We present real-time detection measurements of electron tunneling in a graphene quantum dot. By counting single electron charging events on the dot, the tunneling process in a graphene constriction and the role of localized states are studied in detail. In the regime of low charge detector bias we see only a single time-dependent process in the tunneling rate which can be modeled using a Fermi-broadened energy distribution of the carriers in the lead. We find a non-monotonic gate dependence of the tunneling coupling attributed to the formation of localized states in the constriction. Increasing the detector bias above 2 mV results in an increase of the dot-lead transition rate related to back-action of the charge detector current on the dot.Comment: 8 pages, 6 figure

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Snow is a heterogeneous material with strain-and/or load-rate-dependent strength. In particular, a transition from ductile-to-brittle failure behavior with increasing load rate is observed. The rate-dependent behavior can partly be explained with the existence of a unique healing mechanism in snow that stems from its high homologous temperature (temperature close to melting point). As soon as broken elements in the ice matrix get in contact, they start sintering and the structure may regain strength. Moreover, the ice matrix is subjected to viscous deformation, inducing a relaxation of local load concentrations and, therefore, further counteracting the damage process. Ideal tools for studying the failure process of heterogeneous materials are the fiber-bundle models (FBMs), which allow investigating the effects of basic microstructural characteristics on the general macroscopic failure behavior. We present an FBM with two concurrent time-dependent healing mechanisms: sintering of broken fibers and relaxation of load inhomogeneities. Sintering compensates damage by creating additional intact, load-supporting fibers which lead to an increase of the bundle strength. However, the character of the failure is not changed by sintering alone. With combined sintering and load relaxation, load is distributed from old stronger fibers to new fibers that carry fewer load. So as we additionally incorporated load redistribution to the FBM, the failure occurred suddenly without decrease of the order parameter-describing the amount of damage in the bundle-and without divergence of the fiber failure rate. Moreover, the b value, i.e., the power-law exponent of frequency-magnitude statistics of fibers breaking in load redistribution steps, at failure converged to b ≈ 2, a value higher than that of a classical FBM without healing (b = 3 2 ). These results indicate that healing, as the combined effect of sintering and load relaxation, changes the type of the phase transition at failure. This change of the phase transition is important for quantifying or predicting the failure (e.g., by monitoring acoustic emissions) of snow or other materials for which healing plays an important role.

Snow slab avalanches are caused by cracks forming and propagating in a weak snow layer below a cohesive slab. The gradual damage process leading to the formation of the initial failure within the weak layer (WL) is still not entirely understood. To this end, we designed a novel test apparatus that allows performing loading experiments with large snow samples (0.25 m2) including a WL at different loading rates and simultaneously monitoring the acoustic emissions (AE) response. By analyzing the AE generated by micro-cracking, we studied the evolution of the damage process preceding snow failure. At fast loading rates, the exponent of the AE energy distribution (b-value) gradually changed, and both the energy rate and the inverse waiting time increased exponentially with increasing load. These changes in AE signature indicate a transition from small to large events and an acceleration of the damage processes leading to brittle failure. For the experiments at slow loading rate, these changes in the AE signature were not or only partially present, even if the sample failed, indicating a different evolution of the damage process. The observed characteristics in AE response provide new insights on how to model snow failure as a critical phenomenon.

Abstract. Dry-snow slab avalanches start with the formation of a local failure in a highly porous weak layer underlying a cohesive snow slab. If followed by rapid crack propagation within the weak layer and finally a tensile fracture through the slab, a slab avalanche releases. While the basic concepts of avalanche release are relatively well understood, performing fracture experiments in the laboratory or in the field can be difficult due to the fragile nature of weak snow layers. Numerical simulations are a valuable tool for the study of micromechanical processes that lead to failure in snow. We used a three-dimensional discrete element method (3-D DEM) to simulate and analyze failure processes in snow. Cohesive and cohesionless ballistic deposition allowed us to reproduce porous weak layers and dense cohesive snow slabs, respectively. To analyze the micromechanical behavior at the scale of the snowpack (∼1 m), the particle size was chosen as a compromise between low computational costs and detailed representation of important micromechanical processes. The 3-D-DEM snow model allowed reproduction of the macroscopic behavior observed during compression and mixed-mode loading of dry-snow slab and the weak snow layer. To be able to reproduce the range of snow behavior (elastic modulus, strength), relations between DEM particle and contact parameters and macroscopic behavior were established. Numerical load-controlled failure experiments were performed on small samples and compared to results from load-controlled laboratory tests. Overall, our results show that the discrete element method allows us to realistically simulate snow failure processes. Furthermore, the presented snow model seems appropriate for comprehensively studying how the mechanical properties of the slab and weak layer influence crack propagation preceding avalanche release.