Hilbert's 16th Problem for Quadratic Systems. New Methods Based on a Transformation to the Lienard Equation

Fractionally-quadratic transformations which reduce any two-dimensional quadratic system to the special Lienard equation are introduced. Existence criteria of cycles are obtained

Correlation strength, Lifshitz transition and the emergence of a two- to three-dimensional crossover in FeSe under pressure

We report a detailed theoretical study of the electronic structure, spectral properties, and lattice parameters of bulk FeSe under pressure using a fully charge self-consistent implementation of the density functional theory plus dynamical mean-field theory method (DFT+DMFT). In particular, we perform a structural optimization and compute the evolution of the lattice parameters (volume, $c/a$ ratio, and the internal $z$ position of Se) and the electronic structure of the tetragonal (space group $P4/nmm$) paramagnetic FeSe. Our results for the lattice parameters are in good quantitative agreement with experiment. The $c/a$ ratio is slightly overestimated by about $3$~\%, presumably due to the absence of the van der Waals interactions between the FeSe layers in our calculations. The lattice parameters determined within DFT are off the experimental values by a remarkable $\sim$$6$-$15$~\%, implying a crucial importance of electron correlations. Upon compression to $10$~GPa, the $c/a$ ratio and the lattice volume show a decrease by $2$ and $10$~\%, respectively, while the Se $z$ coordinate weakly increases by $\sim$$2$~\%. Most importantly, our results reveal a topological change of the Fermi surface (Lifshitz transition) which is accompanied by a two- to three-dimensional crossover. Our results indicate a small reduction of the quasiparticle mass renormalization $m^*/m$ by about $5$~\% for the $e$ and less than $1$~\% for the $t_2$ states, as compared to ambient pressure. The behavior of the momentum-resolved magnetic susceptibility $\chi({\bf q})$ shows no topological changes of magnetic correlations under pressure, but demonstrates a reduction of the degree of the in-plane $(\pi,\pi)$ stripe-type nesting. Our results for the electronic structure and lattice parameters of FeSe are in good qualitative agreement with recent experiments on its isoelectronic counterpart FeSe$_{1-x}$S$_x$.Comment: 10 pages, 6 figure

A Frequency-Domain Criterion for Global Stability of Systems with Angular Coordinates

  &nbsp

EVALUATION OF SUBMERGED HEALING OF COLONIC ANASTOMOSES IN SURGICAL HOSPITAL

Thus, the main causes of «hand technique» anastomosis by invagination are technical defects of the intervention in telescopic anastomosis by invagination and the ischemic disorders in colorectal anastomosis by invagination. 48 patients were operated on the colon and rectum with «hand technique» anastomosis. Invalidated «manual technique» anastomosis after 70 days of the formation were fully functional, and processes of healing and morphological transformation of mucosa were completed

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

Change in stability of solid solution at radiation influence

Stability of solid solution at radiation influence has been investigated. Expressions for diffusion streams of binary alloy components, which specify the existence of temperature interval in which the phenomenon of ascending diffusion of elements is observed, were received. Vacancy characters of diffusion, configuration entropy, and potential energy of atomic bonds were considered at derivation. The ascending diffusion testifies to stability infringement of homogeneous solid solution - stratification. Influence of radiation is connected with increase in concentration of vacancies which changes the energy of atomic bonds and, simultaneously, accelerates diffusion processes. The condition of alloy stability with regard to stratification at radiating influence was obtaine

Calculation of thermal parameters of SiGe microbolometers

The thermal parameters of a SiGe microbolometer were calculated using numerical modeling. The calculated thermal conduction and thermal response time are in good agreement with the values found experimentally and range between 2x10$^-7$ and 7x10$^-8$ W/K and 1.5 and 4.5 ms, respectively. High sensitivity of microbolometer is achieved due to optimization of the thermal response time and thermal conduction by fitting the geometry of supporting heat-removing legs or by selection of a suitable material providing boundary thermal resistance higher than 8x10$^-3$ cm$^2$K/W at the SiGe interface.Comment: 11 pages, 6 figure

Polaron physics and crossover transition in magnetite probed by pressure-dependent infrared spectroscopy

The optical properties of magnetite at room temperature were studied by infrared reflectivity measurements as a function of pressure up to 8 GPa. The optical conductivity spectrum consists of a Drude term, two sharp phonon modes, a far-infrared band at around 600 cm$^{-1}$, and a pronounced mid-infrared absorption band. With increasing pressure both absorption bands shift to lower frequencies and the phonon modes harden in a linear fashion. Based on the shape of the MIR band, the temperature dependence of the dc transport data, and the occurrence of the far-infrared band in the optical conductivity spectrum the polaronic coupling strength in magnetite at room temperature should be classified as intermediate. For the lower-energy phonon mode an abrupt increase of the linear pressure coefficient occurs at around 6 GPa, which could be attributed to minor alterations of the charge distribution among the different Fe sites.Comment: 7 pages, 7 figure

Orbital-selective coherence-incoherence crossover and metal-insulator transition in Cu-doped NaFeAs

We study the effects of electron-electron interactions and hole doping on the electronic structure of Cu-doped NaFeAs using the density functional theory plus dynamical mean-field theory (DFT+DMFT) method. In particular, we employ an effective multiorbital Hubbard model with a realistic band structure of NaFeAs in which Cu-doping was modeled within a rigid band approximation and compute the evolution of the spectral properties, orbital-selective electronic mass renormalizations, and magnetic properties of NaFeAs on doping with Cu. In addition, we perform fully charge self-consistent DFT+DMFT calculations for the long-range antiferromagnetically ordered Na(Fe,Cu)As with Cu x=0.5 with a real-space ordering of Fe and Cu ions. Our results reveal a crucial importance of strong electron-electron correlations and local potential difference between the Cu and Fe ions for understanding the k-resolved spectra of Na(Fe,Cu)As. On Cu-doping, we observe a strong orbital-selective localization of the Fe 3d states accompanied by a large renormalization of the Fe xy and xz/yz orbitals. Na(Fe,Cu)As exhibits bad-metal behavior associated with a coherence-to-incoherence crossover of the Fe 3d electronic states and local moments formation near a Mott metal-insulator transition (MIT). For heavily doped NaFeAs with Cu x∼0.5 we obtain a Mott insulator with a band gap of ∼0.3 eV which is characterized by divergence of the quasiparticle effective mass of the Fe xy states. In contrast to this, the quasiparticle weights of the Fe xz/yz and e states remain finite at the MIT. The MIT occurs via an orbital-selective Mott phase to appear at Cu x≃0.375 with the Fe xy states being Mott localized. We propose the possible importance of Fe/Cu disorder to explain the magnetic properties of Cu-doped NaFeAs. © 2021 American Physical Society.The DMFT model calculations of NaFeAs were supported by the state assignment of Minobrnauki of Russia (theme “Electron” No. AAAA-A18-118020190098-5). The electronic structure calculations and magnetic properties analysis of were supported by the Russian Science Foundation (Project No. 19-12-00012)

Theory of vortex states in magnetic nanodisks with induced Dzyaloshinskii-Moriya interactions

Vortex states in magnetic nanodisks are essentially affected by surface/interface induced Dzyaloshinskii-Moriya interactions. Within a micromagnetic approach we calculate the equilibrium sizes and shape of the vortices as functions of magnetic field, the material and geometrical parameters of nanodisks. It was found that the Dzyaloshinskii-Moriya coupling can considerably increase sizes of vortices with "right" chirality and suppress vortices with opposite chirality. This allows to form a bistable system of homochiral vortices as a basic element for storage applications.Comment: 8 pages, 8 figure