Twisted Magnetic Fields Tie Information in a Knot: Scientific American

Twisted Magnetic Fields Tie Information in a Knot: Scientific American: Writing in Science, von Bergmann and her collaborators describe how they created skyrmions on a thin magnetic film of palladium and iron on an iridium crystal. They began with a sample in which all the atomic bar magnets were aligned. The team then used the tip of a scanning tunnelling microscope to apply a small current made up of electrons that had their spins aligned, or polarized, in a particular way. The polarized current interacted with the atomic bar magnets to twist them into knot-like configurations of skyrmions, each a few nanometers, or about 300 atoms, in diameter, says von Bergmann. The scientists could also use the polarized current to erase the knot, deleting the skyrmion...

...this is the first time that scientists have created and deleted individual magnetic skyrmions...

First fluid knots created in the lab

First fluid knots created in the lab: To investigate, Dustin Kleckner and William Irvine of the University of Chicago, Illinois 3D-printed strips of plastic shaped into a trefoil knot and a Hopf link. Crucially, the strips had a cross section shaped like a wing, or hydrofoil (see picture).

Next, the researchers dragged the knots through water filled with microscopic bubbles. Just as a wing passing through air creates a trailing vortex, the acceleration of the hydrofoils created a knot-shaped vortex that sucked in the bubbles. The result was a knot-shaped flow of moving bubbles – the first fluid knot created in a lab – which the team imaged with lasers.

A revolution in knot theory

A revolution in knot theory: In the mid-1990s, mathematicians discovered something strange. There are Gauss codes for which it is impossible to draw planar knot diagrams but which nevertheless behave like knots in certain ways. In particular, those codes, which Nelson calls *nonplanar Gauss codes*, work perfectly well in certain formulas that are used to investigate properties of knots. Nelson writes: "A planar Gauss code always describes a [knot] in three-space; what kind of thing could a nonplanar Gauss code be describing?" As it turns out, there are "virtual knots" that have legitimate Gauss codes but do not correspond to knots in three-dimensional space. These virtual knots can be investigated by applying combinatorial techniques to knot diagrams.

Silica microspheres in liquid crystals offer the possibility of creating every knot conceivable

Silica microspheres in liquid crystals offer the possibility of creating every knot conceivable: "The glass plates were treated in such a manner as to force the liquid crystalline molecules to align parallel to the surface", explains Tkalec. A single silica microsphere entering the layer changes the surrounding alignment substantially: around the sphere a ring-shaped region forms in which no preferred direction can be discerned... "It looks as if every microsphere were surrounded by its own ring – similar to the planet Saturn..."
In an essential step, the researchers discovered a way of manipulating the regions between the spheres by joining and separating neighbouring rings. First, they heated the region between the spheres with a laser. This destroys the characteristic alignment of the molecules. After switching off the laser, the alignment is re-established – but often in a different way than before.

Miniature 'knot lab' could help untangle DNA mystery - New Scientist - New Scientist

Miniature 'knot lab' could help untangle DNA mysteryEach silica particle was coated with a surfactant, making its surface hydrophobic. This disrupted the crystal's highly ordered structure – any liquid crystal molecule adjacent to a silica particle aligned itself perpendicular to the curved surface of the particle and these "disordered" molecules formed a three-dimensional Saturn's ring around the surface. "It's visible like a black ring around the particle," says Tkalec.

When the team trapped the loops with a laser and brought them close together, they immediately joined up to form a bigger, twisted loop around both the particles. A similar thing happened with three particles. By bringing just the right combination of twisted loops into contact, these arrays could be made to unknot and then re-knot to form loops that aren't just twisted, but are intertwined.

Make: Online | The Knot Zoo

Make: Online | The Knot Zoo: Old but very interesting page from Canadian Robert Scharein, programmer of the visualization software KnotPlot. The knots are organized by the number of crossings, and can be clicked on to display rotatable 3D models.

Tying the knot with computer-generated holograms: Winding optical path moves matter

Tying the knot with computer-generated holograms: Winding optical path moves matter: Knotted traps are made by imprinting a computer-generated hologram on the wavefronts of an otherwise ordinary beam of light. NYU undergraduate student Elisabeth Shanblatt and NYU physicist David Grier, the authors of the Optics Express paper, use a "liquid-crystal spatial light modulator" to project their holograms. This is essentially the first cousin of a conventional LCD television screen. The spatial light modulator imprints a calculated pattern of phase shifts onto the light. When the modified beam is brought to a focus with a high-power lens, the region of maximum intensity takes the form of a 3-D curve. This curve can cross over and through itself to trace out a knot. Moreover, the same hologram can redirect the light's radiation pressure to have a component along the curve, so that the total optical force "threads the knot."
When Shanblatt and Grier began this investigation, they thought that creating knots would be a compelling and aesthetically pleasing demonstration of their method's power. Once the knots actually worked, they realized that there are very few—if any—other practical ways to create knotted force fields. Previously reported knotted vortex fields have intensity minima along the knot, rather than the intensity maxima, or "bright knots" that can be created using the computer-generated holograms.

Fundamental secrets are tied up in knots

Knot theory and quantum mechanics

http://www.newscientist.com/article/mg20026781.500-fundamental-secrets-are-tied-up-in-knots.html

Tied Up in Knots

By tumbling a string of rope inside a box, biophysicists Dorian Raymer and Douglas Smith have discovered that knots—even complex knots—form surprisingly fast and often.

http://www.sciencenews.org/view/feature/id/9226/title/Tied_Up_in_Knots