### Article

## Development of the advanced mechanistic fuel performance and safety code using the multi-scale approach

The SFPR code designed for mechanistic modeling of single fuel rod behavior under various regimes ofLWR reactor operation (normal and off-normal, including severe accidents), is under development atIBRAE during the last two decades and currently, being extended to Fast Reactors, serves as a prototypefor a new mechanistic fuel performance code BERKUT. The SFPR meso-scale models include an extendedset of microscopic parameters, characterizing the crystal defect structure, thermo-physical and thermo-chemical properties of irradiated fuel. Increasing computational capabilities and rapid development ofeffective interatomic potentials allow micro-scale representations of the materials and physics to inform– via meso-scale code – the macro-level simulation. The first examples of atomistic calculations (bymolecular dynamics and Monte-Carlo methods) of the key microscopic parameters for input in SFPR andBERKUT, validation of the modified code and application of the 3D finite element method for improvementand verification of the 1D thermo-mechanical model, are presented.

A multiscale concept for irradiated materials simulation is formulated based on coupling molecular dynamics simulations (MD) where the potential was obtained from ab initio data of energies of the basic defect structures, with kinetic mesoscale models. The evolution of a system containing self-interstitial atoms (SIAs) and vacancies in crystalline molybdenum is investigated by means of MD. The kinetics of formation of di-SIA clusters and SIA–vacancy recombination is analyzed via approaches used in the kinetic theory of radiation ageing. The effects of 1D diffusion of SIAs, temperature, and defect concentrations on the reaction rates are also studied. This approach can validate both the kinetic mechanisms and the appropriate kinetic coefficients, offering the potential to significantly reduce the uncertainty of the kinetic methodology and providing a powerful predictive tool for simulating irradiation behavior of nuclear materials.

The scientific program of the conference Ion-Surface Interactions included the main aspects of this scientific discipline: ion scattering and penetration, sputtering and secondary ion emission, electron excitation, ion-induced electron, photon and X-ray emission, ion-assisted processes in thin films and nanostructures, radiation damage accumulation and plasma-surface interactions.

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.

Event logs collected by modern information and technical systems usually contain enough data for automated process models discovery. A variety of algorithms was developed for process models discovery, conformance checking, log to model alignment, comparison of process models, etc., nevertheless a quick analysis of ad-hoc selected parts of a journal still have not get a full-fledged implementation. This paper describes an ROLAP-based method of multidimensional event logs storage for process mining. The result of the analysis of the journal is visualized as directed graph representing the union of all possible event sequences, ranked by their occurrence probability. Our implementation allows the analyst to discover process models for sublogs defined by ad-hoc selection of criteria and value of occurrence probability

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.

Let G be a semisimple algebraic group whose decomposition into the product of simple components does not contain simple groups of type A, and P⊆G be a parabolic subgroup. Extending the results of Popov [7], we enumerate all triples (G, P, n) such that (a) there exists an open G-orbit on the multiple flag variety G/P × G/P × . . . × G/P (n factors), (b) the number of G-orbits on the multiple flag variety is finite.

I give the explicit formula for the (set-theoretical) system of Resultants of m+1 homogeneous polynomials in n+1 variables