Analytic model for a frictional shallow-water undular bore

We use the integrable Kaup-Boussinesq shallow water system, modified by a small viscous term, to model the formation of an undular bore with a steady profile. The description is made in terms of the corresponding integrable Whitham system, also appropriately modified by friction. This is derived in Riemann variables using a modified finite-gap integration technique for the AKNS scheme. The Whitham system is then reduced to a simple first-order differential equation which is integrated numerically to obtain an asymptotic profile of the undular bore, with the local oscillatory structure described by the periodic solution of the unperturbed Kaup-Boussinesq system. This solution of the Whitham equations is shown to be consistent with certain jump conditions following directly from conservation laws for the original system. A comparison is made with the recently studied dissipationless case for the same system, where the undular bore is unsteady.Comment: 24 page

Formation and study of the RRAM memory elements by local anodic oxidation method

This work was supported by RFBR according to the research project № 18-37-00299 and by Grant of the President of the Russian Federation No. MK-2721.2018.8

Modeling of titanium oxide nanostructures formation process by local anodic oxidation

This work was supported by Grant of the President of the Russian Federation No. MK-2721.2018.8. and by RFBR according to the research project № 18-37-00299

The investigation of regularities of the memristor effect of oxide nanosized titanium structures from the parameters of local anodized oxidation

This work was supported by Grant of the President of the Russian Federation No. MK-2721.2018.8. and by RFBR according to the research project № 18-37-00299

Formation of memristor structures based on ZnO thin films by scratching probe nanolithography

This work was supported by Grant of the President of the Russian Federation No. MK-2721.2018.8. and by RFBR according to the research project № 18-37-0029

Whitham method for Benjamin-Ono-Burgers equation and dispersive shocks in internal waves in deep fluid

The Whitham modulation equations for the parameters of a periodic solution are derived using the generalized Lagrangian approach for the case of damped Benjamin-Ono equation. The structure of the dispersive shock in internal wave in deep water is considered by this method.Comment: 8 pages, 4 figure

Whitham systems and deformations

We consider the deformations of Whitham systems including the "dispersion terms" and having the form of Dubrovin-Zhang deformations of Frobenius manifolds. The procedure is connected with B.A. Dubrovin problem of deformations of Frobenius manifolds corresponding to the Whitham systems of integrable hierarchies. Under some non-degeneracy requirements we suggest a general scheme of the deformation of the hyperbolic Whitham systems using the initial non-linear system. The general form of the deformed Whitham system coincides with the form of the "low-dispersion" asymptotic expansions used by B.A. Dubrovin and Y. Zhang in the theory of deformations of Frobenius manifolds.Comment: 27 pages, Late

Application of Probe Nanotechnologies for Memristor Structures Formation and Characterization

This chapter presents the results of experimental studies of the formation and investigation of the memristors by probe nanotechnologies. This chapter also perspectives and possibilities of application of local anodic oxidation and scratching probe nanolithography for the manufacture of memristors based on titanium oxide structures, nanocrystalline ZnO thin film, and vertically aligned carbon nanotubes. Memristive properties of vertically aligned carbon nanotubes, titanium oxide, and ZnO nanostructures were investigated by scanning probe microscopy methods. It is shown that nanocrystalline ZnO films manifest a stable memristor effect slightly dependent on its morphology. Titanium oxide nanoscale structures of different thicknesses obtained by local anodic oxidation demonstrate a memristive effect without the need to perform any additional electroforming operations. This experimentally confirmed the memristive switching of a two-electrode structure based on a vertically aligned carbon nanotube. These results can be used in the development of designs and technological processes of resistive random access memory (ReRAM) units based on the memristor devices

Application of random search algorithms at optimization of electric energy quality in networks of stationary railway enterprises

The possibility of constructing the optimal control system of electric energy quality based on the established deviation and asymmetry of voltage at stationary railway enterprises applying the principle of correcting device decentralized arrangement has been shown

Influence of the focused ion beam parameters on the etching of planar nanosized multigraphene/SiC field emitters

The equipment of the Collective Usage Center “Nanotechnologies” and the Research and Educational Center "Nanotechnologies" of Southern Federal University was used for this study. This work was funded by Internal grant of Southern Federal University No. VnGr-07/2017-26