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Vortex coherent structures on arrays of nonlinear oscillators joined by weak links into topologically nontrivial two-dimensional discrete manifolds have been theoretically studied. A circuit of nonlinear electric oscillators coupled by…
We analyze the creeping flow generated by a spherical particle moving through a viscous fluid with nematic directional order, in which momentum diffusivity is anisotropic and which opposes resistance to bending. Specifically, we provide…
We investigate the dynamics of a charged particle confined to move on a toroidal helix while being driven by an external time-dependent electric field. The underlying phase space is analyzed for linearly and circularly polarized fields. For…
We consider the physics of transport through quantum dots in the presence of two tunneling paths. The first path sees electrons hopping on and off the dot while the second path is modeled through a potential scattering-like term. To study…
We investigate the transverse oscillations of a line-tied multi-stranded coronal loop composed of several parallel cylindrical strands. First, the collective fast normal modes of the loop are found with the T-matrix theory. There is a huge…
A brief review of a self-contained genuinely three-dimensional monodromy-matrix based non-perturbative covariant path-integral approach to {\it polynomial invariants} of knots and links in the framework of (topological) quantum Chern-Simons…
The dimer model on a graph embedded in the torus can be interpreted as a collection of random self-avoiding loops. In this paper, we consider the uniform toroidal honeycomb dimer model. We prove that when the mesh of the graph tends to zero…
In the context of the Franks-Misiurewicz Conjecture, we study homeomorphisms of the two-torus semiconjugate to an irrational rotation of the circle. As a special case, this conjecture asserts uniqueness of the rotation vector in this class…
We use a special kind of 2-dimensional extended Topological Quantum Field Theories (TQFTs), so-called open-closed TQFTs, in order to extend Khovanov homology from links to arbitrary tangles, not necessarily even. For every plane diagram of…
In this paper, we give a complete topological and smooth classification of non-invertible Anosov maps on torus. We show that two non-invertible Anosov maps on torus are topologically conjugate if and only if their corresponding periodic…
We introduce a framework to analyze knots and links in an unmarked solid torus. We discuss invariants that detect when such links are equivalent under an ambient homeomorphism, and show that the multivariable Alexander polynomial is such in…
In topology, a torus remains invariant under certain non-trivial transformations known as modular transformations. In the context of topologically ordered quantum states of matter, these transformations encode the braiding statistics and…
In this paper we show that the non-alternating torus knots are homologically thick, i.e. that their Khovanov homology occupies at least three diagonals. Furthermore, we show that we can reduce the number of full twists of the torus knot…
Consider a Hodge manifold and assume that a torus acts on it in a Hamiltonian and holomorphic manner and that this action linearizes on a given quantizing line bundle. Inside the dual of the line bundle one can define the circle bundle,…
For a smooth Morse-Smale vector field with Lyapunov constraints (Lyapunov function) one shows how and why the non-triviality of the cohomology, as concluded from its additive structure, detects rest points and the multiplicative structure…
The fundamental polarization singularities of monochromatic light are normally associated with invariance under coordinated rotations: symmetry operations that rotate the spatial dependence of an electromagnetic field by an angle $\theta$…
Tunneling conductance of an Aharonov-Bohm circuit including two quantum dots is calculated based on the general expression of the conductance in the linear response regime of the bias voltage. The calculation is performed in a wide…
Quantization of superflow-circulation and of magnetic-flux are considered for systems, such as superfluid $^3$He-A and unconventional superconductors, having nonscalar order parameters. The circulation is shown to be the anholonomy in the…
Finite-order invariants of knots in arbitrary 3-manifolds (including non-orientable ones) are constructed and studied by methods of the topology of discriminant sets. Obstructions to the integrability of admissible weight systems to…
Here we report on the translocation of folded polymers through nano-pores using molecular dynamic simulations. Two cases are studied; one in which a folded molecule unfolds upon passage and one in which the folding remains intact as the…