Exact isoholonomic motion of the planar Purcell's swimmer

Exact solutions of the isoholonomic problem and the optimal control problem in holonomic quantum computation

The isoholonomic problem in a homogeneous bundle is formulated and solved exactly. The problem takes a form of a boundary value problem of a variational equation. The solution is applied to the optimal control problem in holonomic quantum computer. We provide a prescription to construct an optimal controller for an arbitrary unitary gate and apply it to a k-dimensional unitary gate which operat...

Planar Motion

Exact Solution of Two Planar Polygon Models

Using a simple transfer matrix approach we have derived long series expansions for the perimeter generating functions of both three-choice polygons and punctured staircase polygons. In both cases we find that all the known terms in the generating function can be reproduced from a linear Fuchsian differential equation of order 8. We report on an analysis of the properties of the differential equ...

Recursive Updating of Planar Motion

This paper presents a recursive algorithm to recover the 3D structure and motion of a planar facet moving with arbitrary but constant motion relative to a single camera. By integrating discrete measurements of visual motion over time, the algorithm imposes a coupling between the scene structure and rotational motion otherwise absent in instantaneous motion processing. The algorithm disambiguate...

Modelling and controllability of the motion of a slender, flexible micro-swimmer

The mechanism of swimming at very low Reynolds number conditions is a topic of interest to biologists and engineering community. We develop a novel kinematic model of a slender flexible swimmer which locomotes in a low Reynolds number regime. In contrast to existing techniques that model such systems as a connected set of straight, rigid links, the novelty of our technique stems from the fact t...