Computational automation for efficient design of acoustic metamaterials

Acoustic metamaterials (AMMs) are an exciting technology because they are capable of responding to vibrations in ways that are impossible to achieve with conventional materials. However, realization of AMMs requires engineering design to provide a connection between first-principles research and production of parts that perform as expected. Designing AMMs is a challenging endeavor because evaluating designs is costly and manufacturing metamaterials requires precise techniques with small minimum resolutions. To address these challenges, new computational tools are necessary to aid design. This work proposes three tasks that improve the capabilities of design for AMM while being extensible to other engineering design automation tasks. The first task is to develop a design exploration tool that improves the computational efficiency of identifying sets of high-performing designs in a design space that is sparse and comprises mixed discrete/continuous data. The second task is to develop a process for designers to evaluate manufacturability of difficult-to-manufacture parts and drive co-development of manufacturing methods and AMM. In the final task, a machine learning based method is developed to efficiently model AMM with heterogeneous arrangements of their microstructures such that strict homogenization is infeasible. The outcomes from completing these tasks will provide a significant and novel improvement over existing methods of designing AMMs.Mechanical Engineerin

Research in Applied Mathematics, Fluid Mechanics and Computer Science

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period October 1, 1998 through March 31, 1999

Reinforcing connectionism: learning the statistical way

Connectionism's main contribution to cognitive science will prove to be the renewed impetus it has imparted to learning. Learning can be integrated into the existing theoretical foundations of the subject, and the combination, statistical computational theories, provide a framework within which many connectionist mathematical mechanisms naturally fit. Examples from supervised and reinforcement learning demonstrate this. Statistical computational theories already exist for certainn associative matrix memories. This work is extended, allowing real valued synapses and arbitrarily biased inputs. It shows that a covariance learning rule optimises the signal/noise ratio, a measure of the potential quality of the memory, and quantifies the performance penalty incurred by other rules. In particular two that have been suggested as occuring naturally are shown to be asymptotically optimal in the limit of sparse coding. The mathematical model is justified in comparison with other treatments whose results differ. Reinforcement comparison is a way of hastening the learning of reinforcement learning systems in statistical environments. Previous theoretical analysis has not distinguished between different comparison terms, even though empirically, a covariance rule has been shown to be better than just a constant one. The workings of reinforcement comparison are investigated by a second order analysis of the expected statistical performance of learning, and an alternative rule is proposed and empirically justified. The existing proof that temporal difference prediction learning converges in the mean is extended from a special case involving adjacent time steps to the general case involving arbitary ones. The interaction between the statistical mechanism of temporal difference and the linear representation is particularly stark. The performance of the method given a linearly dependent representation is also analysed

Quantification of Localized Brain Iron Sources Using Magnetic Resonance Phase

Brain microbleeds (BMB), often present in cerebrovascular and neurodegenerative diseases and neurotrauma, are associated with both chronic and acute illness of significant social and economic impact. Because BMB present a source of potentially cyctotoxic iron to the brain proportional to the amount of extravasated blood, non-invasive quantification of this iron pool is potentially valuable both to assess tissue risk and as a biomarker to monitor disease progression, treatment efficacy, and inform treatment. Past efforts to quantify brain iron have focused on distributed (e.g., anatomical) brain regions. However, BMB represent localized sources of iron deposition. In addition, conventional magnitude MR images have significant limitations, especially for localized iron quantification. Moreover, due to susceptibility effects, the localized bypointensities in gradient recalled T2* magnitude images associated with BMB typically appear larger than the actual tissue lesion (the blooming effect) and obscure the true dimensions of an iron susceptibility source. In the present research, we proposed a family of techniques that use magnetic resonance phase images (instead of magnitude images) to quantify the iron content and dimensions of localized iron sources such as BMB. The techniques were tested in four systems: 1) magnetic resonance agarose phantom and 2) postmortem rat brain, using a ferric iron oxy0hydroxide mimic for hemosiderin, 3) the living rat brain, using collagenase-induced bleeds, and 4) with actual BMB in postmortem cerebral amyloid angiopathy brain. Measurements of geometric features in phase images were related to source iron content and diameter using mathematical models. Iron samples and BMB lesions were assayed for iron content using atomic absorption spectrometry. Results from experiments 1 and 3 in particular showed very good agreement with predictions of the theory underlying the techniques, providing validation for the methods and demonstrating that prominent phase image features can potentially be used to measure localized iron content including iron in real BMB. Our methods potentially allow the calculation of brain iron load indices based on BMB iron content as well as classification of BMB by size unobscured by the blooming effect. These results represent significant steps toward the use of similar localized iron quantification methods in experimental and clinical settings

Doctor of Philosophy

dissertationThe goal of the work presented in this dissertation was to find out how physical ordering of organic semiconductors affects spin-dependent electronic charge carrier transitions. Organic light emitting diodes in distinct morphological phases were created out of thin films of the -conjugated polymer poly[9,9-dioctylfluorenyl-2,7-diyl] (polyfluorene), allowing diodes to be studied with the sole difference being the degree of polymeric order in the active layer of the device. The polyfluorene morphologies studied ranged from an amorphous (glassy) phase through mixed phases, to a highly ordered (beta) phase. The phase control was achieved through a dipping procedure where a glassy polyfluorene layer is immersed in a solvent mixture that structures the side chains of a monomer unit into an alternating planar ladder structure. Continuous-wave (cw) and pulsed (p) electrically detected magnetic resonance (EDMR) spectroscopies were used to probe charge carrier spin states within the polyfluorene layers. For cw EDMR, microwave frequencies between ~1 and 20 GHz were used, while all pEDMR measurements were conducted at X-band (~9.6 GHz). The experiments allowed for a comparison of how polymer morphology affects spin-dependent charge carrier transitions, coherent spin motion, spin relaxation times, the local nuclear (hyperfine) magnetic fields and spin-orbit effects. In addition to film morphology, temperature and device-bias dependencies of the spin-dependent charge carrier transitions were studied experimentally and a set of global fit and bootstrap error analysis techniques were adapted for EDMR spectroscopy

Random dynamics in collective behaviour: consensus, clustering & extinction of populations

Le modèle de la chambre d'écho décrit le développement de groupes dans des réseaux sociaux hétérogènes. Par réseau social hétérogène, nous entendons un ensemble d'individus dont chacun représente exactement une opinion. Les relations existantes entre les individus peuvent alors être représentées par un graphique. Le modèle de la chambre d'écho est un modèle discret dans le temps qui, à l'instar d'un jeu de société, se déroule par coups. A chaque tour, une relation existante est sélectionnée de manière aléatoire et uniforme dans le réseau et les deux individus reliés interagissent. Si les opinions des individus concernés sont suffisamment similaires, ils continuent à se rapprocher dans leurs opinions, alors que dans le cas d'opinions trop éloignées, ils rompent leur relation et un des individus cherche une nouvelle relation. Dans ce travail, nous examinons les éléments constitutifs de ce modèle. Nous partons de l'observation que les changements de structure des relations dans le réseau peuvent être décrits par un système de particules en interaction dans un espace plus abstrait. Ces réflexions conduisent à la définition d'un nouveau graphe abstrait qui englobe toutes les configurations relationnelles possibles du réseau social. Cela nous fournit la compréhension géométrique nécessaire pour analyser les composantes dynamiques du modèle de chambre d'écho dans la partie III. Dans un premier temps, dans la partie 7, nous laissons de côté les opinions des individus et supposons que la position des arêtes change à chaque coup comme décrit précédemment, afin d'obtenir une compréhension de base de la dynamique sous-jacente. En utilisant la théorie des chaînes de Markov, nous trouvons des limites supérieures à la vitesse de convergence d'une chaîne de Markov associée vers sa distribution stationnaire unique et montrons qu'il existe des réseaux identifiables entre eux et non apparents dans la dynamique analysée, en ce sens que la distribution stationnaire de la chaîne de Markov associée attribue le même poids à ces réseaux. Dans les cas réversible, nous nous concentrons en particulier sur la forme explicite de la distribution stationnaire ainsi que sur les limites inférieures de la constante de Cheeger pour décrire la vitesse de convergence. Le résultat final de la section 8, basé sur les chaînes de Markov absorbantes, montre que dans une version réduite du modèle de la chambre d'écho, une structure hiérarchique du nombre de relations conflictuelles peut être identifiée. Nous pouvons utiliser cette structure pour déterminer une limite supérieure au temps d'absorption attendu, à l'aide d'une distribution quasi-stationnaire. Cette hiérarchie de la structure constitue également un pont vers les théories classiques des processus de mort pur. Nous concluons en montrant comment les recherches futures peuvent exploiter ce lien et en discutant de l'importance des résultats comme éléments constitutifs d'une compréhension théorique complète du modèle de la chambre d'écho. Enfin, la partie IV présente un article publié consacré au processus de naissance-mort avec catastrophe partielle. L'article repose d'une part, le calcul explicite du premier moment d'une catastrophe. Cette première partie est entièrement basée sur une approche analytique des récurrences du second degré à coefficients linéaires. La convergence vers 0 de la suite résultante ainsi que la vitesse de convergence sont prouvées. D'autre part, la détermination des limites supérieures de la valeur attendue de la taille de la population ainsi que de la variance de celle-ci et de la différence entre la limite supérieure déterminée et la valeur réelle de la valeur attendue. Pour ces résultats, nous utilisons presque exclusivement la théorie des équations différentielles non linéaires ordinaires.The echo chamber model describes the development of groups in heterogeneous social networks. By heterogeneous social network we mean a set of individuals, each of whom represents exactly one opinion. The existing relationships between individuals can then be represented by a graph. The echo chamber model is a time-discrete model which, like a board game, is played in rounds. In each round, an existing relationship is randomly and uniformly selected from the network and the two connected individuals interact. If the opinions of the individuals involved are sufficiently similar, they continue to move closer together in their opinions, whereas in the case of opinions that are too far apart, they break off their relationship and one of the individuals seeks a new relationship. In this paper we examine the building blocks of this model. We start from the observation that changes in the structure of relationships in the network can be described by a system of interacting particles in a more abstract space. These reflections lead to the definition of a new abstract graph that encompasses all possible relational configurations of the social network. This provides us with the geometric understanding necessary to analyse the dynamic components of the echo chamber model in Part III. As a first step, in Part 7, we leave aside the opinions of the inidividuals and assume that the position of the edges changes with each move as described above, in order to obtain a basic understanding of the underlying dynamics. Using Markov chain theory, we find upper bounds on the speed of convergence of an associated Markov chain to its unique stationary distribution and show that there are mutually identifiable networks that are not apparent in the dynamics under analysis, in the sense that the stationary distribution of the associated Markov chain gives equal weight to these networks. In the reversible cases, we focus in particular on the explicit form of the stationary distribution as well as on the lower bounds of the Cheeger constant to describe the convergence speed. The final result of Section 8, based on absorbing Markov chains, shows that in a reduced version of the echo chamber model, a hierarchical structure of the number of conflicting relations can be identified. We can use this structure to determine an upper bound on the expected absorption time, using a quasi-stationary distribution. This hierarchy of structure also provides a bridge to classical theories of pure death processes. We conclude by showing how future research can exploit this link and by discussing the importance of the results as building blocks for a full theoretical understanding of the echo chamber model. Finally, Part IV presents a published paper on the birth-death process with partial catastrophe. The paper is based on the explicit calculation of the first moment of a catastrophe. This first part is entirely based on an analytical approach to second degree recurrences with linear coefficients. The convergence to 0 of the resulting sequence as well as the speed of convergence are proved. On the other hand, the determination of the upper bounds of the expected value of the population size as well as its variance and the difference between the determined upper bound and the actual value of the expected value. For these results we use almost exclusively the theory of ordinary nonlinear differential equations

Visually guided flight in birds using the budgerigar (Melopsittacus undulatus) as a model system

Keywords: Edge detection, Optic flow, Obstacle avoidanc

In-situ TEM Investigation of Rapid Solidification of Aluminum and Aluminum Copper Alloys

Measuring and observing rapidly evolving interfaces of irreversible transient states such as rapid solidification have been a long time standing problem in materials science as characterization techniques that deliver the necessary requirements, i.e. nanosecond temporal and nano-meter spatial resolution, have not been present. Dynamical TEM utilizes a process initiation photon laser pulse coupled with a timed electron pulse train to observe transient states of rapidly evolving phase transformations. Nanoscale spatio-temporal resolution in-situ TEM revealed growth mode changes and enabled quantitative measurements of locally resolved instantaneous and averaged interface velocities for pure Aluminum and hypo-eutectic Aluminum-Copper alloys. Post-mortem TEM was employed to gain insights on micro-structural evolution morphology regarding texture, morphology changes, grain size and grain size development, phase formation and orientations relationships during the laser processing. Post-mortem TEM studies revealed that resultant microstructures found in thin film solidification are equivalent with microstructures found in bulk sample experimentation utilizing CW-lasers. DTEM allows systematical studies of far-from equilibrium phase transformation and were employed to investigate PL initiated directional rapid solidification in Al and Al-Cu alloys