Related papers: Rigidity and persistence for ensuring shape mainte…
In this paper, we analyze processes of conjecture generation in the context of open problems proposed in a dynamic geometry environment, when a particular dragging modality, maintaining dragging, is used. This involves dragging points while…
The graphical notion of effective resistance has found wide-ranging applications in many areas of pure mathematics, applied mathematics and control theory. By the nature of its construction, effective resistance can only be computed in…
Mixing, and coherence are fundamental issues at the heart of understanding transport in fluid dynamics and other non-autonomous dynamical systems. Recently, the notion of coherence has come to a more rigorous footing, and particularly…
This paper focuses on the stability analysis of a formation shape displayed by a team of mobile robots that uses heterogeneous sensing mechanism. Depending on the convenience and reliability of the local information, each robot utilizes the…
Using dynamic models of tensegrity structures, we derive provable, distributed control laws for stabilizing and changing the shape of a formation of vehicles in the plane. Tensegrity models define the desired, controlled, multi-vehicle…
The aim of this work is to study the dynamics and stability of soft shape-morphing configurations and specifically the modes of interaction between the front and rear airfoil segments. Initially we present several steady-state solutions,…
A different perspective on the long-standing problem of amorphous solidification is offered, based on an alternative definition of a solid as a porous medium. General, model-free results are obtained concerning the growing dynamic length…
In this paper, structural controllability of a leader-follower multi-agent system with multiple leaders is studied from a graph-theoretic point of view. The problem of preservation of structural controllability under simultaneous failures…
Self-stabilization is a versatile technique to withstand any transient fault in a distributed system. Mobile robots (or agents) are one of the emerging trends in distributed computing as they mimic autonomous biologic entities. The…
In this article we explain the theory of rigid residue complexes in commutative algebra and algebraic geometry, summarizing the background, recent results and anticipated future results. Unlike all previous approaches to Grothendiec…
A 2-dimensional direction-length framework is a collection of points in the plane which are linked by pairwise constraints that fix the direction or length of the line segments joining certain pairs of points. We represent it as a pair…
We discuss a link between graph theory and geometry that arises when considering graph dynamical systems with odd interactions. The equilibrium set in such systems is not a collection of isolated points, but rather a union of manifolds,…
As we enter the age of designer matter - where objects can morph and change shape on command - what tools do we need to create shape-shifting structures? At the heart of an elastic deformation is the combination of dilation and distortion,…
In this study, we present a concept of morphing structure -- featuring an arch mounted on a compliant base -- that can be reconfigured via snap-through buckling and leverages bistability to retain its morphed shape. We show that…
Resilience is a concept of rising interest in computer science and software engineering. For systems in which correctness w.r.t. a safety condition is unachievable, fast recovery is demanded. We investigate resilience problems of graph…
A theorem of Laman gives a combinatorial characterisation of the graphs that admit a realisation as a minimally rigid generic bar-joint framework in $\bR^2$. A more general theory is developed for frameworks in $\bR^3$ whose vertices are…
The problem of distributed control and estimation for multi-agent systems with limited sensing capabilities is a practical challenge motivated by incomplete and imperfect sensing. This article addresses an important case where each agent in…
A standard way of approximating or discretizing a metric space is by taking its Rips complexes. These approximations for all parameters are often bound together into a filtration, to which we apply the fundamental group or the first…
The stability of shapes formed by three viscoelastic droplets during their arrested coalescence has been investigated using micromanipulation experiments. Addition of a third droplet to arrested droplet doublets is shown to be controlled by…
Colloidal and other granular media experience a transition to rigidity known as jamming if the fill fraction is increased beyond a critical value. The resulting jammed structures are locally disordered, bear applied loads inhomogenously,…