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Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…
Rigidity transitions in simple models of confluent cells have been a powerful organizing principle in understanding the dynamics and mechanics of dense biological tissue. In this work we explore the interplay between geometry and rigidity…
Stickiness is a well known phenomenon in which chaotic orbits expend an expressive amount of time in specific regions of the chaotic sea. This phenomenon becomes important when dealing with area-preserving open systems because, in this…
Emergence and maintenance of excitability is often phrased in terms of arriving at and remaining about a manifold of 'solutions' embedded in a high dimensional parameter space. Alongside studies that extend traditional focus on…
Building upon the classical chemo-mechanical theory of Larch{\'e} and Cahn for equilibrium, numerous studies have investigated the transport of species in solids, with or without trapping phenomena. In most applications -- such as the…
The problem of polycube construction or deformation is an essential problem in computer graphics. In this paper, we present a robust, simple, efficient and automatic algorithm to deform the meshes of arbitrary shapes into their polycube…
We present sufficient conditions so that a conformal map between planar domains whose boundary components are Jordan curves or points has a continuous or homeomorphic extension to the closures of the domains. Our conditions involve the…
Circle packings are arrangement of circles satisfying specified tangency requirements. Many problems about packing of circles and spheres occur in nature particularly in material design and protein structure. Surprisingly, little is known…
The principle of permanence of large eddies is one of the central pillars onto which our understanding of decaying homogeneous turbulence is built. The validity conditions of this principle have been thoroughly discussed for constant…
Aggregation of like-charged polymers is widely observed in biological and soft matter systems. In many systems, bundles are formed when a short-range attraction of diverse physical origin like charge-bridging, hydrogen-bonding or…
We consider a two-dimensional athermal binary mixture of Lennard-Jones particles with persistent random active forces. The liquid phase of this system for active forces exceeding a threshold value exhibits self-organization with long-range…
Model robustness indicates a model's capability to generalize well on unforeseen distributional shifts, including data corruptions and adversarial attacks. Data augmentation is one of the most prevalent and effective ways to enhance…
This work addresses the topic of knotted stable structures in excitable media. These structures appear in a wide variety of situations, such as cardiac fibrillation, chemical reactions, etc. Entangled curves have been found in numerical…
Through the enhancement of transport, turbulence is expected to contribute to the fast reconnection. However the effects of turbulence are not so straightforward. In addition to the enhancement of transport, turbulence under some…
Understanding which system structure can sustain stable dynamics is a fundamental step in the design and analysis of large scale dynamical systems. Towards this goal, we investigate here the structural stability of systems with a random…
We investigate stability of a solution of a hybrid system in the sense that the graphs of solutions from nearby initial conditions remain close and tend towards the graph of the given solution. In this manner, a small continuous-time…
Recently it has been reported that biased range-measurements among neighboring agents in the gradient distance-based formation control can lead to predictable collective motion. In this paper we take advantage of this effect and by…
Synthetic turbulence is a relevant tool to study complex astrophysical and space plasma environments inaccessible by direct simulation. However, conventional models lack intermittent coherent structures, which are essential in realistic…
This paper studies consensus problems for multi-agent systems defined on directed graphs where the consensus dynamics involves nonlinear and discontinuous functions. Sufficient conditions, involving the nonlinear functions and the topology…
This article is concerned with the stability and long-time dynamics of structures arising from a structureless state. The paradigm is suggested by developmental biology, where morphogenesis is thought to result from a competition between…