Talks and presentations for various audiences.
A mechanical model for thin sheets
Audience: Technical, soft matter physics community
Simulations of thin sheets are a valuable tool for augmenting experimental data sets and revealing the hidden internal dynamics of the sheet’s deformations. However, it is challenging to develop a model that performs independently of the underlying mesh topology, maps to physical parameters, and scales in a computationally efficient way. Here we employ a mechanical model for a thin sheet based on a general triangular mesh, with linear springs along edges and torsion springs between adjacent triangles. We develop a procedure for locally setting spring constants to match continuum mechanical properties. We test the model's accuracy by running simulations of instabilities in twisted elastic ribbons. We also develop an extension to the model that captures the phenomenology of plastic damage accumulation. Our simulations bridge the gap between image-based experimental data and energy-based theoretical analysis of thin sheet deformations by generating data with fine temporal and spatial resolution.
Buckling, wrinkling, crumpling-- oh my! Simulations of thin sheet deformations
Audience: General, undergraduate physics majors
Buckling, wrinkling, and crumpling occur across all length scales, from thermal fluctuations in thin sheets of graphene to the large scale deformation of the Earth's crust. Sometimes these phenomena arise as a feature (such as the energy-dissipating crushing of a car body during a collision), and other times as a bug (like material damage or failure in industrial processes). If we can learn to predict and control these deformations, the consequences of buckling, wrinkling, and crumpling could be exploited to design programmable materials. These mechanical transitions remain poorly understood, though some progress has come through studying the crease network of physically crumpled thin sheets, or buckling instabilities of thin plates and rods. To supplement these experimental snapshots, we introduce an efficient computational model for thin sheets that reproduces their mechanical properties and captures the features of elastic buckling and plastic deformation. Our simulations allow careful analysis of the sheet's topography and curvature; temporal resolution of the buckling and crumpling transitions; and reveal the hidden internal energy dynamics of the evolving system.
A computational model of thin sheets crumpled via twisting
Audience: Technical, soft matter physics community
Crumpling occurs across all length scales, sometimes arising as a feature (such as the energy-dissipating crushing of a car body during a collision) and other times as a bug (like material damage or failure in industrial manufacturing processes). In all instances, it is essential we understand the complex buckling and wrinkling modes which result in disordered, crumpled configurations. These mechanical transitions remain poorly understood, although some progress has come through studying the crease networks of physically crumpled thin sheets. To supplement these experimental snapshots, we introduce an efficient computational model for thin sheets that reproduces their mechanical properties and captures the phenomenology of plastic deformation under confinement. Our simulations allow careful analysis of the sheet’s topography and curvature; temporal resolution of damage accumulation and ridge fragmentation; and reveal the hidden internal energy intricate, evolving system.
Applications of Gaussian Curvature in Physics
Audience: General, STEM undergraduates
Anyone who has ever attempted to gift wrap a basketball is familiar with surfaces of differing curvatures. Gift wrap is flat and cannot smoothly conform to the ball's curved surface. All surfaces can be characterized by their Gaussian curvature, which describes the geometry of the surface: Euclidean, elliptic, or hyperbolic. Furthermore, curvature dictates how a vector may be transported across the surface or within the space. Calculus and most of physics was formulated in Euclidean geometry, which assumes an identically flat space. However, non-Euclidean spaces arise naturally in the physical world, and are of particular interest in physics subfields such as General Relativity. Summarized here are the various types of geometries, how to determine the curvature of a given space or surface, and the geodesic movement of test particles in a curved spacetime. Finally, we explore the connections between geometry and physics, focusing on gravity as deviations in the curvature of spacetime.
The Stability of Condensed Dark Matter Candidates
Audience: Technical, cosmology/particle physics community
Axions are elementary particles, which have zero spin and obey Bose statistics, that have been postulated to solve the strong CP problem in quantum chromodynamics, the theory of strong interactions. At low temperatures bosons condense in the same energy state and form Bose-Einstein Condensates, due to their quantum mechanical properties. Further, these condensates, or "axion stars", are gravitationally bound. It has been proposed that axion stars could be contributing to dark matter. Previous studies have found axion stars have a dilute metastable state with a critical mass of ~10^19 kg and a radius of ~200 km. By improving previous approximations of the configuration's energy, we determine a stable dense state exists at a radius of ~10 m. Furthermore, if the mass of the axion star is supercritical (including masses much greater than 10^19 kg), the star will begin to collapse from its dilute state to the dense state. As it contracts, the star will decay and rapidly emit relativistic axions.