Topological Solitons 2024 pdf epub mobi 电子书 图书描述 Topological solitons occur in many nonlinear classical field theories. They are stable, particle-like objects, with finite mass and a smooth structure. Examples are monopoles and Skyrmions, Ginzburg-Landau vortices and sigma-model lumps, and ...
Conditions under which a quotient space is Hausdorff are of particular interest. Sections 7–8 prove and apply Urysohn’s Lemma, which says that any two disjoint closed sets in a normal topological space may be separated by a real-valued continuous function. This result is fundamental to ...
A topological space is a pair (X, T) where X is a non-empty set and T is a topology on X. Examples 1.2 1. For any X, let T be the set of all subsets of X. This topology is called the discrete topology on X. 2. For any X, let T = {∅, X}. T is called the ...
The coated elastomer maintains hydrophilicity and lubricity after stretch, scratch, swell, and slide. As a further demonstration, a hydrogel substrate is primed for hydrophobic coating. Topological prime opens an enormous space for applications in engineering and biomedicine....
Introduction A topological space X is called n–arc connected (n–ac) if for any points p1,p2,...,pn in X, there exists an arc ↵ in X such that p1,p2,...pn are all in ↵. If a space is n–ac for all n 2 N, then we will say that it is !–ac. Note that this ...
Structure and topology of band structures in the 1651 magnetic space groups. Sci. Adv. 4, eaat8685 (2018). Article ADS Google Scholar Elcoro, L. et al. Magnetic topological quantum chemistry. Preprint at https://arXiv.org/abs/2010.00598 (2020). Xu, Y. et al. High-throughput ...
2e,f. At certain typical points in the spectra, real-space distributions of electromagnetic fields are imaged using an infrared camera (see examples in Fig. 2g–j). Figure 2g,h records light distributions before and after TPTs, while Fig. 2i displays an always existing edge mode at bandgap...
Dirac introduced his famous equation as the simplest relativistic wave-equation describing a free electron in a 3+1 space–time continuum. He realized that the equation has to be first-order in the time-derivative:(1)iℏ∂Ψ∂t=HDΨ in order to ensure the interpretation of the wave fu...
The latter is special because, when continuously evolving in the right direction, the system will necessarily cross the desired value but this is not at all the case if the tuning space was of higher dimension. As such, the tuning may even happen by random chance, as often is the case ...
2017 DOI: 10.1038/ncomms14022 OPEN Topological Dirac nodal lines and surface charges in fcc alkaline earth metals Motoaki Hirayama1,2, Ryo Okugawa1, Takashi Miyake3 & Shuichi Murakami1,2 In nodal-line semimetals, the gaps close along loops in k space, which are not at high-symmetry points...