\,\mu_B/\mathrm{Hz}^{1/2}$. For the gradiometer we find $S_{\Phi}^{1/2}=300\,\mathrm{n}\Phi_0/\mathrm{Hz}^{1/2}$ and $S^{1/2}_\mu\,\ge\,44\,\mu_B/\mathrm{Hz}^{1/2}$. The devices can still be optimized with respect to flux noise and coupling between a magnetic particle and the SQUID, leaving room for further improvement towards single spin resolution., Comment: 4 pages, 3 figures

We propose to couple a trapped single electron to superconducting structures located at a variable distance from the electron. The electron is captured in a cryogenic Penning trap using electric fields and a static magnetic field in the Tesla range. Measurements on the electron will allow investigating the properties of the superconductor such as vortex structure, damping and decoherence. We propose to couple a superconducting microwave resonator to the electron in order to realize a circuit QED-like experiment, as well as to couple superconducting Josephson junctions or superconducting quantum interferometers (SQUIDs) to the electron. The electron may also be coupled to a vortex which is situated in a double well potential, realized by nearby pinning centers in the superconductor, acting as a quantum mechanical two level system that can be controlled by a transport current tilting the double well potential. When the vortex is trapped in the interferometer arms of a SQUID, this would allow its detection both by the SQUID and by the electron., Comment: 13 pages, 5 figures

YBa$_2$Cu$_3$O$_7$ 24$^\circ$ (30$^\circ$) bicrystal grain boundary junctions (GBJs), shunted with 60\,nm (20\,nm) thick Au, were fabricated by focused ion beam milling with widths $80\,{\rm nm} \le w \le 7.8\,\mu$m. At 4.2\,K we find critical current densities $j_c$ in the $10^5\,{\rm A/cm^2}$ range %\dkc{\#1} (without a clear dependence on $w$) and an increase in resistance times junction area $\rho$ with an approximate scaling $\rho\propto w^{1/2}$. For the narrowest GBJs $j_c\rho\approx 100\,\mu$V, which is promising for the realization of sensitive nanoSQUIDs for the detection of small spin systems. We demonstrate that our fabrication process allows the realization of sensitive nanoscale dc SQUIDs; for a SQUID with $w\approx 100$\,nm wide GBJs we find an rms magnetic flux noise spectral density of $S_\Phi^{1/2}\approx 4\,\mu\Phi_0/{\rm Hz}^{1/2}$ in the white noise limit. We also derive an expression for the spin sensitivity $S_\mu^{1/2}$, which depends on $S_\Phi^{1/2}$, on the location and orientation of the magnetic moment of a magnetic particle to be detected by the SQUID, and on the SQUID geometry. For the not optimized SQUIDs presented here, we estimate $S_\mu^{1/2}=390\,\mu_B/\sqrt{\rm{Hz}}$, which could be further improved by at least an order of magnitude.

We experimentally demonstrate the occurrence of negative absolute resistance (NAR) up to about $-1\Omega$ in response to an externally applied dc current for a shunted Nb-Al/AlO$_x$-Nb Josephson junction, exposed to a microwave current at frequencies in the GHz range. The realization (or not) of NAR depends crucially on the amplitude of the applied microwave current. Theoretically, the system is described by means of the resistively and capacitively shunted junction model in terms of a moderately damped, classical Brownian particle dynamics in a one-dimensional potential. We find excellent agreement of the experimental results with numerical simulations of the model., Comment: 4 pages, 3 figures, submitted to Physical Review

We completely revised the paper after the referee's comments. In the new version, we replaced two erroneous examples, studied a link with earlier work of Koh and Stilmann, and strengthened the main theorem., Comment: revised version, to appear in Comm. Math. Helv