The direct closure of the quantum metrological triangle consists in achieving Ohm's law with the three effects used and investigated in quantum electrical metrology: the Josephson effect (JE), the quantum Hall effect (QHE) and the single-electron tunnelling effect (SET). The aim is to check the consistency of the phenomenological constants K J , R K and Q X associated with these effects and theoretically expressed with the fundamental constants e and h (elementary charge and Planck constant, respectively). Such an experiment is a contribution to a future redefinition of the International System of units (SI). In this paper, the experimental setup developed at LNE is described and the main obtained results are given. From a set of four measurements, agreement at a level of 1.3 parts in 10 5 was found between the quantum charge involved in the SET, i.e. Q X , and the CODATA value of the elementary charge. The best measurement has shown a relative type-A uncertainty of 1.9 parts in 10 6 , while the amplitude of the current generated by a metallic electron pump was as low as 3.6 pA.

The stability of an electron pump composed of three junctions and on-chip chromium resistors at the ends is investigated as a function of applied frequencies on the gate electrodes. For the first time current steps have been obtained with frequencies f SET as high as 100 MHz. Moreover in the complete studied frequency range we show that the nature (white) and the level of the noise are independent of pumping speed within the noise floor. By generating a single-electron current close to 16.02 pA and measuring over 7 h, a relative type A uncertainty has been found of 3.9 parts in 10 6 . Although the experimental set-up described in this paper does not allow one to measure accurately an absolute value of the current, an alternative set-up including an external current source is proposed for investigating the eventual deviation of the current from the quantization level, e • f SET . As a matter of fact this set-up proves to be similar to the quantum metrological triangle experiment (QMT). We have demonstrated that the electron R-pump is a plausible candidate for closing the QMT experiment with a type A uncertainty level of 10 −6 .

The combination of a Watt balance, a calculable capacitor and a single-electron tunnelling device forms a triangle that yields a value for the single-electron charge quantum QS in terms of the SI coulomb. Importantly, this result is independent of the Josephson and quantum Hall effects, and thus avoids the possible confounding corrections from these two effects that arise in the traditional quantum metrology triangle. This new triangle can be used to test for corrections to the expected relation QS = e, where e is the elementary charge. Combining existing results for Watt balances, calculable capacitors and an electron counting capacitance standard yields (QS/e) − 1 = (−0.09 ± 0.92) × 10−6.

Summary Geophysical imaging using the inversion procedure is a powerful tool for the exploration of the Earth's subsurface. However, the interpretation of inverted images can sometimes be difficult, due to the inherent limitations of existing inversion algorithms, which produce smoothed sections. In order to improve and automate the processing and interpretation of inverted geophysical models, we propose an approach inspired from data mining. We selected an algorithm known as DBSCAN (Density-Based Spatial Clustering of Applications with Noise) to perform clustering of inverted geophysical sections. The methodology relies on the automatic sorting and clustering of data. DBSCAN detects clusters in the inverted electrical resistivity values, with no prior knowledge of the number of clusters. This algorithm has the advantage of being defined by only two parameters: the neighbourhood of a point in the data space, and the minimum number of data points in this neighbourhood. We propose an objective procedure for the determination of these two parameters. The proof of concept described here is applied to simulated ERT (Electrical Resistivity Tomography) sections, for the following three cases: two layers with a step, two layers with a rebound, and two layers with an anomaly embedded in the upper layer. To validate this approach, sensitivity studies were carried out on both of the above parameters, as well as to assess the influence of noise on the algorithm's performance. Finally, this methodology was tested on real field data. DBSCAN detects clusters in the inverted electrical resistivity models, and the former are then associated with various types of earth materials, thus allowing the structure of the prospected area to be determined. The proposed data-mining algorithm is shown to be effective, and to improve the interpretation of the inverted ERT sections. This new approach has considerable potential, as it can be applied to any geophysical data represented in the form of sections or maps.

The flow of the pore water in porous media generates an electrical current known as the streaming current. This current is due to the drag of the excess of charge contained in the electrical diffuse layer coating the surface of the grains. This current is associated with an electric field called the streaming potential field. The fluctuations of this field can be remotely measured using a set of non-polarizable electrodes located at the ground surface or in wells and a sensitive voltmeter. The self-potential method (SP) aims at passively measuring the streaming potential anomalies associated with ground water flow. We present a stochastic numerical framework for inverting self-potential data in order to localize seepages in dams and characterize their permeability and Darcy velocity. Our approach is based on the use of Markov chains Monte Carlo (McMC) method for solving the inverse problem. We performed first a validation of the method on a synthetic case study and then on large-scale field surveys on three different dams. Our approach is successful in localizing seepages and determining their permeability. A sensitivity study is performed on each of these three dams to better define the hydraulic and electrical parameters influencing the self-potential signal and the uncertainties associated with the estimation of those parameters. Our results show that the self-potential method can provide quantitative hydrogeological information for the characterization of seepages in dams and dikes.