Mathematical model of electricity loading process in an organization

Обґрунтовано науково-технічні задачі математичного моделювання даних вимірювань у задачах статистичного моніторингу процесу електронавантаження організації. Запропоновано нову математичну модель процесу електронавантаження у вигляді кусково-однорідного періодичного процесу білого шуму і визначено її основні характеристики в задачах поточного і довготермінового моніторингу електронавантаження.Study of scientific and technical problems of mathematical modeling of measurement data in the problems of statistical monitoring of an electricity loading process in an organization is substantiated in the article. A new mathematical model of an electricity loading process as a piece-homogeneous periodic process of white noise is proposed and its principal characteristics in the problems of current and long-term monitoring of electricity loading are defined

Detection and imaging in strongly backscattering randomly layered media

Abstract. Echoes from small reflectors buried in heavy clutter are weak and difficult to distinguish from the medium backscatter. Detection and imaging with sensor arrays in such media requires filtering out the unwanted backscatter and enhancing the echoes from the reflectors that we wish to locate. We consider a filtering and detection approach based on the singular value decomposition of the local cosine transform of the array response matrix. The algorithm is general and can be used for detection and imaging in heavy clutter, but its analysis depends on the model of the cluttered medium. This paper is concerned with the analysis of the algorithm in finely layered random media. We obtain a detailed characterization of the singular values of the transformed array response matrix and justify the systematic approach of the filtering algorithm for detecting and refining the time windows that contain the echoes that are useful in imaging

Isoperiodic deformations of the acoustic operator and periodic solutions of the Harry Dym equation

We consider the problem of describing the possible spectra of an acoustic operator with a periodic finite-gap density. We construct flows on the moduli space of algebraic Riemann surfaces that preserve the periods of the corresponding operator. By a suitable extension of the phase space, these equations can be written with quadratic irrationalities.Comment: 15 page

Large Deviations of the Maximum Eigenvalue for Wishart and Gaussian Random Matrices

We present a simple Coulomb gas method to calculate analytically the probability of rare events where the maximum eigenvalue of a random matrix is much larger than its typical value. The large deviation function that characterizes this probability is computed explicitly for Wishart and Gaussian ensembles. The method is quite general and applies to other related problems, e.g. the joint large deviation function for large fluctuations of top eigenvalues. Our results are relevant to widely employed data compression techniques, namely the principal components analysis. Analytical predictions are verified by extensive numerical simulations.Comment: 4 pages, 3 .eps figures include

Modelling of the effect of ELMs on fuel retention at the bulk W divertor of JET

Effect of ELMs on fuel retention at the bulk W target of JET ITER-Like Wall was studied with multi-scale calculations. Plasma input parameters were taken from ELMy H-mode plasma experiment. The energetic intra-ELM fuel particles get implanted and create near-surface defects up to depths of few tens of nm, which act as the main fuel trapping sites during ELMs. Clustering of implantation-induced vacancies were found to take place. The incoming flux of inter-ELM plasma particles increases the different filling levels of trapped fuel in defects. The temperature increase of the W target during the pulse increases the fuel detrapping rate. The inter-ELM fuel particle flux refills the partially emptied trapping sites and fills new sites. This leads to a competing effect on the retention and release rates of the implanted particles. At high temperatures the main retention appeared in larger vacancy clusters due to increased clustering rate

On the mechanisms governing gas penetration into a tokamak plasma during a massive gas injection

A new 1D radial fluid code, IMAGINE, is used to simulate the penetration of gas into a tokamak plasma during a massive gas injection (MGI). The main result is that the gas is in general strongly braked as it reaches the plasma, due to mechanisms related to charge exchange and (to a smaller extent) recombination. As a result, only a fraction of the gas penetrates into the plasma. Also, a shock wave is created in the gas which propagates away from the plasma, braking and compressing the incoming gas. Simulation results are quantitatively consistent, at least in terms of orders of magnitude, with experimental data for a D 2 MGI into a JET Ohmic plasma. Simulations of MGI into the background plasma surrounding a runaway electron beam show that if the background electron density is too high, the gas may not penetrate, suggesting a possible explanation for the recent results of Reux et al in JET (2015 Nucl. Fusion 55 093013)

Tritium distributions on W-coated divertor tiles used in the third JET ITER-like wall campaign

Tritium (T) distributions on tungsten (W)-coated plasma-facing tiles used in the third ITER-like wall campaign (2015–2016) of the Joint European Torus (JET) were examined by means of an imaging plate technique and β-ray induced x-ray spectrometry, and they were compared with the distributions after the second (2013–2014) campaign. Strong enrichment of T in beryllium (Be) deposition layers was observed after the second campaign. In contrast, T distributions after the third campaign was more uniform though Be deposition layers were visually recognized. The one of the possible explanations is enhanced desorption of T from Be deposition layers due to higher tile temperatures caused by higher energy input in the third campaign

Impact of fast ions on density peaking in JET: fluid and gyrokinetic modeling

The effect of fast ions on turbulent particle transport, driven by ion temperature gradient (ITG)/ trapped electron mode turbulence, is studied. Two neutral beam injection (NBI) heated JET discharges in different regimes are analyzed at the radial position ρ$_{t}$=0.6, one of them an L-mode and the other one an H-mode discharge. Results obtained from the computationally efficient fluid model EDWM and the gyro-fluid model TGLF are compared to linear and nonlinear gyrokinetic GENE simulations as well as the experimentally obtained density peaking. In these models, the fast ions are treated as a dynamic species with a Maxwellian background distribution. The dependence of the zero particle flux density gradient (peaking factor) on fast ion density, temperature and corresponding gradients, is investigated. The simulations show that the inclusion of a fast ion species has a stabilizing influence on the ITG mode and reduces the peaking of the main ion and electron density profiles in the absence of sources. The models mostly reproduce the experimentally obtained density peaking for the L-mode discharge whereas the H-mode density peaking is significantly underpredicted, indicating the importance of the NBI particle source for the H-mode density profile

The effect of beryllium oxide on retention in JET ITER-like wall tiles

Preliminary results investigating the microstructure, bonding and effect of beryllium oxide formation on retention in the JET ITER-like wall beryllium tiles, are presented. The tiles have been investigated by several techniques: Scanning Electron Microscopy (SEM) equipped with Energy Dispersive X-ray (EDX), Transmission Electron microscopy (TEM) equipped with EDX and Electron Energy Loss Spectroscopy (EELS), Raman Spectroscopy and Thermal Desorption Spectroscopy (TDS). This paper focuses on results from melted materials of the dump plate tiles in JET. From our results and the literature, it is concluded, beryllium can form micron deep oxide islands contrary to the nanometric oxides predicted under vacuum conditions. The deepest oxides analyzed were up to 2-micron thicknesses. The beryllium Deuteroxide (BeOxDy) bond was found with Raman Spectroscopy. Application of EELS confirmed the oxide presence and stoichiometry. Literature suggests these oxides form at temperatures greater than 700 °C where self-diffusion of beryllium ions through the surface oxide layer can occur. Further oxidation is made possible between oxygen plasma impurities and the beryllium ions now present at the wall surface. Under Ultra High Vacuum (UHV) nanometric Beryllium oxide layers are formed and passivate at room temperature. After continual cyclic heating (to the point of melt formation) in the presence of oxygen impurities from the plasma, oxide growth to the levels seen experimentally (approximately two microns) is proposed. This retention mechanism is not considered to contribute dramatically to overall retention in JET, due to low levels of melt formation. However, this mechanism, thought the result of operation environment and melt formation, could be of wider concern to ITER, dependent on wall temperatures