Related papers: Arresting the collapse of a catenary arch
The remarkable robustness of isolated columnar vortices suggests the existence of fundamental constraints that prevent spontaneous disintegration. In this work, we investigate the weakly nonlinear stability of such flows, demonstrating that…
Coupled oscillator networks show a complex interrelations between topological characteristics of the network and the nonlinear stability of single nodes with respect to large but realistic perturbations. We extend previous results on these…
Our recent interest is focused on establishing the necessary and sufficient conditions that guarantee a long-term stable evolution of both natural and artificial systems. Two necessary conditions, called global and local boundedness, are…
We propose a simple model that aims at describing, in a stylized manner, how local breakdowns due unbalances or congestion propagate in real dynamical networks. The model converges to a self-organized critical stationary state in which the…
This work considers the robustness of uncertain consensus networks. The first set of results studies the stability properties of consensus networks with negative edge weights. We show that if either the negative weight edges form a cut in…
Contraction theory is an analytical tool to study differential dynamics of a non-autonomous (i.e., time-varying) nonlinear system under a contraction metric defined with a uniformly positive definite matrix, the existence of which results…
We study necessary and sufficient conditions for contraction and incremental stability of dynamical systems with respect to non-Euclidean norms. First, we introduce weak pairings as a framework to study contractivity with respect to…
We extend the study of the inertial effects on the dynamics of active agents to the case where self-alignment is present. In contrast with the most common models of active particles, we find that self-alignment, which couples the rotational…
Frequency responses of multi-degree-of-freedom mechanical systems with weak forcing and damping can be studied as perturbations from their conservative limit. Specifically, recent results show how bifurcations near resonances can be…
Atomistic deformation simulations in the nominally elastic regime are performed for a model binary glass with strain rates as low as $10^{4}$/sec (corresponding to 0.01 shear strain per 1$\mu$sec). A robust elasticity is revealed that…
When the structure deformation is dominated by the low-energy deformation mode, the structure hardens with the increase in the size (number of units) at small sizes. This anomalous behavior will eventually disappear with the decay length of…
At a critical point of a second order phase transition the intrinsic energy surface is flat and there is no stable minimum value of the deformation. However, for a finite system, we show that there is an effective deformation which can…
The design of compliant mechanisms is crucial in several technologies and relies on the availability of solutions for nonlinear structural problems. One of these solutions is given and experimentally validated in the present article for a…
Conventional approaches to grasp planning require perfect knowledge of an object's pose and geometry. Uncertainties in these quantities induce uncertainties in the quality of planned grasps, which can lead to failure. Classically, grasp…
Inspired by the issue of stability of molecular structures, we investigate the strict minimality of point sets with respect to configurational energies featuring two- and three-body contributions. Our main focus is on characterizing those…
Many physical systems can be modelled as parameter-dependent variational problems. In numerous cases, multiple equilibria co-exist, requiring the evaluation of their stability, and the monitoring of transitions between them. Generally, the…
We study the steady-state low-temperature dynamics of an elastic line in a disordered medium below the depinning threshold. Analogously to the equilibrium dynamics, in the limit T->0, the steady state is dominated by a single configuration…
Disordered spring networks that are undercoordinated may abruptly rigidify when sufficient strain is applied. Since the deformation in response to applied strain does not change the generic quantifiers of network architecture - the number…
States of self-stress, tensions and compressions of structural elements that result in zero net forces, play an important role in determining the load-bearing ability of structures ranging from bridges to metamaterials with tunable…
A growing or compressed thin elastic sheet adhered to a rigid substrate can exhibit a buckling instability, forming an inward hump. Our study shows that the strip morphology depends on the delicate balance between the compression energy and…