Related papers: A complete topological invariant for braided magne…
This paper investigates spaces equipped with a family of metric-like functions satisfying certain axioms. These functions provide a unified framework for defining topology, uniformity, and diffeology. The framework is based on a family of…
Both physical arguments and simulations of the global heliosphere indicate that the tailward heliopause is flattened considerably in the direction perpendicular to both the incoming flow and the large-scale interstellar magnetic field.…
Topological implications of the total generalized electron-flow magnetic helicity He in electron magnetohydrodynamics(EMHD) are explored. The invariance of He is shown to imply the invariance of the sum of the linkage of the magnetic field…
We investigate a square-lattice architecture of superconducting transmon qubits with inter-qubit interactions mediated by inductive couplers. Therein, the inductive couling between the qubit and couplers is suggested to be designed into the…
Continuous interpolation of real-valued data is characterized by piecewise monotone functions on a compact metric space. Topological total variation of piecewise monotone function f:X->R is a homeomorphism-invariant generalization of 1D…
Nonlinear tranlational symmetric equilibria with up to quartic flux terms in the free functions, reversed magnetic shear and sheared flow are constructed in two ways: i) quasianalytically by an ansatz which reduces the pertinent generalized…
We define the topological multiplicity of an invertible topological system $(X,T)$ as the minimal number $k$ of real continuous functions $f_1,\cdots, f_k$ such that the functions $f_i\circ T^n$, $n\in\mathbb Z$, $1\leq i\leq k,$ span a…
The topological framework of circuit topology has recently been introduced to complement knot theory and to help in understanding the physics of molecular folding. Naturally evolved linear molecular chains, such as proteins and nucleic…
A cosmological model connecting the evolution of universe with a sequence of topology changes described by a collection of specific graph cobordisms, is constructed. It is shown that an adequate topological field theory (of BF-type) can be…
Functional brain networks exhibit topological structures that reflect neural organization; however, statistical comparison of these networks is challenging for several reasons. This paper introduces a topologically invariant permutation…
In this lecture we explain the intimate relationship between modular invariants in conformal field theory and braided subfactors in operator algebras. Our analysis is based on an approach to modular invariants using braided sector induction…
In this work we establish that finite directed graphs give rise to semiflows on the power set of their nodes. We analyze the topological dynamics for semiflows on finite directed graphs by characterizing Morse decompositions, recurrence…
We find and investigate via numerical simulations self-sustained two-dimensional turbulence in a magnetohydrodynamic flow with a maximally simple configuration: plane, noninflectional (with a constant shear of velocity) and threaded by a…
The topology of the coronal magnetic field produces a strong impact on the properties of the solar corona and presumably on the origin of the slow solar wind. To advance our understanding of this impact, we revisit the concept of so-called…
We present a class of topological plasma configurations characterized by their toroidal and poloidal winding numbers, $n_t$ and $n_p$ respectively. The special case of $n_t=1$ and $n_p=1$ corresponds to the Kamchatnov-Hopf soliton, a…
Recent studies have demonstrated that in fully developed turbulence, the effective magnetic pressure of a large-scale field (non-turbulent plus turbulent contributions) can become negative. In the presence of strongly stratified turbulence,…
Topological properties play an increasingly important role in future research and technology. This also applies to the field of topological magnetic excitations which has recently become a very active and broad field. In this Perspective…
We briefly review helicity dynamics, inverse and bi-directional cascades in fluid and magnetohydrodynamic (MHD) turbulence, with an emphasis on the latter. The energy of a turbulent system, an invariant in the non-dissipative case, is…
Uncovering topologically nontrivial states in nature is an intriguing and important issue in recent years. While most studies are based on the topological band insulators, the topological state in strongly correlated low-dimensional systems…
The energy of the stochastic magnetic field is bounded from below by a topological quantity expressing the degree of linkage of the field lines. When the bound is saturated one can assume that the storage of a certain magnetic energy…