The Capture of Spring: Hooke’s “Vibrative Pulse Communicated”

In 1678, Robert Hooke published a treatise on his metaphysics of vibration. Lectures de Potentia Restitutiva or Of Spring contains not only experimental and geometrical demonstrations of the spring law (which mutated into Hooke’s law after his time), but also a principle at the heart of his dynamic matter theory – Congruity and Incongruity. Namely, that harmonious and discordant forces unify, shape and separate vibrating matter. This thesis reconstructs Hooke’s production of congruity and incongruity, and the spring law, analysing the inversions, reversals and paradoxes moulding his knowledge-making practices. I argue that artificial instruments and apparatuses capable of magnifying and measuring never-before-seen minute bodies and motions also made the creation of a novel geometry necessary. I attempt to show how Hooke addressed these challenges by reassessing and reconfiguring the role of traditional Euclidean geometry, and reformulating practical-geometrical definitions to create a geometry that could demonstrate the spring law. Specifically, I focus on Hooke’s studies of vibrating bodies and vibrations, and his practical geometry. By investigating Hooke’s studies within the context of his matter theory, I show that, in an epistemological inversion, Hooke used optical instruments to shift frames of reference from the microscopic to the celestial and vice versa for his knowledge production. Further, Hooke’s work is a cohesive whole centred on his studies of the similitudes between vibrating phenomena. Finally, his knowledge-making practices are a conflation of his predominant careers as an experimentalist and geometer. By constructing natural laws from physical reality, thereby implying that nature, artificial instruments, and laws such as the spring law are related, Hooke legitimised the application of instruments and mathematics to the study of nature. This process was far from straightforward or self-evident

Fundamentals of flow through packed beds

Since the time of D'Arcy, the study of the flow of fluids through packed beds of particles has used a convenient analogy from electrical theory. Resistivity, or its inverse, permeability is ascribed to the bed and, at low Reynolds numbers at least, this property is sufficient to describe the behaviour of flow. However, the permeability of a bed is not the fundamental property that electrical resistivity is and it is necessary to relate it to a more fundamental property of the system if it is ever to be possible to exercise predictable control over it. In this thesis, the relationship between the permeability of a bed and the particle size distribution of its constituent particles is considered. A literature review is presented which surveys all the attempts which have partially succeeded in producing such a relationship. A new theoretical model, based on the mean pore diameter and tortuosity is derived which relates the permeability of a bed directly to its particle size distribution. Experimental measurements of permeability are presented and compare well with the model in some cases. In other cases, the bed is found to be unstable and the permeability of the bed is itself influenced by the flow of fluid. The reasons for the instability of the bed are discussed

The behaviour of a bed of particles under the influence of shear stress

The four characterisation groups of microscopic, state, macroscopic and behavioural properties are discussed for a packed system of particles, with particular reference to the shear strength and flow behaviour of particulate material. The relationships between the behavioural and macroscopic and between the behavioural and microscopic properties have been shown to be deficient in dBscribing what actually happens with a material under shear stress. It is postulated that a clearer understanding of the flow behaviour of particulate material will be obtained when the relationships have been obtained between the microscopic, state and macroscopic properties. The present links between these groups are reviewed and discussed. [Continues.

Self Assembly Problems of Anisotropic Particles in Soft Matter.

Anisotropic building blocks assembled from colloidal particles are attractive building blocks for self-assembled materials because their complex interactions can be exploited to drive self-assembly. In this dissertation we address the self-assembly of anisotropic particles from multiple novel computational and mathematical angles. First, we accelerate algorithms for modeling systems of anisotropic particles via massively parallel GPUs. We provide a scheme for generating statistically robust pseudo-random numbers that enables GPU acceleration of Brownian and dissipative particle dynamics. We also show how rigid body integration can be accelerated on a GPU. Integrating these two algorithms into a GPU-accelerated molecular dynamics code (HOOMD-blue), make a single GPU the ideal computing environment for modeling the self-assembly of anisotropic nanoparticles. Second, we introduce a new mathematical optimization problem, filling, a hybrid of the familiar shape packing and covering problem, which can be used to model shaped particles. We study the rich mathematical structures of the solution space and provide computational methods for finding optimal solutions for polygons and convex polyhedra. We present a sequence of isosymmetric optimal filling solutions for the Platonic solids. We then consider the filling of a hyper-cone in dimensions two to eight and show the solution remains scale-invariant but dependent on dimension. Third, we study the impact of size variation, polydispersity, on the self-assembly of an anisotropic particle, the polymer-tethered nanosphere, into ordered phases. We show that the local nanoparticle packing motif, icosahedral or crystalline, determines the impact of polydispersity on energy of the system and phase transitions. We show how extensions of the Voronoi tessellation can be calculated and applied to characterize such micro-segregated phases. By applying a Voronoi tessellation, we show that properties of the individual domains can be studied as a function of system properties such as temperature and concentration. Last, we consider the thermodynamically driven self-assembly of terminal clusters of particles. We predict that clusters related to spherical codes, a mathematical sequence of points, can be synthesized via self-assembly. These anisotropic clusters can be tuned to different anisotropies via the ratio of sphere diameters and temperature. The method suggests a rich new way for assembling anisotropic building blocks.Ph.D.Applied Physics and Scientific ComputingUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/91576/1/phillicl_1.pd