Stochastic Lattice | A Generative Design Tool for Material Conscious Free Form Timber Surface Architecture

This thesis attempts to resolve the contradictory relationship between the ecological merits of wood construction and the significant material intensity of recent free form timber surface structures. The building industry is now adept in the design and construction of freeform surface architecture, however new challenges have been introduced with the environmentally conscious desire to build these structures in wood. Lacking the formal versatility of steel and concrete, wood introduces a great deal of difficulty in the realization of complex form at an architectural scale. Powerful digital design and fabrication tools have recently made it possible to model, analyze and construct these buildings, but at the cost of heavy structural solutions that involve energy intensive fabrication processes and significant material waste. This approach contradicts the ecological benefits of wood, and raises the question of whether it is possible to achieve free and expressive form in timber surface architecture while maintaining an economy of means and material. This question is addressed through the development of a generative design tool for the creation of material conscious free form timber surface architecture. The formation of the tool is informed by the field of computational morphogenesis, which draws from the natural growth processes of biological structures in the virtual synthesis of form. The tool is conceived as a morphogenetic material system, which consists of a generative algorithm that integrates material, structure and form in a single computational process. Specific material saving techniques deployed in the algorithm draw from existing research in timber shell design and material optimization. Established methods in the use of geodesic lines for the structural patterning of wood shells and stress driven material distribution make up the core concepts deployed in the algorithm. The material system is developed, refined and tested through the design and construction of an experimental free form timber lattice

Novel inverse methods for crystal self-assembly

Inverse design methods are a promising new strategy to aid the discovery of materials with targeted properties. In this thesis, we employ two novel inverse design methods and apply it to the study of crystal self-assembly in two dimensions. In particular, we introduce a novel zero temperature (ground state -GS) analytical method and find effective interactions that stabilize targeted lattices by means of a constrained non-linear optimization. We demonstrate advantages of this new formulation by designing a square lattice to display increasing energetic differences over relevant lattice competitors and show that such constraints correlate with crystal thermal stability. However, these constraints also reduce density range representation of the target lattice in its phase diagram and suggests an inherent tradeoff in the constrained strategy. Having established a link between crystal property and constraint type, we design the snubsquare lattice by means of energetic constraints over close competitors and show this is in contrast to the design of the kagome lattice which required no such constraints. We then test the limits of the GS method and design the open and challenging truncated square (TS) and truncated hexagonal lattices (TH). Unlike the previous targets, these lattices require the inclusion of a large pool of competitor micro-phases that greatly complicate optimization. Nevertheless, we show the system is still solvable by judicious use of constraints and decision variables. Next, we use a novel relative entropy minimization approach (RE) and the GS method to explore the design space of particles interacting via a potential featuring a single attractive well. Specifically, we design a square, honeycomb and kagome lattice and show that we are able to infer a set of `design rules' from generalities of the resulting interactions in both methods. We validate these rules by designing the challenging TS and TH lattices and show that optimized interactions readily promote target assembly from the fluid state. Finally, we expand the RE method to accommodate multi-component systems and inverse design a variety of crystal binary mixtures featuring triangular, square as well as other intricate and open motifs. We demonstrate how binary systems can help achieve equivalent single component structures but with simpler underlying interactions. Further, we analyze the binary assembly process and find that self interactions act as a `primer' that place particles in the correct local positions while cross interactions, through system coupling, act as the `binder' that lock particles into the correct binary structure.Chemistr

Finite difference and finite volume methods for wave-based modelling of room acoustics

Wave-based models of sound propagation can be used to predict and synthesize sounds as they would be heard naturally in room acoustic environments. The numerical simulation of such models with traditional time-stepping grid-based methods can be an expensive process, due to the sheer size of listening environments (e.g., auditoriums and concert halls) and due to the temporal resolution required by audio rates that resolve frequencies up to the limit of human hearing. Finite difference methods comprise a simple starting point for such simulations, but they are known to suffer from approximation errors that may necessitate expensive grid refinements in order to achieve sufficient levels of accuracy. As such, a significant amount of research has gone into designing finite difference methods that are highly accurate while remaining computationally efficient. The problem of designing and using accurate finite difference schemes is compounded by the fact that room acoustics models require complex boundary conditions to model frequency-dependent wall impedances over non-trivial geometries. The implementation of such boundary conditions in a numerically stable manner has been a challenge for some time. Stable boundary conditions for finite difference room acoustics simulations have been formulated in the past, but generally they have only been useful in modelling trivial geometries (e.g., idealised shoebox halls). Finite volume methods have recently been shown to be a viable solution to the problem of complex boundary conditions over non-trivial geometries, and they also allow for the use of energy methods for numerical stability analyses. Finite volume methods lend themselves naturally to fully unstructured grids and they can simplify to the types of grids typically used in finite difference methods. This allows for room acoustics simulation models that balance the simplicity of finite difference methods for wave propagation in air with the detail of finite volume methods for the modelling of complex boundaries. This thesis is an exploration of these two distinct, yet related, approaches to wave-based room acoustic simulations. The overarching theme in this investigation is the balance between accuracy, computational efficiency, and numerical stability. Higher-order and optimised schemes in two and three spatial dimensions are derived and compared, towards the goal of finding accurate and efficient finite difference schemes. Numerical stability is analysed using frequency-domain analyses, as well as energy techniques whenever possible, allowing for stable and frequency-dependent boundary conditions appropriate for room acoustics modelling. Along the way, the use of non-Cartesian grids is investigated, geometric relationships between certain finite difference and finite volume schemes are explored, and some problems associated to staircasing effects at boundaries are considered. Also, models of sound absorption in air are incorporated into these numerical schemes, using physical parameters that are appropriate for room acoustic scenarios

Symmetry in Applied Mathematics

Applied mathematics and symmetry work together as a powerful tool for problem reduction and solving. We are communicating applications in probability theory and statistics (A Test Detecting the Outliers for Continuous Distributions Based on the Cumulative Distribution Function of the Data Being Tested, The Asymmetric Alpha-Power Skew-t Distribution), fractals - geometry and alike (Khovanov Homology of Three-Strand Braid Links, Volume Preserving Maps Between p-Balls, Generation of Julia and Mandelbrot Sets via Fixed Points), supersymmetry - physics, nanostructures -chemistry, taxonomy - biology and alike (A Continuous Coordinate System for the Plane by Triangular Symmetry, One-Dimensional Optimal System for 2D Rotating Ideal Gas, Minimal Energy Configurations of Finite Molecular Arrays, Noether-Like Operators and First Integrals for Generalized Systems of Lane-Emden Equations), algorithms, programs and software analysis (Algorithm for Neutrosophic Soft Sets in Stochastic Multi-Criteria Group Decision Making Based on Prospect Theory, On a Reduced Cost Higher Order Traub-Steffensen-Like Method for Nonlinear Systems, On a Class of Optimal Fourth Order Multiple Root Solvers without Using Derivatives) to specific subjects (Facility Location Problem Approach for Distributed Drones, Parametric Jensen-Shannon Statistical Complexity and Its Applications on Full-Scale Compartment Fire Data). Diverse topics are thus combined to map out the mathematical core of practical problems

Anisotropic particles at liquid interfaces

In this thesis we study the adsorption dynamics and self-assembly of anisotropic particles at a liquid-liquid interface. Firstly, we couple a Langevin dynamics model with the high-resolution finite element analysis software package Surface Evolver, which explicitly includes interfacial deformations, to study the adsorption dynamics of ellipsoidal particles. Transient contact line pinning due to nanoscale defects on the particle surface are also included by renormalising particle friction coefficients and using dynamic contact angles relevant to the adsorption timescale. We reproduce the monotonic variation of particle orientation with time that is observed experimentally and are able to quantitatively model the adsorption dynamics for some experimental ellipsoidal systems but not others. However, even for the latter case, our model accurately captures the adsorption trajectory (i.e., particle orientation vs. height) of said particles.Secondly, we extend our theoretical model to study cylindrical particles with the goal of using the adsorption kinetics of cylindrical nanorods at a liquid interface as a novel alternative route for assembling vertically aligned nanorod arrays. We find that the final orientation of non-neutrally wetting cylindrical nanorods is determined by their initial attack angle when they contact the liquid interface. Furthermore, the range of attack angles leading to the end-on state is maximised when nanorods approach the liquid interface from the bulk phase that is more energetically favorable.Finally, we move from the role anisotropy plays in the adsorption process to investigating how particle anisotropy can be utilized to direct the self-assembly of particles adsorbed at a liquid-liquid interface. Specifically, by modeling undulating hexagonal-like platelets and changing the relative phase axis of the undulation’s peaks and the hexagonal particles vertices, we can direct the assembly to a number of different self-assembled ground states including hexagonal close packed, honeycomb and kagome lattices