Related papers: Harmonic field in knotted space
In chaotic deterministic systems, seemingly stochastic behavior is generated by relatively simple, though hidden, organizing rules and structures. Prominent among the tools used to characterize this complexity in 1D and 2D systems are…
The equilibrium of current-carrying magnetic fields (e.g. flux tubes) embedded in a large-scale background field is developed and discussed in the astrophysical context. Embedded non-force-free current-carrying fields require a minimum…
We investigate scalar field theories in the multifield scenario, focusing mainly on the possibility to smoothly build internal structure and asymmetry for kinks and domain walls. The procedure requires the inclusion of an extra field which…
We consider the equilibrium equations for a conducting elastic rod placed in a uniform magnetic field, motivated by the problem of electrodynamic space tethers. When expressed in body coordinates the equations are found to sit in a…
Neural network field theory formulates field theory as a statistical ensemble of fields defined by a network architecture and a density on its parameters. We extend the construction to topological settings via the inclusion of discrete…
We perform full-MHD simulations on various initially helical configurations and show that they reconfigure into a state where the magnetic field lines span nested toroidal surfaces. This relaxed configuration is not a Taylor state, as is…
We investigate topological phases induced by a driven electric field coupled to a dimer chain (a model for poly-acetylene) at high frequency regime. It is shown how the topological invariant of the system can be controlled by the field…
We introduce a topological flux function to quantify the topology of magnetic braids: non-zero, line-tied magnetic fields whose field lines all connect between two boundaries. This scalar function is an ideal invariant defined on a…
We numerically investigate and experimentally demonstrate an in-situ topological band transition in a highly tunable mechanical system made of cylindrical granular particles. This system allows us to tune its inter-particle stiffness in a…
The authors showed in a preceding paper that in a connected locally harmonic manifold, the volume of a tube of small radius about a regularly parameterized simple arc depends only on the length of the arc and the radius. In this paper, we…
The notion of topology in physical systems is associated with the existence of a nonlocal ordering that is insensitive to a large class of perturbations. This brings robustness to the behaviour of the system and can serve as a ground for…
The morphology of spherically confined flexoelectric fluid membrane vesicles in an external uniform electric field is studied numerically. Due to the deformations induced by the confinement, the membrane becomes polarized resulting in an…
We investigate the morphology of a toroidal fluid membrane vesicle confined inside a spherical container. The equilibrium shapes are assembled in a geometrical phase diagram as a function of scaled area and reduced volume of the membrane.…
In present work, we discuss some topological features of charged particles interacting a uniform magnetic field in a finite volume. The edge state solutions are presented, as a signature of non-trivial topological systems, the energy…
The entanglement properties of the phase transition in a two dimensional harmonic lattice, similar to the one observed in recent ion trap experiments, are discussed both, for finite number of particles and thermodynamical limit. We show…
Topological techniques are used to study the motions of systems of point vortices in the infinite plane, in singly-periodic arrays, and in doubly-periodic lattices. The reduction of each system using its symmetries is described in detail.…
The lattice definition of the two-dimensional topological quantum field theory [Fukuma, {\em et al}, Commun.~Math.~Phys.\ {\bf 161}, 157 (1994)] is generalized to arbitrary (not necessarily orientable) compact surfaces. It is shown that…
We define a "sutured topological quantum field theory", motivated by the study of sutured Floer homology of product 3-manifolds, and contact elements. We study a rich algebraic structure of suture elements in sutured TQFT, showing that it…
Various director configurations of a nematic liquid crystal, confined in a toroidal volume and subject to an external magnetic field, were evaluated numerically by performing finite element calculations in three dimensions. The equilibrium…
The Hofstadter problem is the lattice analog of the quantum Hall effect and is the paradigmatic example of topology induced by an applied magnetic field. Conventionally, the Hofstadter problem involves adding $\sim 10^4$ T magnetic fields…