1,600 research outputs found
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
crystal structure of paramagnetic FeS, with respect to the lattice constant
and the internal coordinate 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 orbitals at the
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 electrons. While
exhibiting weak effective mass enhancement of the Fe states , correlation effects reveal a strong impact on a position of the Van
Hove singularity at the point, implying a complex interplay between
electronic correlations and band structure effects in FeS
The Theory from Large Deviations for Random Processes and Strong Convergence of Stochastic Approximation Procedures
This paper deals with the application of "large deviation" theory to the analysis of stochastic approximation procedures. The approach allows to get new results in the asymptotical behaviour of stochastic procedures under very mild assumption about the "noise". The paper contains a short but illuminative survey of these results together with some new author's findings. For applications the last section seems to be interesting presenting some new ideas in multiobjective optimization
The neural network art which uses the Hamming distance to measure an image similarity score
This study reports a new discrete neural network of Adaptive Resonance Theory (ART-1H) in which the Hamming distance is used for the first time to estimate the measure of binary images (vectors) proximity. For the development of a new neural network of adaptive resonance theory, architectures and operational algorithms of discrete neural networks ART-1 and discrete Hamming neural networks are used. Unlike the discrete neural network adaptive resonance theory ART-1 in which the similarity parameter which takes into account single images components only is used as a measure of images (vectors) proximity in the new network in the Hamming distance all the components of black and white images are taken into account. In contrast to the Hamming network, the new network allows the formation of typical vector classes representatives in the learning process not using information from the teacher which is not always reliable. New neural network can combine the advantages of the Hamming neural network and ART-1 by setting a part of source information in the form of reference images (distinctive feature and advantage of the Hamming neural network) and obtaining some of typical image classes representatives using learning algorithms of the neural network ART-1 (the dignity of the neural network ART-1). The architecture and functional algorithms of the new neural network ART which has the properties of both neural network ART-1 and the Hamming network were proposed and investigated. The network can use three methods to get information about typical image classes representatives: teacher information, neural network learning process, third method uses a combination of first two methods. Property of neural network ART-1 and ART-1H, related to the dependence of network learning outcomes or classification of input information to the order of the vectors (images) can be considered not as a disadvantage of the networks but as a virtue. This property allows to receive various types of input information classification which cannot be obtained using other neural networks
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, ratio, and the internal position of Se) and the electronic
structure of the tetragonal (space group ) paramagnetic FeSe. Our
results for the lattice parameters are in good quantitative agreement with
experiment. The ratio is slightly overestimated by about ~\%,
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 -~\%, implying a
crucial importance of electron correlations. Upon compression to ~GPa, the
ratio and the lattice volume show a decrease by and ~\%,
respectively, while the Se coordinate weakly increases by ~\%.
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 by about ~\% for the and less than ~\% for
the states, as compared to ambient pressure. The behavior of the
momentum-resolved magnetic susceptibility shows no topological
changes of magnetic correlations under pressure, but demonstrates a reduction
of the degree of the in-plane 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
FeSeS.Comment: 10 pages, 6 figure
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
- …