Search results for "topological [model]"
showing 8 items of 88 documents
A version of Hake’s theorem for Kurzweil–Henstock integral in terms of variational measure
2019
Abstract We introduce the notion of variational measure with respect to a derivation basis in a topological measure space and consider a Kurzweil–Henstock-type integral related to this basis. We prove a version of Hake’s theorem in terms of a variational measure.
Topological properties of mono- and multilayer graphene, flat bands and surface superconductivity
2015
Tutustun Pro Gradu -työssäni topologisiin materiaaleihin ja perehdyn grafeenin sekä romboedrisen grafiitin ominaisuuksiin tästä näkökulmasta. Erityisesti tutkin grafeenin alihilasymmetrian rikkoutumisen vaikutuksia grafiitissa lisäämällä heilahtelevan potentiaalin α grafeenin tight-binding -malliin. Lasken romboedrisen grafiitin matalaenergiatilat tight-binding -mallista ja saan tulokseksi, että α avaa energia-aukon, mutta säilyttää vyön tasomaisen muodon, joka on saatu artikkelissa [16]. Tutkin työssäni myös heilahtelevan potentiaalin vaikutusta romboedrisen grafiitin suprajohtaviin pintatiloihin. Päätulokseni on, että heilahteleva potentiaali rikkoo grafiitin pintojen välisen symmetrian j…
Topological Protection and Control of Quantum Markovianity
2020
This article belongs to the Special Issue Topological Photonics.
Multiplicity results for asymmetric boundary value problems with indefinite weights
2004
We prove existence and multiplicity of solutions, with prescribed nodal properties, to a boundary value problem of the formu″+f(t,u)=0,u(0)=u(T)=0. The nonlinearity is supposed to satisfy asymmetric, asymptotically linear assumptions involving indefinite weights. We first study some auxiliary half-linear, two-weighted problems for which an eigenvalue theory holds. Multiplicity is ensured by assumptions expressed in terms of weighted eigenvalues. The proof is developed in the framework of topological methods and is based on some relations between rotation numbers and weighted eigenvalues.
Magnetoelectric effects in superconductor/ferromagnet bilayers
2018
We demonstrate that the hybrid structures consisting of a superconducting layer with an adjacent spin-textured ferromagnet demonstrate the variety of equilibrium magnetoelectric effects originating from coupling between the conduction electron spin and superconducting current. By deriving and solving the generalized Usadel equation which takes into account the spin-filtering effect we find that a supercurrent generates spin polarization in the superconducting film which is non-coplanar with the local ferromagnetic moment. The inverse magnetoelectric effect in such structures is shown to result in the spontaneous phase difference across the magnetic topological defects such as a domain wall …
Dynamic tuning of the director field in liquid crystal shells using block copolymers
2020
When an orientationally ordered system, like a nematic liquid crystal (LC), is confined on a self-closing spherical shell, topological constraints arise with intriguing consequences that depend critically on how the LC is aligned in the shell. We demonstrate reversible dynamic tuning of the alignment, and thereby the topology, of nematic LC shells stabilized by the nonionic amphiphilic block copolymer Pluronic F127. Deep in the nematic phase, the director (the average molecule orientation) is tangential to the interface, but upon approaching the temperature TNI of the nematic– isotropic transition, the director realigns to normal. We link this to a delicate interplay between an interfacial …
Neural Classification of Compost Maturity by Means of the Self-Organising Feature Map Artificial Neural Network and Learning Vector Quantization Algo…
2019
Self-Organising Feature Map (SOFM) neural models and the Learning Vector Quantization (LVQ) algorithm were used to produce a classifier identifying the quality classes of compost, according to the degree of its maturation within a period of time recorded in digital images. Digital images of compost at different stages of maturation were taken in a laboratory. They were used to generate an SOFM neural topological map with centres of concentration of the classified cases. The radial neurons on the map were adequately labelled to represent five suggested quality classes describing the degree of maturation of the composted organic matter. This enabled the creation of a neural separator classify…
Eksperimenti ar topoloģisko datu analīzi
2022
Maģistra darba mērķis ir iepazīstināt ar topoloģisko datu analīzi, kas ir pieeja datu kopu analīzei, izmantojot topoloģijas, kā matemātikas novirziena, metodes. Šī inovatīvā datu analīzes metode pasaulē pēdējos gados strauji attīstās un ar vien plašāk tiek pielietota, lai iegūtu informāciju no sarežģītiem, liela apjoma, daudzdimensionāliem datiem. Pašreiz nekur nav atrodams topoloģiskās datu analīzes apraksts un pielietojamība, latviešu valodā. Darbā tiek apskatīti divi dažādi uz topoloģiskās datu analīzes balstīti algoritmi - Mapper un ToMATo, kuru veiksmīgā izmantošanā noteicošais ir pareizu parametru izvēle. Darbā tiek pētītas un piedāvātas šo algoritmu parametru optimizācijas metodes un…