Related papers: Rational Maps, Monopoles and Skyrmions
Stable fold maps are fundamental tools in a generalization of the theory of Morse functions on smooth manifolds and its application to studies of topological properties of smooth manifolds. Round fold maps were introduced as stable fold…
We discuss the baryon properties under a strong magnetic field. We adopt the Skyrme model and calculate the magnetic field dependence of the mass and the pressure distribution in the soliton. We elucidate a magnetically induced contribution…
The generation of topologically non-trivial magnetic configurations has been a pivotal topic in both basic and applied nanomagnetism research. Localized non-coplanar magnetic defects such as skyrmions or merons were found to interact…
We are interested in the challenging problem of modelling densities on Riemannian manifolds with a known symmetry group using normalising flows. This has many potential applications in physical sciences such as molecular dynamics and…
The moduli spaces of compact and connected Riemann surfaces has been a central topic in modern mathematics in recent years. Thus their homological dimensions become important invariants. Motivated by the emergence mathematical counterparts…
Magnetic skyrmions, which are topological particle-like excitations in ferromagnets, have attracted a lot of attention recently. Skyrmionics is an attempt to use magnetic skyrmions as information carriers in next generation spintronic…
The problem of construction of fiber bundle over the moduli space of the Skyrme model is considered. We analyse an extension of the original Skyrme model which includes the minimal interaction with fermions. An analogy with modili space of…
A magnetic bimeron is a pair of two merons and can be understood as the in-plane magnetized version of a skyrmion. Here we theoretically predict the existence of single magnetic bimerons as well as bimeron crystals, and compare the emergent…
Based on Morse theory for the energy functional on path spaces we develop a deformation theory for mapping spaces of spheres into orthogonal groups. This is used to show that these mapping spaces are weakly homotopy equivalent, in a stable…
We study factorizations of rational matrix functions with simple poles on the Riemann sphere. For the quadratic case (two poles) we show, using multiplicative representations of such matrix functions, that a good coordinate system on this…
In this paper, we investigate the scattering of BPS magnetic monopoles through numerical simulations. We present an ansatz for various multi-monopole configurations suitable for analyzing monopole scattering processes. Our study includes…
We introduce a family of models for magnetic skyrmions in the plane for which infinitely many solutions can be given explicitly. The energy defining the models is bounded below by a linear combination of degree and total vortex strength,…
In this article we address a number of features of the moduli space of spherical metrics on connected, compact, orientable surfaces with conical singularities of assigned angles, such as its non-emptiness and connectedness. We also consider…
Magnetic monopoles, despite their ongoing experimental search as elementary particles, have inspired the discovery of analogous excitations in condensed matter systems. In chiral condensed matter systems, emergent monopoles are responsible…
Skyrmions and domain walls are typical spin textures of significant technological relevance to magnetic memory and logic applications, where they are used as carriers of information. The unique topology of skyrmions makes them to display…
For some symmetric pyramids of $R^3$ , we find Galois obstruction for their Dehn invariant to be zero, i.e. for the pyramids to be scissor equivalent to a cube. These conditions are that some associated Kummer extensions of number fields…
We study a new biholomorphic invariant of holomorphic maps between domains in different dimensions based on generic initial ideals. We start with the standard generic monomial ideals to find invariants for rational maps of spheres and…
Magnetic skyrmions are emerging as key elements of unconventional operations having unique properties such as small size and low current manipulation. In particular, it is possible to design skyrmion-based neurons and synapses for…
In our preprint q-alg/9703005 q-analogues of bounded symmetric domains were defined to be homogeneous spaces of the associated quantum groups. The investigation of a simplest among those domains, the quantum matrix ball, was started in…
In this work we explore the relationship between two ideas recently introduced in the literature. The first one deals with a quantity related to the informational contents of solutions of spatially localized structures, and the second…