Liquid-Solid Transitions with Applications to Self-Assembly.

We study the thermodynamic and kinetic pathways by which liquids transform into solids, and their relation to the metastable states that commonly arise in self-assembly applications. As a case study in the formation of ordered metastable solids, we investigate the atomistic mechanism by which quasicrystals form. We show that the aperiodic growth of quasicrystals is controlled by the ability of the growing quasicrystal "nucleus" to incorporate kinetically trapped atoms into the solid phase with minimal rearrangement. In a related study, we propose a two-part mechanism for forming 3d dodecagonal quasicrystals by self-assembly. Our mechanism involves (1) attaching small mobile particles to the surface of spherical particles to encourage icosahedral packing and (2) allowing a subset of particles to deviate from the ideal spherical shape, to discourage close-packing. In addition to studying metastable ordered solids, we investigate the phenomenology and mechanism of the glass transition. We report measurements of spatially heterogeneous dynamics in a system of air-driven granular beads approaching a jamming transition, and show that the dynamics in our granular system are quantitatively indistinguishable from those for a supercooled liquid approaching a glass transition. In a second study of the glass transition, we use transition path sampling to study the structure, statistics and dynamics of localized excitations for several model glass formers. We show that the excitations are sparse and localized, and their size is temperature-independent. We show that their equilibrium concentration is proportional to exp[-Ja(1/T-1/To)], where "Ja" is the energy scale for irreversible particle displacements of length "a," and "To" is an onset temperature. We show that excitation dynamics is facilitated by the presence of other excitations, causing dynamics to slow in a hierarchical way as temperature is lowered. To supplement our studies of liquid-solid transitions, we introduce a shape matching framework for characterizing structural transitions in systems with complex particle shapes or morphologies. We provide an overview of shape matching methods, explore a particular class of metrics known as "harmonic descriptors," and show that shape matching methods can be applied to a wide range of nanoscale and microscale assembly applications.Ph.D.Chemical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/78931/1/askeys_1.pd

Logic and intuition in architectural modelling: philosophy of mathematics for computational design

This dissertation investigates the relationship between the shift in the focus of architectural modelling from object to system and philosophical shifts in the history of mathematics that are relevant to that change. Particularly in the wake of the adoption of digital computation, design model spaces are more complex, multidimensional, arguably more logical, less intuitive spaces to navigate, less accessible to perception and visual comprehension. Such spatial issues were encountered much earlier in mathematics than in architectural modelling, with the growth of analytical geometry, a transition from Classical axiomatic proofs in geometry as the basis of mathematics, to analysis as the underpinning of geometry. Can the computational design modeller learn from the changing modern history, philosophy and psychology of mathematics about the construction and navigation of computational geometrical architectural system model space? The research is conducted through a review of recent architectural project examples and reference to three more detailed architectural modelling case studies. The spatial questions these examples and case studies raise are examined in the context of selected historical writing in the history, philosophy and psychology of mathematics and space. This leads to conclusions about changes in the relationship of architecture and mathematics, and reflections on the opportunities and limitations for architectural system models using computation geometry in the light of this historical survey. This line of questioning was motivated as a response to the experience of constructing digital associative geometry models and encountering the apparent limits of their flexibility as the graph of dependencies grew and the messiness of the digital modelling space increased. The questions were inspired particularly by working on the Narthex model for the Sagrada Família church, which extends to many tens of thousands of relationships and constraints, and which was modelled and repeatedly partially remodelled over a very long period. This experience led to the realisation that the limitations of the model were not necessarily the consequence of poor logical schema definition, but could be inevitable limitations of the geometry as defined, regardless of the means of defining it, the ‘shape’ of the multidimensional space being created. This led to more fundamental questions about the nature of Space, its relationship to geometry and the extent to which the latter can be considered simply as an operational and notational system. This dissertation offers a purely inductive journey, offering evidence through very selective examples in architecture, architectural modelling and in the philosophy of mathematics. The journey starts with some questions about the tendency of the model space to break out and exhibit unpredictable and not always desirable behaviour and the opportunities for geometrical construction to solve these questions is not conclusively answered. Many very productive questions about computational architectural modelling are raised in the process of looking for answers