Lightweight compliant surfaces are commonly used as roofs (awnings), filtration systems or propulsive appendages, that operate in a fluid environment. Their flexibility allows for shape to change in fluid flows, to better endure harsh or fluctuating conditions, or enhance flight performance of insect wings for example. The way the structure deforms is however key to fulfill its function, prompting the need for control levers. In this talk, we will consider two ways to tailor the deformation of surfaces in a flow, making use of the properties of origami (folded sheet) and kirigami (sheet with a network of cuts). Previous literature showed that the substructure of folds or cuts allows for sophisticated shape morphing, and produces tunable mechanical properties. We will discuss how those original features impact the way the structure interacts with a flow, through combined experiments and theory. We will notably show that a sheet with a symmetric cutting pattern can produce an asymmetric deformation, and study the underlying fluid-structure couplings to further program shape morphing through the cuts arrangement. We will also show that extreme shape reconfiguration through origami folding can cap fluid drag.

My group is developing a roadmap to replace bulky electric motors in miniature robots requiring large mechanical work output.

First, I will describe the mechanics of coiled muscles made by twisting nylon fishing lines, and how these actuators use internal strain energy to achieve a “record breaking” performance. Then I will describe intriguing hierarchical super-, and hyper-coiled artificial muscles which exploit the interplay between nonlinear mechanics and material microstructure. Next, I will describe their use to actuate the dynamic snapping of insect-scale jumping robots. The combination of strong but slow muscles with a fast-snapping beam gives rise to dynamic buckling cascade phenomena leading to effective robotic jumping mechanisms.

These examples shed light on the future of automation propelled by new bioinspired materials, nonlinear mechanics, and unusual manufacturing processes.

Toward a characterization of modularity using shatter functions, we show that an o-minimal expansion of the  real ordered additive group $(\mathbb{R}; 0, +,<)$ does not define restricted multiplication if and only if the shatter function of every definable family is asymptotic to a polynomial. Our result implies that vc-density can only take integer values in $(\mathbb{R}; 0, +,<)$ confirming a special case of a conjecture by Chernikov. (Joint with Abdul Basit.)

On supercomputers that exist today, achieving even close to the peak performance is incredibly difficult if not impossible for many applications. Techniques designed to improve the performance of matrix computations - making computations less expensive by reorganizing an algorithm, making intentional approximations, and using lower precision - all introduce what we can generally call ``inexactness''. The questions to ask are then:

1. With all these various sources of inexactness involved, does a given algorithm still get close enough to the right answer?
2. Given a user constraint on required accuracy, how can we best exploit and balance different types of inexactness to improve performance?

Studying the combination of different sources of inexactness can thus reveal not only limitations, but also new opportunities for developing algorithms for matrix computations that are both fast and provably accurate. We present few recent results toward this goal, icluding mixed precision randomized decompositions and mixed precision sparse approximate inverse preconditioners.