arXiv subjects

William Stephenson

Publications and source records attributed to William Stephenson.

4 recordsLinked to original sources

arXiv2025

Rigidity of generic random tensegrity structures

Many mechanical structures, both engineered and biological, combine heavy rigid elements such as bones and beams with lightweight flexible ones such as cables and membranes. These are referred to as tensegrities, reflecting that cables can only support extensile tension. We model such systems via simulations of depleted triangular lattices in which we minimize the energies of tensegrities subject to strained boundary conditions. When there are equal numbers of cables and struts (which support only compressive tension), a cable and a strut together each contribute as much toward rigidity as a rod, with the two contributions being equal in the case of shear strain. Due to the highly nonaffine deformations at the rigidity transitions, the contribution of a cable (strut) can be significant even under global compression (dilation) despite a cable's inability to resist local compression. Further, we find that when neighboring elements tend to point away from one another, as is common in real systems, cables interact significantly more strongly with other cables than do cables with struts in supporting stress. These phenomena shed new light on a variety of realistic, disordered systems at the threshold of mechanical stability.

cond-mat.soft↗

arXiv2025

A unified model for linear responses of physical networks

Many physical systems--from mechanical lattices and electrical circuits to biological tissues and architected metamaterials--can be understood as networks transmitting physical quantities. We present a unified mathematical framework for describing linear responses of such physical networks using tools from algebraic graph theory. This approach captures static and dynamic behaviors across multiple domains, including mechanical, electrical, thermal, and diffusive responses using node and edge variables (e.g., potentials, flows). Our formalism connects multiscale and multi-domain responses to the underlying network structure. We demonstrate how this framework enables efficient, generalizable solutions to a wide class of linear response problems, including stress propagation, charge transport, and wave dynamics, and provide insights into network duality and entropy production.

cond-mat.soft↗

arXiv2022

Rigidity percolation in a random tensegrity via analytic graph theory

Functional structures from across the engineered and biological world combine rigid elements such as bones and columns with flexible ones such as cables, fibers and membranes. These structures are known loosely as tensegrities, since these cable-like elements have the highly nonlinear property of supporting only extensile tension. Marginally rigid systems are of particular interest because the number of structural constraints permits both flexible deformation and the support of external loads. We present a model system in which tensegrity elements are added at random to a regular backbone. This system can be solved analytically via a directed graph theory, revealing a novel mechanical critical point generalizing that of Maxwell. We show that even the addition of a few cable-like elements fundamentally modifies the nature of this transition point, as well as the later transition to a fully rigid structure. Moreover, the tensegrity network displays a fundamentally new collective avalanche behavior, in which the addition of a single cable leads to the elimination of multiple floppy modes, a phenomenon that becomes dominant at the transition point. These phenomena have implications for systems with nonlinear mechanical constraints, from biopolymer networks to soft robots to jammed packings to origami sheets.

cond-mat.soft↗

arXiv2018

Global-Local Airborne Mapping (GLAM): Reconstructing a City from Aerial Videos

Monocular visual SLAM has become an attractive practical approach for robot localization and 3D environment mapping, since cameras are small, lightweight, inexpensive, and produce high-rate, high-resolution data streams. Although numerous robust tools have been developed, most existing systems are designed to operate in terrestrial environments and at relatively small scale (a few thousand frames) due to constraints on computation and storage. In this paper, we present a feature-based visual SLAM system for aerial video whose simple design permits near real-time operation, and whose scalability permits large-area mapping using tens of thousands of frames, all on a single conventional computer. Our approach consists of two parallel threads: the first incrementally creates small locally consistent submaps and estimates camera poses at video rate; the second aligns these submaps with one another to produce a single globally consistent map via factor graph optimization over both poses and landmarks. Scale drift is minimized through the use of 7-degree-of-freedom similarity transformations during submap alignment. We quantify our system's performance on both simulated and real data sets, and demonstrate city-scale map reconstruction accurate to within 2 meters using nearly 90,000 aerial video frames - to our knowledge, the largest and fastest such reconstruction to date.

cs.CV↗