Calculations are presented for a series of interrelated problems in the theory of disordered solids. The simple mean field theory of tricriticality in the layered Ising metamagnet is modified by inclusion of the Bethe-Peierls equation of state for the planar interactions. The approximation allows for a model of dilution with a finite percolation concentration for the layers. The calculated behaviour as a function of dilution for anisotropic coupling strengths allows comparison with experimental results on dilute ferrous chloride. Estimation is made of the effects of treating fluctuations by theories with mean field singularities. A discussion is given of first order phase transitions in disordered systems. A mean field theory of the implications of introducing quenched disorder to a system undergoing a transition of first order is effected by reformulating the problem in terms of a translationally invariant one via the replica method. The conclusions are examined in terms of a simple scaling theory and criteria derived for smearing of the singularities. Dynamic and thermodynamic properties of diluted magnetic insulators near the percolation concentration are considered in terms of simple geometric models of the percolating cluster as introduced by de Gennes. New scaling relations for the spin wave stiffness and conductivity exponents are derived and differences from previous relations interpreted geometrically. The scaling models of the percolating cluster so found, in which correlations propagate locally via effectively one-dimensional paths, are applied to the determination of the mobility edge for spin wave excitations in a dilute Heisenberg magnet near the percolation threshold. A prediction for the functional form of the mobility edge is made by means of results known for the Anderson model and a localisation length derived from an exact solution of a random problem by Dyson.

Thesis (Ph. D.)--University of Missouri-Columbia, 2007. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on October 17, 2007) Vita. Includes bibliographical references.

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This dissertation comprises three articles that propose explanations for the eventual extinction of Neanderthals in Europe after a period of several thousand years of coexistence with anatomically modern humans (AMH). I propose that bioenergetic differences between Neanderthals and AMH favored the persistence of AMH. This difference in energetic efficiency was augmented by any behavior that was advantageous to AMH. Consequently, such behaviors directly impacted the rate of Neanderthal extinction. The first article proposes a mathematical model that reconstructs Neanderthal and AMH energetic budgets to predict how using fire for cooking might have affected the success of each species. I first use the model to establish that energetic differences alone result in Neanderthal extinction when Neanderthals and AMH occupy the same landscape. I then establish that cooking meat increases its caloric value, and incorporate that parameter into the model. The outcome indicates that differential fire use by Neanderthals and AMH significantly affects the rate of Neanderthal extinction. The second article analyzes the evidence for marrow and bone grease extraction from reindeer carcasses by Neanderthals and AMH during cold climate phases. I analyze two assemblages produced by Neanderthals and three produced by AMH to determine how each group exploited these crucial nutritional resources. Results indicate that marrow processing intensity correlates with site function rather than with human species while bone grease may have been more intensively processed by AMH. In the third article, I integrate these studies within a new theoretical framework combining self-organizing criticality (SOC) and resilience thinking (RT). I explore Neanderthal extinction across multiple scales. SOC explores how interactions at the scale of the individual can combine to cause events such as an extinction. RT provides a systems-level framework for understanding how patterns of change among Neanderthals, AMH, prey populations, and the landscapes they inhabit may lead to instability and collapse. I identify the arrival of AMH into a landscape occupied by Neanderthals as a threshold point that set the process of Neanderthal demise in motion. I then use SOC and RT together to explain Neanderthal extinction as a slow and patchy process, rather than a sudden extinction.

The brain is a complex system par excellence. Its intricate structure has become clearer recently, and it has been reported that it shares some properties common to complex networks, such as the small-world property, the presence of hubs, and assortative mixing, among others. These properties provide the brain with a robust architecture appropriate for efficient information transmission across different brain regions. Nevertheless, how these topological properties emerge in neural networks is still an open question. Moreover, in the last decade the observation of neuronal avalanches in neocortical circuits suggested the presence of self-organised criticality in neural systems. The occurrence of this kind of dynamics implies several benefits to neural computation. However, the mechanisms that give rise to critical behaviour in these systems, and how they interact with other neuronal processes such as synaptic plasticity are not fully understood. In this thesis, we study self-organised criticality and neural systems in the context of complex networks. Our work differs from other similar approaches by stressing the importance of analysing the influence of hubs, high clustering coefficients, and synaptic plasticity into the collective dynamics of the system. Additionally, we introduce a metric that we call node success to assess the effectiveness of a spike in terms of its capacity to trigger cascading behaviour. We present a synaptic plasticity rule based on this metric, which enables the system to reach the critical state of its collective dynamics without the need to fine-tune any control parameter. Our results suggest that retro-synaptic signals could be responsible for the emergence of self-organised criticality in brain networks. Furthermore, based on the measure of node success, we find what kind of topology allows nodes to be more successful at triggering cascades of activity. Our study comprises four different scenarios: i) static synapses, ii) dynamic synapses under spike-timing-dependent plasticity (STDP), iii) dynamic synapses under node-success-driven plasticity (NSDP), and iv) dynamic synapses under both NSDP and STDP mechanisms. We observe that small-world structures emerge when critical dynamics are combined with STDP mechanisms in a particular type of topology. Moreover, we go beyond simple spike pairs of STDP, and implement spike triplets to assess their influence on the dynamics of the system. To the best of our knowledge this is the first study that implements this version of STDP in the context of critical dynamics in complex networks.

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Made available in DSpace on 2014-10-09T12:34:20Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T14:10:33Z (GMT). No. of bitstreams: 0 / Em testes físicos de reatores que são realizados na criticalização, após uma troca de combustível, por exemplo, como ocorre nos reatores PWR, é muito importante monitorar continuamente a reatividade durante o processo de criticalização. Medir a reatividade utilizando o método da Cinética Inversa é um processo bastante utilizado durante a operação de um reator nuclear, e é possível determinar a reatividade em tempo real baseado nas equações de cinética pontual. Essa técnica é aplicada com sucesso a altas potências, ou em núcleos que trabalham sem a existência de uma fonte externa, já que nesse caso o Termo Fonte na equação de cinética pontual pode ser desprezado. Para operações a baixas potências, a contribuição da fonte de nêutrons precisa ser levada em consideração, e isso implica em conhecer um valor proporcional à intensidade da fonte e, portanto esse valor precisa ser determinado. O Método dos Mínimos Quadrados em Cinética Inversa (Least Square Inverse Kinetics Method LSIKM) foi testado com modelo teórico e aplicado em experimentos no Reator Nuclear IPEN/MB-01 para a determinação do Termo Fonte com a utilização de um reatímetro que ignora o Termo Fonte em primeira instância. Após a determinação da Fonte S de forma consistente, seu valor foi inserido ao algoritmo de Cinética Inversa, e utilizando dados de detectores durante a criticalização, o reatímetro com Termo Fonte foi usado para medir a reatividade no domínio subcrítico, nos passos de criticalização, após experimento. / Dissertação (Mestrado) / IPEN/D / Instituto de Pesquisas Energeticas e Nucleares - IPEN-CNEN/SP