Absolute differential cross sections for electron-impact excitation of CO near threshold: II. The Rydberg states of CO

Absolute differential cross sections for electron-impact excitation of Rydberg states of CO have been measured from threshold to 3.7 eV above threshold and for scattering angles between 20° and 140°. Measured excitation functions for the b 3Σ+, B 1Σ+ and E 1π states are compared with cross sections calculated by the Schwinger multichannel method. The behaviour of the excitation functions for these states and for the j 3Σ+ and C 1Σ+ states is analysed in terms of negative-ion states. One of these resonances has not been previously reported

XPS Investigations of Ruthenium Deposited onto Representative Inner Surfaces of Nuclear Reactor Containment Buildings

International audienceIn the case of a hypothetical severe accident in a nuclear power plant, interactions of gaseous RuO4 with reactor containment building surfaces (stainless steel and epoxy paint) could possibly lead to a black Ru-containing deposit on these surfaces. Some scenarios include the possibility of formation of highly radiotoxic RuO4(g) by the interactions of these deposits with the oxidising medium induced by air radiolysis, in the reactor containment building, and consequently dispersion of this species. Therefore, the accurate determination of the chemical nature of ruthenium in the deposits is of the high importance for safety studies. An experiment was designed to model the interactions of RuO4(g) with samples of stainless steel and of steel covered with epoxy paint. Then, these deposits have been carefully characterised by scanning electron microscopy (SEM/EDS), electron probe microanalysis (EPMA) and X-ray photoelectron spectroscopy (XPS). The analysis by XPS of Ru deposits formed by interaction of RuO4(g), revealed that the ruthenium is likely to be in the IV oxidation state, as the shapes of the Ru3d core levels are very similar with those observed on the RuO2,xH2O reference powder sample. The analysis of O1s peaks indicates a large component attributed to the hydroxyl functional groups. From these results, it was concluded that Ru was present on the surface of the deposits as an oxyhydroxide of Ru(IV). It has also to be pointed out that the presence of “pure” RuO2, or of a thin layer of RuO3 or Ru2O5, coming from the decomposition of RuO4 on the surface of samples of stainless steel and epoxy paint, could be ruled out. These findings will be used for further investigations of the possible revolatilisation phenomena induced by ozone

Phenomenological Models of Socio-Economic Network Dynamics

We study a general set of models of social network evolution and dynamics. The models consist of both a dynamics on the network and evolution of the network. Links are formed preferentially between 'similar' nodes, where the similarity is defined by the particular process taking place on the network. The interplay between the two processes produces phase transitions and hysteresis, as seen using numerical simulations for three specific processes. We obtain analytic results using mean field approximations, and for a particular case we derive an exact solution for the network. In common with real-world social networks, we find coexistence of high and low connectivity phases and history dependence.Comment: 11 pages, 8 figure

Combined investigation of water sorption on TiO2TiO_2 rutile (1 1 0) single crystal face: XPS vs. periodic DFT

XPS and periodic DFT calculations have been used to investigate water sorption on the TiO2 rutile (1 1 0) face. Two sets of XPS spectra were collected on the TiO2 (1 1 0) single crystal clean and previously exposed to water: the first set with photoelectrons collected in a direction parallel to the normal to the surface; and the second set with the sample tilted by 70°, respectively. This tilting procedure promotes the signals from surface species and reveals that the first hydration layer is strongly coordinated to the surface and also that, despite the fact that the spectra were recorded under ultra-high vacuum, water molecules subsist in upper hydration layers. In addition, periodic DFT calculations were performed to investigate the water adsorption process to determine if molecular and/or dissociative adsorption takes place. The first step of the theoretical part was the optimisation of a dry surface model and then the investigation of water adsorption. The calculated molecular water adsorption energies are consistent with previously published experimental data and it appears that even though it is slightly less stable, the dissociative water sorption can also take place. This assumption was considered, in a second step, on a larger surface model where molecular and dissociated water molecules were adsorbed together with different ratio. It was found that, due to hydrogen bonding stabilisation, molecular and dissociated water molecules can coexist on the surface if the ratio of dissociated water molecules is less than ≈33%. These results are consistent with previous experimental works giving a 10–25% range

BKT-like transition in the Potts model on an inhomogeneous annealed network

We solve the ferromagnetic q-state Potts model on an inhomogeneous annealed network which mimics a random recursive graph. We find that this system has the inverted Berezinskii--Kosterlitz--Thouless (BKT) phase transition for any $q \geq 1$, including the values $q \geq 3$, where the Potts model normally shows a first order phase transition. We obtain the temperature dependences of the order parameter, specific heat, and susceptibility demonstrating features typical for the BKT transition. We show that in the entire normal phase, both the distribution of a linear response to an applied local field and the distribution of spin-spin correlations have a critical, i.e. power-law, form.Comment: 7 pages, 3 figure

Structure-preserving deep learning

Over the past few years, deep learning has risen to the foreground as a topic of massive interest, mainly as a result of successes obtained in solving large-scale image processing tasks. There are multiple challenging mathematical problems involved in applying deep learning: most deep learning methods require the solution of hard optimisation problems, and a good understanding of the tradeoff between computational effort, amount of data and model complexity is required to successfully design a deep learning approach for a given problem. A large amount of progress made in deep learning has been based on heuristic explorations, but there is a growing effort to mathematically understand the structure in existing deep learning methods and to systematically design new deep learning methods to preserve certain types of structure in deep learning. In this article, we review a number of these directions: some deep neural networks can be understood as discretisations of dynamical systems, neural networks can be designed to have desirable properties such as invertibility or group equivariance, and new algorithmic frameworks based on conformal Hamiltonian systems and Riemannian manifolds to solve the optimisation problems have been proposed. We conclude our review of each of these topics by discussing some open problems that we consider to be interesting directions for future research

Correlations in interacting systems with a network topology

We study pair correlations in cooperative systems placed on complex networks. We show that usually in these systems, the correlations between two interacting objects (e.g., spins), separated by a distance $\ell$, decay, on average, faster than $1/(\ell z_\ell)$. Here $z_\ell$ is the mean number of the $\ell$-th nearest neighbors of a vertex in a network. This behavior, in particular, leads to a dramatic weakening of correlations between second and more distant neighbors on networks with fat-tailed degree distributions, which have a divergent number $z_2$ in the infinite network limit. In this case, only the pair correlations between the nearest neighbors are observable. We obtain the pair correlation function of the Ising model on a complex network and also derive our results in the framework of a phenomenological approach.Comment: 5 page