Locomotion of One Degree of Freedom Worm Robots

Worm-like robots have been widely designed for applications including maintenance of small pipes and medical procedures in biological vessels such as the lungs, intestines, urethra and blood vessels. The robots must be small, reliable, energy efficient and capable of carrying cargos such as cameras, biosensors, and drugs. Earthworm and inchworm robots have been traditionally designed with three or more cells and clamps and a corresponding number of actuators. The use of multiple actuators complicates the design, makes the system more cumbersome, reduces power efficiency and requires more control for coordination. In the present study, we analyze the worm locomotion, in terms of the distance between the cells and clamping modes, and model it as a cyclic function of the time. That is, the worm locomotion can be represented by a single degree of freedom. Consequently, multi-cells worm-like robots actuated by a single motor were designed. The robots employ a rotating screw-like shaft that mechanically coordinates the sequencing of the cell displacement as well as the clamping modes with no external control for each separate cell. This design allows for significant miniaturization and reduces complexity and cost of the system. Two prototypes of earthworm and inchworm robots for locomotion within 20mm and 70mm wide tubes were manufactured. The robots demonstrated high reliability and strong grip. They can crawl vertically while carrying a payload at a rate of few cm/s for the larger robots and roughly 1cm/s for the smaller ones. Furthermore, the low power consumption enables the robots to crawl wirelessly for hundreds of meters using standard off the shelf batteries.

Heart valve function: a biomechanical perspective

Heart valves (HVs) are cardiac structures whose physiological function is to ensure directed blood flow through the heart over the cardiac cycle. While primarily passive structures that are driven by forces exerted by the surrounding blood and heart, this description does not adequately describe their elegant and complex biomechanical function. Moreover, they must replicate their cyclic function over an entire lifetime, with an estimated total functional demand of least 3×10 9 cycles. As in many physiological systems, one can approach HV biomechanics from a multi-length-scale approach, since mechanical stimuli occur and have biological impact at the organ, tissue and cellular scales. The present review focuses on the functional biomechanics of HVs. Specifically, we refer to the unique aspects of valvular function, and how the mechanical and mechanobiological behaviours of the constituent biological materials (e.g. extracellular matrix proteins and cells) achieve this remarkable feat. While we focus on the work from the authors' respective laboratories, the works of most investigators known to the authors have been included whenever appropriate. We conclude with a summary and underscore important future trends.

l-PARTS OF DIVISOR CLASS GROUPS OF CYCLIC FUNCTION FIELDS OF DEGREE l

Let l be a prime number and K be a cyclic extension of degree l of the rational function field 𝔽q(T) over a finite field of characteristic ≠ = l. Using class field theory we investigate the l-part of Pic 0(K), the group of divisor classes of degree 0 of K, considered as a Galois module. In particular we give deterministic algorithms that allow the computation of the so-called (σ - 1)-rank and the (σ - 1)2-rank of Pic 0(K), where σ denotes a generator of the Galois group of K/𝔽q(T). In the case l = 2 this yields the exact structure of the 2-torsion and the 4-torsion of Pic 0(K) for a hyperelliptic function field K (and hence of the 𝔽q-rational points on the Jacobian of the corresponding hyperelliptic curve over 𝔽q). In addition we develop similar results for l-parts of S-class groups, where S is a finite set of places of K. In many cases we are able to prove that our algorithms run in polynomial time.

A Lower Bound on the Number of Cyclic Function Fields With Class Number Divisible byn

In this paper, we find a lower bound on the number of cyclic function fields of prime degreelwhose class numbers are divisible by a given integern. This generalizes a previous result of D. Cardon and R. Murty which gives a lower bound on the number of quadratic function fields with class numbers divisible byn.