The transformation behavior of an embedded shape memory alloy (SMA) ribbon was investigated experimentally and numerically. Single SMA ribbons (55% Ni, 45% Ti) were pre-strained to 1% and then embedded in a room-temperature-cured epoxy resin. The embedded ribbons were heated resistively to a temperature above the austenite start temperature to induce transformation. The development of displacem...

We investigate the rich morphologies of an electrically charged flexible ribbon, which is a prototype for many beltlike structures in biology and nanomaterials. Long-range electrostatic repulsion is found to govern the hierarchical buckling of the ribbon from its initially flat shape to its undulated and out-of-plane twisted conformations. In this process, the screening length is the key contro...

The Reshetikhin-Turaev invariant, Turaev's TQFT, and many related constructions rely on the encoding of certain ribbon tangles (n-string links, or n-ribbon handles) as n-forms on the coend of a ribbon category. We introduce the monoidal category of Hopf diagrams, and describe a universal encoding of ribbon string links as Hopf diagrams. This universal encoding is an injective monoidal functor a...

This thesis begins with the study of a class of symmetric functions {x} which are generating functions for ribbon tableaux (hereon called ribbon functions), first defined by Lascoux, Leclerc and Thibon. Following work of Fomin and Greene, I introduce a set of operators called ribbon Schur operators on the space of partitions. I develop the theory of ribbon functions using these operators in an ...

In this note, I discuss a dual version of the ribbon graph decomposition of the moduli spaces of Riemann surfaces with boundary and marked points, which I introduced in the unpublished preprint [1], and used in [2] to construct open-closed topological conformal field theories. This dual version of the ribbon graph decomposition is a compact orbi-cell complex with a natural weak homotopy equival...

Ribbon-type presynaptic active zones are a hallmark of excitatory retinal synapses, and the ribbon organelle is thought to serve as the organizing point of the presynaptic active zone. Imaging of exocytosis from isolated retinal neurons, however, has revealed ectopic release (i.e., release away from ribbons) in significant quantities. Here, we demonstrate in an in vitro mouse retinal slice prep...

We prove that a crossing change along a double point circle on a 2-knot is realized by ribbon-moves for a knotted torus obtained from the 2-knot by attaching a 1-handle. It follows that any 2-knots for which the crossing change is an unknotting operation, such as ribbon 2-knots and twistspun knots, have trivial Khovanov-Jacobsson number. A surface-knot or -link is a closed surface embedded in 4...

This paper explores the effect of impeller design on the chaotic mixing in a helical ribbon mixer. Numerical simulations using the Smoothed Particle Hydrodynamics (SPH) method are used to solve for the fluid flow around the moving impellor. The mixing flow is visualised by extracting the hyperbolic Lagrangian Coherent Structures (LCS) of the flow from the Finite-Time Lyapunov Exponent (FTLE) fi...