N-symmetric interaction of N hetons. Part I. Analysis of the case N = 2

Funding: This work was carried out as part of a joint project funded by the Russian Foundation for Basic Research (grant 20-55-10001) and UK Royal Society (grant IEC\R2\192170). MAS was also supported by the program 0147-2019-0001 (State Registration No.AAAA-A18-118022090056-0) and by the Ministry of Science and Education of the Russian Federation (Project No. N14.W03.31.0006), KVK was supp orted by RFBR project No.20-05-00083.We examine the motion of N symmetric hetons (oppositely signed vertical dipoles) in a two-layer quasi-geostrophic model. We consider the special case of N-fold symmetry in which the original system of 4N ordinary differential equations reduces to just two equations for the so-called “equivalent” heton. We perform a qualitative analysis to classify the possible types of vortex motions for the case N = 2. We identify the regions of the parameter space corresponding to unbounded motion and to different types of bounded, or localized, motions. We focus on the properties of localized, in particular periodic, motion. We identify classes of absolute and relative “choreographies” first introduced by Simó [“New families of solutions to the N-body problems,” in Proceedings of the European 3rd Congress of Mathematics, Progress in Mathematics Vol. 201, edited by C. Casacuberta, R. M. Miró-Roig, J. Verdera, and S. Xambó-Descamps (Birkhäuser, Basel, Barcelona, 2000), pp. 101–115]. We also study the forms of vortex trajectories occurring for unbounded motion, which are of practical interest due to the associated transport of heat and mass over large distancesPostprintPeer reviewe

Vortex merger in surface quasi-geostrophy

The merger of two identical surface temperature vortices is studied in the surface quasi- geostrophic model. The motivation for this study is the observation of the merger of sub- mesoscale vortices in the ocean. Firstly, the interaction between two point vortices, in the absence or in the presence of an external deformation field, is investigated. The rotation rate of the vortices, their stationary positions and the stability of these positions are determined. Then, a numerical model provides the steady states of two finite-area, constant-temperature, vortices. Such states are less deformed than their counterparts in two-dimensional incom- pressible flows. Finally, numerical simulations of the nonlinear surface quasi-geostrophic equations are used to investigate the finite-time evolution of initially identical and sym- metric, constant temperature vortices. The critical merger distance is obtained and the deformation of the vortices before or after merger is determined. The addition of external deformation is shown to favor or to oppose merger depending on the orientation of the vor- tex pair with respect to the strain axes. An explanation for this observation is proposed. Conclusions are drawn towards an application of this study to oceanic vortices.PostprintPeer reviewe

Chaos and nonlinear resonances in the problems of geophysical fluid

In the framework of background currents, we examine a dynamically consistent model of a periodic flow over an isolated submerged obstacle of Gaussian shape. Chaotic advection of passive scalars in the ocean is studied from the viewpoint of the dynamic system theory. Much attention is given to the nonlinear resonance role. The relationship between the rotation frequency of an unperturbed fluid particle and the appearance and disappearance of a nonlinear resonance is established. So, the frequency gives us the opportunity to explain the trajectories' chaotization via the Chirikov criteria. This simple estimation is verified by numerical calculations. A simplified model is used for more exact reasoning. The distance between nonlinear resonance and its width was established for large action, and accurate estimation of chaotic region boundary was calculated. Also, numerically and analytically, there are studied chaotization dependencies from some other flow parameters

Динамика бароклинных вихрей с нулевой суммарной интенсивностью (хетонов)

Приводится обзор работ, посвященных изучению свойств вихревых движений в устойчиво стратифицированной быстро вращающейся жидкости и описываемых уравнением эволюции потенциального вихря в квазигеострофическом приближении. Основное внимание уделено вихрям с нулевой суммарной циркуляцией — так называемым хетонам. Рассматриваются задачи самодвижения дискретных хетонов, устойчивости единичного распределенного хетона, взаимодействия двух хетонов конечных размеров. Приводятся также новые решения задач о трех и более дискретных вихрях хетонной структуры. Даются примеры возникновения хаотических режимов. Обсуждаются область применимости хетонной теории и перспективыее возможных приложений, в частности, — для анализа динамической стадии развития глубокой конвекции в океане

First Principles Investigation of Magnetic Properties of Fe-Ni-Mn-Al Heusler Alloys

AbstractThe composition dependences of crystal lattice parameters, magnetic moments and magnetic exchange parameters in FexNi2−xMn1+y Al1−y (0.0 ≤ x ≤ 2.0; 0.0 ≤ y ≤ 0.6) Heusler alloys are investigated with the help of first principles calculations. Our simulations have shown that crystal lattice parameter is decreased with Fe content (x) increasing. Our calculations show that increase of Fe content (x) leads increasing of magnetic exchange interactions between Mn atoms at regular positions and Mn atoms at Al positions and change of interaction sign from antiferromagnetic type to ferromagnetic one for Fe content x ≥ 1.4. Competitive behavior between ferromagnetic and antiferromagnetic interactions shows that these alloys have a complex magnetic structure. Calculated data for crystal lattice parameter, magnetic moment and magnetic exchange parameters for pure compounds (x = 0.0 and x = 2.0) are in an agreement with theoretical and experimental data

Investigation of Optical Properties and Radiation Stability of TiO2 Powders before and after Modification by Nanopowders of Various Oxides

The titanium dioxide powders are widely used as a pigment for coatings and paints, the important characteristics of which are reflectivity and stability to irradiation. The results of investigations of the optical properties and radiation stability of titanium dioxide powders before and after high-temperature modification with nanopowders are presented in this chapter. The diffuse reflection spectra of various titanium dioxide powders in the UV, visible, and near-IR ranges, and their change during irradiation by electrons with 30 keV energy and a different fluence in vacuum in situ were investigated: (1) TiO2 powders with particle size in the range 60–240 nm; (2) Microsized TiO2 powder (240 nm) modified by Al2O3, ZrO2, SiO2, TiO2, ZnO, MgO nanoparticles with grain size from 30 up to 60 nm; (3) Microsized TiO2 powder (260 nm) modified by SiO2 with the grain size of 12–14 nm at the temperature of 150, 400, and 800°C. The reduction in reflectivity in entire spectrum with decrease in grain sizes of TiO2 nanopowders was established. Nanopowder with the grain size of 80 nm possesses the highest stability to irradiation. It was shown that the average grain size and specific surface of introduced nanoparticles effect noticeably on the radiation stability increase of titanium dioxide powders modified with nanoparticles of various oxides. The micro-sized TiO2 powder heating at temperature of 800оС is the factor which positively influences on the radiation stability

Effects of magnetic and structural phase transitions on the normal and anomalous Hall effects in Ni-Mn-In-B Heusler alloys

Magnetization, electrical resistivity, magnetoresistance, and Hall resistivity of Ni50Mn35In14.25B0.75 and Ni50Mn35In14.5B0.5 Heusler alloys were studied in a temperature range T=80-400K in magnetic fields up to 20 kOe. Both alloys exhibit a martensitic transformation from a higherature ferromagnetic austenite phase to a lowerature, low-magnetization martensitic phase. The electrical resistivity nearly doubles as a result of the martensitic transformation, reaching 180 and 100 μ cm in the martensitic states of Ni50Mn35In14.25B0.75 and Ni50Mn35In14.5B0.5, respectively. The temperature dependence of the electrical resistivity does not corresponded with the Mooij correlation. The magnetoresistance is negative with a narrow negative peak at the martensitic transition. Normal and anomalous Hall effect coefficients were determined by fitting the field dependences of the Hall resistivity using magnetization data. The coefficients of the normal Hall effect for both compositions were found to decrease with temperature from positive values in the austenite to negative values in the martensite phase. None of the known correlations between the anomalous Hall effect coefficient and resistivity were satisfied. Significant changes in the values of the anomalous Hall coefficients during the martensitic transformation are explained by the difference in spin-up and spin-down state occupations in the martensite and austenite phases. First-principles calculations of the electronic structures confirm this explanation