Colloidal particles on curved surfaces are widely used as biophysical models, for example, to study virus assembly and maturation or to represent proteins on cell membranes. The crystalline structure of these interacting colloidal particles influences the system's physical properties. Crystalline structures and their defects are often studied using Voronoi tessellations. Although Voronoi tessellation is a widely adopted and effective method to analyze colloidal structures on smooth and convex surfaces, it is often inadequate to study colloidal packing on non-convex, highly deformed surfaces. Computing order parameters is an alternative approach to identify lattice defects, but their accuracy depends on the definition of the search radius for neighboring interacting particles and other, often ad-hoc, criteria. This again hinders the applicability of order parameters to study the lattice's defects on highly deformed colloidal structures on 2D surfaces. To overcome these problems, I present a new tessellation algorithm based on a dynamic search for neighboring particles and a local triangulation that preserves the physics of the interaction between particles. The proposed algorithm is successful in constructing clean tessellation of particles on zero, positive, and negative Gaussian curvature surfaces and highly deformed substrates. In addition to enabling a better characterization of colloidal particles' structures, the proposed tessellation method may be leveraged to design an unfolding strategy for curved surfaces on a flat hexagonal template. This is demonstrated in a simple case scenario of an achiral icosahedral virus structure and the results are compared to the established Caspar-Klug construction. This example is a preliminary result for significantly more general applications related to unfolding 3D structures, which is a key process in micro fabrication, packaging, and the design of deployable structures.
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Master of Science in Mechanical Engineering (M.S.M.E.)
College of Engineering and Computer Science
Mechanical and Aerospace Engineering
Mechanical Engineering; Mechanical Systems Track
Length of Campus-only Access
Masters Thesis (Campus-only Access)
Sazzad, Shah Wasif, "A New Tessellation Algorithm for Interacting Particles on 2D Manifolds: From Locating Defects to Unfolding Structures" (2022). Electronic Theses and Dissertations, 2020-. 1435.
Restricted to the UCF community until December 2025; it will then be open access.