Related papers: Tunnel One, Fibered Links
This paper examines the relationship between the knotting of an embedded surface in $\R^3$ and the knotting of its fold curves, formed by the singular set of projection to a plane. The first result shows that every surface, no matter how…
We explore the tunneling behavior of a quantum particle on a finite graph, in the presence of an asymptotically large potential. Surprisingly the behavior is governed by the local symmetry of the graph around the wells.
We prove that a monotone Lagrangian torus in $S^2\times S^2$ which suitably sits in a symplectic fibration with two sections in its complement is Hamiltonian isotopic to the Clifford torus.
A periodic tangle is a one-dimensional submanifold in $\mathbb{R}^3$ that has translational symmetry in one, two or three transverse directions. A periodic tangle can be seen as the universal cover of a link in the solid torus, the…
This paper is devoted to the study of the knot Floer homology groups HFK(S^3,K_{2,n}), where K_{2,n} denotes the (2,n) cable of an arbitrary knot, K. It is shown that for sufficiently large |n|, the Floer homology of the cabled knot depends…
We prove that the tunnel number of the sum of n knots is at least n.
We say that a given knot $J\subset S^3$ is detected by its knot Floer homology and $A$-polynomial if whenever a knot $K\subset S^3$ has the same knot Floer homology and the same $A$-polynomial as $J$, then $K=J$. In this paper we show that…
A single electron shared between two levels threaded by a magnetic flux is an irreducibly simple quantum system in which interference is predicted to occur. We demonstrate tuning of the tunnel coupling between two such electronic levels…
We present an extended discussion of a recently proposed theoretical approach for off-resonance tunneling transport. The proofs and the arguments are explained at length and simple analogies and illustrations are used where possible. The…
We describe a proposal to probe the quantum tunneling mechanism of an individual ion trapped in a double-well electromagnetic potential. The time-evolution of the probability of fluorescence measurement of the electronic ground state is…
By imposing the constraints of structural compatibility, stability and a large tunneling magneto-resistance, we have identified the Fe$_3$Al/BiF$_3$/Fe$_3$Al stack as a possible alternative to the well-established FeCoB/MgO/FeCoB in the…
We theoretically investigate resonant tunneling through S- and U-shaped nanostructured graphene nanoribbons. A rich structure of resonant tunneling peaks are found eminating from different quasi-bound states in the middle region. The…
Let $E$ and $F$ be locally solid vector lattices. In this short note, we establish a locally solid topology on the Fremlin tensor product $E\overline{\otimes}F$ and we denote it by $\tau_{E\overline{\otimes}F}$. It extends the Fremlin…
A torti-rational knot, denoted by K(2a,b|r), is a knot obtained from the 2-bridge link B(2a,b) by applying Dehn twists an arbitrary number of times, r, along one component of B(2a,b). We determine the genus of K(2a,b|r) and solve a question…
Echeverria recently introduced an invariant for a smoothly embedded torus in a homology $S^1\times S^3$, using gauge theory for singular connections. We define a new topological invariant of such an embedded torus, analogous to the…
It is known that the unknotting number $u(L)$ of a link $L$ is less than or equal to half the crossing number $c(L)$ of $L$. We show that there are a planar graph $G$ and its spatial embedding $f$ such that the unknotting number $u(f)$ of…
Ferroelectric tunnel junctions (FTJs) have attracted increasing research interest as a promising candidate for non-volatile memories. Recently, significant enhancements of tunneling electroresistance (TER) have been realized through…
In this paper, we describe a new surprising example of a fibration of the Clifford torus S3 x S3 in the 7-sphere by great 3-spheres, which is fiberwise homogeneous but whose fibers are not parallel to one another. In particular it is not…
Sangyop Lee has done much work to determine the knot types of twisted torus knots, including classifying the twisted torus knots which are the unknot. Among the unknotted twisted torus knots are those of the form $K(F_{n+2}, F_n, F_{n+1},…
Toroidal carbon nanotubes can serve as hosts for encapsulated loops of atomic metal wires. Such composite structures have been analyzed using density functional theory for a semiconducting C$_{120}$ torus encapsulating chains of Fe, Au and…