Here, we propose a planning method for knotting/unknotting of deformable linear objects. First, we propose a topological description of the state of a linear object. Second, transitions between these states are defined by introducing four basic operations. Then, possible sequences of crossing state transitions, i.e. possible manipulation processes, can be generated once the initial and the obje...

Monte Carlo simulations are used to study the knotting probability of circular DNA confined in a slit. We systematically vary the slit height, the width, and the contour length of the DNA molecule. We find that the trend in knotting probability with respect to slit height can be monotonic or nonmonotonic, depending on the width and contour length. The nonmonotonic trend is caused by two competi...

The ileo-sigmoid knot is a rare surgical entity, corresponding to the wrapping of ileum around base sigmoid colon forming knot.An associated condition with rapid progression intestinal gangrene and high mortality. It cause obstruction especially during pregnancy. We report here case patient at 13 weeks amenorrhea an diagnosed late stage fetal loss.

A 3-manifold is tame if it is homeomorphic to the interior of a compact manifold with boundary. Marden’s conjecture asserts that any hyperbolic 3-manifold M = H/Γ with π1(M) finitely-generated is tame. This paper presents a criterion for tameness. We show that wildness ofM is detected by large-scale knotting of orbits of Γ. The elder sibling property prevents knotting and implies tameness by a ...

For a polygonal knot K, it is shown that a tube of radius R(K), the polygonal thickness radius, is an embedded torus. Given a thick configuration K, perturbations of size r < R(K) define satellite structures, or local knotting. We explore knotting within these tubes both theoretically and numerically. We provide bounds on perturbation radii for which we can see small trefoil and figure-eight su...