Multiply periodic states and isolated skyrmions in an anisotropic frustrated magnet

Multiply periodic states appear in a wide variety of physical contexts, such as the Rayleigh-Benard convection, Faraday waves, liquid crystals, domain patterns in ferromagnetic films and skyrmion crystals recently observed in chiral magnets. Here we study a simple model of an anisotropic frustrated magnet and show that its zero-temperature phase diagram contains numerous multi-q states including the skyrmion crystal. We clarify the mechanism for stabilization of these states, discuss their multiferroic properties and formulate rules for finding new skyrmion materials. In addition to skyrmion crystal, we find stable isolated skyrmions with topological charge 1 and 2. Physics of isolated skyrmions in frustrated magnets is very rich. Their statical and dynamical properties are strongly affected by the new zero mode - skyrmion helicity.Comment: 9 pages, 6 figure

Target-skyrmions and skyrmion clusters in nanowires of chiral magnets

In bulk non-centrosymmetric magnets the chiral Dzyaloshinskii-Moriya exchange stabilizes tubular skyrmions with a reversed magnetization in their centers. While the double-twist is favorable in the center of a skyrmion, it gives rise to an excess of the energy density at the outskirt. Therefore, magnetic anisotropies are required to make skyrmions more favorable than the conical spiral state in bulk materials. Using Monte Carlo simulations, we show that in magnetic nanowires unusual skyrmions with a doubly twisted core and a number of concentric helicoidal undulations (target-skyrmions) are thermodynamically stable even in absence of single-ion anisotropies. Such skyrmions are free of magnetic charges and, since the angle describing the direction of magnetization at the surface depends on the radius of the nanowire and an applied magnetic field, they carry a non-integer skyrmion charge s > 1. This state competes with clusters of spatially separated s=1 skyrmions. For very small radii, the target-skyrmion transforms into a skyrmion with s < 1, that resembles the vortex-like state stabilized by surface-induced anisotropies

Hidden attractors in fundamental problems and engineering models

Recently a concept of self-excited and hidden attractors was suggested: an attractor is called a self-excited attractor if its basin of attraction overlaps with neighborhood of an equilibrium, otherwise it is called a hidden attractor. For example, hidden attractors are attractors in systems with no equilibria or with only one stable equilibrium (a special case of multistability and coexistence of attractors). While coexisting self-excited attractors can be found using the standard computational procedure, there is no standard way of predicting the existence or coexistence of hidden attractors in a system. In this plenary survey lecture the concept of self-excited and hidden attractors is discussed, and various corresponding examples of self-excited and hidden attractors are considered

Theory of differential inclusions and its application in mechanics

The following chapter deals with systems of differential equations with discontinuous right-hand sides. The key question is how to define the solutions of such systems. The most adequate approach is to treat discontinuous systems as systems with multivalued right-hand sides (differential inclusions). In this work three well-known definitions of solution of discontinuous system are considered. We will demonstrate the difference between these definitions and their application to different mechanical problems. Mathematical models of drilling systems with discontinuous friction torque characteristics are considered. Here, opposite to classical Coulomb symmetric friction law, the friction torque characteristic is asymmetrical. Problem of sudden load change is studied. Analytical methods of investigation of systems with such asymmetrical friction based on the use of Lyapunov functions are demonstrated. The Watt governor and Chua system are considered to show different aspects of computer modeling of discontinuous systems

Review on the collection of documents: Famine in the Middle Volga region in the 20–30-ies of the XX century. Vol. 1. Paramonov V.N. (Ed.) Famine in the Samara province in the 20-ies of the XX century. Samara, 2014. 514 р.; Vol. 2. Paramonov V.N. (Ed.) Famine in the Middle Volga region in the 30-ies of the XX century. Samara, 2021. 798 р.

The peer-reviewed two-volume publication of documents was prepared by Samara archivists (responsible compiler Dubrovina E.N.) under the supervision of Doctor of Historical Sciences, Professor Paramonov V.N. The authors set out to recreate a multifactorial complex documentary picture of the social humanitarian tragedy of the 1920–1930-ies in the Samara province and the Middle Volga region. The implementation of this task required a lot of effort and many years of work. The first volume, entitled «Famine in the Samara Province in the 20-ies of the XX century», is more than 32 printed sheets (514 p.) was published in 2014, the second – «Famine in the Middle Volga Territory in the 30-ies of the XX century», with a volume of 50 printed sheets (798 p.) was published in 2021. Both volumes contain 718 documents from six local and central archives, as well as a number of published collections of documents. Such a voluminous publication significantly supplements the factual base of previous editions, primarily due to materials from local archives. The scientific and reference apparatus of the publication has been professionally completed; archaeographic processing of documents was carried out at a high level. The publication under review is a significant event in historical knowledge and allows in many respects to take a different look at the events of the 1920–1930-ies

Limitations of PLL simulation: hidden oscillations in MatLab and SPICE

Nonlinear analysis of the phase-locked loop (PLL) based circuits is a challenging task, thus in modern engineering literature simplified mathematical models and simulation are widely used for their study. In this work the limitations of numerical approach is discussed and it is shown that, e.g. hidden oscillations may not be found by simulation. Corresponding examples in SPICE and MatLab, which may lead to wrong conclusions concerning the operability of PLL-based circuits, are presented