Localization and duality for ABJM latitude Wilson loops

We investigate several aspects of BPS latitude Wilson loops in gauge theories in three dimensions with $$ \mathcal{N} $$ N ≥ 4 supersymmetry. We derive a matrix model for the bosonic latitude Wilson loop in ABJM using supersymmetric localization, and show how to extend the computation to more general Chern-Simons-matter theories. We then define latitude type Wilson and vortex loop operators in theories without Chern-Simons terms, and explore a connection to the recently derived superalgebra defining local Higgs and Coulomb branch operators in these theories. Finally, we identify a BPS loop operator dual to the bosonic latitude Wilson loop which is a novel bound state of Wilson and vortex loops, defined using a worldvolume supersymmetric quantum mechanics.

A simple vortex-loop-based model for unsteady rotating wings

An analytical model is developed for the lift force produced by unsteady rotating wings; this configuration is a simple representation of a flapping wing. Modelling this is important for the aerodynamic and control-system design for bio-inspired drones. Such efforts have often been limited to being two-dimensional, semi-empirical, sometimes computationally expensive, or quasi-steady. The current model is unsteady and three-dimensional, yet simple to implement, requiring knowledge of only the wing kinematics and geometry. Rotating wings produce a vortex loop consisting of the root vortex, leading-edge vortex, tip vortex and trailing-edge vortex, which grows with time. This is modelled as a tilted planar loop, geometrically specified by the wing size, orientation and motion. By equating the angular impulse of the vortex loop to that of the fluid volume driven by the wing, the circulatory lift force is derived. Potential flow theory gives the fluid-inertial lift. Adding these two contributions yields the total lift formula. The model shows good agreement with a range of experimental and computational cases. Also, a steady-state lift model is developed that compares well with previous work for various angles of attack.

Characteristics of Dynamic Forces Generated by a Flapping Butterfly and its Wake Structure

A typical example of the flow field around a moving elastic body is that around butterfly wings. Butterflies fly by skillfully controlling this flow field, and vortices are generated around their bodies. The motion of their elastic wings produces dynamic fluid forces by manipulating the flow field. For this reason, there has been increased academic interest in the flow field and dynamic fluid forces produced by butterfly wings. A number of recent studies have qualitatively and quantitatively examined the flow field around insect wings. In some such previous studies, the vortex ring or vortex loop formed on the wing was visualized. However, the characteristics of dynamic forces generated by the flapping insect wing are not yet sufficiently understood. The purpose of the present study is to investigate the characteristics of dynamic lift and thrust produced by the flapping butterfly wing and the relationship between the dynamic lift and thrust and the flow field around the butterfly. We conducted the dynamic lift and thrust measurements of a fixed flapping butterfly, Idea leuconoe, using a six-axes sensor. Moreover, two-dimensional PIV measurement was conducted in the wake of the butterfly. The butterfly produced dynamic lift in downward flapping which became maximum at a flapping angle of approximately 0.0 deg. At the same time, the butterfly produced negative dynamic thrust during downward flapping. The negative dynamic thrust was not produced hydrodynamically by a flapping butterfly wing because a jet was not formed in front of the butterfly. The negative dynamic thrust was the kicking force for jumping and the maximum of this kicking force was about 6.0 times as large as the weight. On the other hand, the butterfly produced dynamic thrust in upward flapping which was approximately 6.0 times as large as the weight of the butterfly. However, the attacking force by the abdomen of the butterfly was included in the dynamic thrust and we have not yet clarified quantitatively the dynamic thrust produced by the butterfly wing.