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

Correlated electronic structure, orbital-dependent correlations, and Lifshitz transition in tetragonal FeS

Using density functional plus dynamical mean-field theory method (DFT+DMFT) with full self-consistency over the charge density, we study the effect of electronic correlations on the electronic structure, magnetic properties, orbital-dependent band renormalizations, and Fermi surface of the tetragonal phase of bulk FeS. We perform a direct structural optimization of the $P_4/nmm$ crystal structure of paramagnetic FeS, with respect to the lattice constant $a$ and the internal coordinate $z_\mathrm{S}$ of atom S. Our results show an anomalous sensitivity of the electronic structure and magnetic properties of FeS to fine details of its crystals structure. Upon expansion of the lattice volume, we observe a remarkable change of the electronic structure of FeS which is associated with a complete reconstruction of the Fermi surface topology (Lifshitz transition). This behavior is ascribed to a correlation-induced shift of the Van Hove singularity associated with the Fe $t_2$ orbitals at the $M$ point across the Fermi level. The Lifshitz phase transition is accompanied by a significant growth of local magnetic moments and emergence of strong orbital-selective correlations. It is seen as a pronounced anomaly (`kink') in the total energies upon expansion of the lattice, associated with a remarkable enhancement of compressibility. This behavior is accompanied by an orbital-dependent formation of local moments, a crossover from itinerant to localized orbital-selective moment behavior of the Fe $3d$ electrons. While exhibiting weak effective mass enhancement of the Fe $3d$ states $m^*/m \sim 1.3-1.4$, correlation effects reveal a strong impact on a position of the Van Hove singularity at the $M$ point, implying a complex interplay between electronic correlations and band structure effects in FeS

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

Integral equations of a cohesive zone model for history-dependent materials and their numerical solution

A nonlinear history-dependent cohesive zone (CZ) model of quasi-static crack propagation in linear elastic and viscoelastic materials is presented. The viscoelasticity is described by a linear Volterra integral operator in time. The normal stress on the CZ satisfies the history-dependent yield condition, given by a nonlinear Abel-type integral operator. The crack starts propagating, breaking the CZ, when the crack tip opening reaches a prescribed critical value. A numerical algorithm for computing the evolution of the crack and CZ in time is discussed along with some numerical results

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

Image preprocessing for artistic robotic painting

Artistic robotic painting implies creating a picture on canvas according to a brushstroke map preliminarily computed from a source image. To make the painting look closer to the human artwork, the source image should be preprocessed to render the effects usually created by artists. In this paper, we consider three preprocessing effects: aerial perspective, gamut compression and brushstroke coherence. We propose an algorithm for aerial perspective amplification based on principles of light scattering using a depth map, an algorithm for gamut compression using nonlinear hue transformation and an algorithm for image gradient filtering for obtaining a well-coherent brushstroke map with a reduced number of brushstrokes, required for practical robotic painting. The described algorithms allow interactive image correction and make the final rendering look closer to a manually painted artwork. To illustrate our proposals, we render several test images on a computer and paint a monochromatic image on canvas with a painting robot

Imidazole-imidazole hydrogen bonding in the pH-sensing histidine side chains of influenza A M2.

The arrangement of histidine side chains in influenza A M2 tetramer determines their pKa values, which define pH-controlled proton conduction critical to the virus lifecycle. Both water-associated and hydrogen-bonded imidazole-imidazolium histidine quaternary structures have been proposed, based on crystal structures and NMR chemical shifts, respectively. Here we show, using the conduction domain construct of M2 in lipid bilayers, that the imidazole rings are hydrogen bonded even at a pH of 7.8 in the neutral charge state. An intermolecular 8.9 ± 0.3 Hz 2hJNN hydrogen bond is observed between H37 Nε and Nδ recorded in a fully protonated sample with 100 kHz magic-angle spinning. This interaction could not be detected in the drug-bound sample

Unusual Mott transition associated with charge-order melting in BiNiO3 under pressure

We study the electronic structure, magnetic state, and phase stability of paramagnetic BiNiO3 near a pressure-induced Mott insulator-to-metal transition (MIT) by employing a combination of density functional and dynamical mean-field theory. We obtain that BiNiO3 exhibits an anomalous negative-charge-transfer insulating state, characterized by charge disproportionation of the Bi 6s states, with Ni2+ ions. Upon a compression of the lattice volume by ∼4.8%, BiNiO3 is found to make a Mott MIT, accompanied by the change of crystal structure from triclinic P1 to orthorhombic Pbnm. The pressure-induced MIT is associated with the melting of charge disproportionation of the Bi ions, caused by a charge transfer between the Bi 6s and O 2p states. The Ni sites remain to be Ni2+ across the MIT, which is incompatible with the valence-skipping Ni2+/Ni3+ model. Our results suggest that the pressure-induced change of the crystal structure drives the MIT in BiNiO3. © 2019 American Physical Society

Lifshitz transition and frustration of magnetic moments in infinite-layer NdNiO2 upon hole doping

Motivated by the recent discovery of superconductivity in infinite-layer (Sr,Nd)NiO2 films with Sr content x≃0.2 [D. Li, Nature (London) 572, 624 (2019)NATUAS0028-083610.1038/s41586-019-1496-5], we examine the effects of electron correlations and Sr doping on the electronic structure, Fermi-surface topology, and magnetic correlations in (Nd,Sr)NiO2 using a combination of dynamical mean-field theory of correlated electrons and band-structure methods. Our results reveal a remarkable orbital-selective renormalization of the Ni 3d bands, with m∗/m∼3 and 1.3 for the dx2-y2 and d3z2-r2 orbitals, respectively, that suggests orbital-dependent localization of the Ni 3d states. We find that upon hole doping, (Nd,Sr)NiO2 undergoes a Lifshitz transition of the Fermi surface which is accompanied by a change of magnetic correlations from three-dimensional (3D) Néel G-type (111) to quasi-2D C-type (110). We show that magnetic interactions in (Nd,Sr)NiO2 demonstrate an unanticipated frustration, which suppresses magnetic order, implying the importance of in-plane spin fluctuations to explain its superconductivity. Our results suggest that frustration is maximal for Sr doping x≃0.1-0.2, which is in agreement with an experimentally observed doping value Sr x≃0.2 of superconducting (Nd,Sr)NiO2. © 2020 American Physical Society.We acknowledge support by the Russian Foundation for Basic Research (Project No. 18-32-20076). The theoretical analysis of the electronic structure was supported by the state assignment of Minobrnauki of Russia (theme “Electron” No. AAAA-A18-118020190098-5). S.Y.S. was supported by National Science Foundation DMR Grant No. 1832728

Membrane-embedded TSPO: an NMR view

Translocator Protein (18 kDa) (TSPO) is a mitochondrial transmembrane protein commonly used as a biomarker for neuroinflammation and is also a potential therapeutic target in neurodegenerative diseases. Despite intensive research efforts, the function of TSPO is still largely enigmatic. Deciphering TSPO structure in the native lipid environment is essential to gain insight into its cellular activities and to design improved diagnostic and therapeutic ligands. Here, we discuss the influence of lipid composition on the structure of mammalian TSPO embedded into lipid bilayers on the basis of solid-state NMR experiments. We further highlight that cholesterol can influence both the tertiary and quaternary TSPO structure and also influence TSPO localization in mitochondria-associated endoplasmic reticulum membranes