Omni-directional acoustic wave source interactions with a rough seabed with a continuously varying density and sound speed in a fluid-like sediment layer. The acoustic properties in the sediment layer possess an exponential type of variation in density and one of the three classes of sound speed profiles, which are constant,~$k^2$-linear, or inverse-square variations. Analytical solution of mean field. The mean field reflection coefficients corresponding to the aforementioned density and sound speed profiles for various frequencies, roughness parameters, are numberically generated and analyzed. Physical interpretations are provided for various results. This simple model characterizes two important features of sea floor, including seabed roughness, sediment inhomogenieties, therefore, provide a canonical analysis in seabed acoustics.

This study gives our calculations for the temperature-pressure and temperature-concentration phase diagrams using the mean field models applied to ammonium halides (NH4Cl, ND4Cl), ammonium sulfate ((NH4)2SO4/H2O), lithium potassium rubidium sulfate (LiK1-xRbxSO4), potassium pyrosulfate-potassium hydrogensulfate (K2S2O7-KHSO4), cholestanyl myristate-cholesteryl myristate (CnM-CrM), cholestanyl myristate-cholesteryl oleate (CnM-CO), benzene (C6H6) and ice. The phase line equations are derived from the free energies expanded in terms of the order parameters and they are fitted to the experimental data. Some thermodynamic quantities are calculated close to phase transitions in these crystalline systems. We also calculate the specific heat CV using the Raman frequency shifts for NH4Br on the basis of an Ising model close to the lambda-phase transition. A linear relationship is obtained between the specific heat CP and the frequency shifts (1/v)(dv/dT)P near the lambda-point in NH4Br.

Point defects control many properties of technological importance in intermetallic compounds such as atomic diffusion, creep, hardness, mechanical properties and sintering. Farther, since intermetallic compounds are characterized by long range atomic order, the point defects in these compounds can be qualitatively different from those in pure metals and disordered alloys. In the present study, we have chosen β-NiAl for our point defect studies since it is a potential candidate for high temperature applications and a model system for the study of basic phenomena in ordered alloys. We have used a mean field formulation for studying point defect concentrations. The outline of the formulation is as follows: We divide the rigid, body centred cubic lattice into two interpenetrating cubic sublattices called α and j3 which are made up of the cube corners and body centres respectively. We write a generic free energy function (G) that involves the temperature T and the six sublattice occupancies viz., the A (Ni), B (Al) and vacancies (V) on the two sublattices α andβ. We use the constraints on the number of α and β sublattice sites viz., the number of α sublattice sites is equal to the number of β sublattice sites, to write G as a function of four of the six sublattice occupancies and T. We define three auxiliary parameters η1, η2 and η3 which correspond to the vacancy concentration, the differential B species population on the two sublatices (the chemical or atomic order), and the differential vacancy population on the two sublattices, respectively. We then rewrite G as a function of T, xB and ηi. The G can now be minimized with respect to the three auxiliary variables so that we recover the free energy (G) as a function of XB and T only. The formulation requires as inputs the Ni-Ni, Al-Al, Ni-Al, Ni-V and Al-V interaction energies in the nn and nnn shells. We have obtained the Ni-Ni, Al-Al and Ni-Al interaction energies from the effective pair potentials reported in the literature. For the Ni-V and Al-V interaction energies we have used a bond breaking model in which we have assumed that the Ni-V and Al-V interaction energies in the nnn shell to be zero. Using the above interaction parameters in our mean field formulation we have determined the concentrations of various types of point defects in β-NiAL We have specifically chosen the temperature range of 800 - 2000 K and the composition range of 45 - 55 atomic% Al. Our results can be summarised as follows: 1.The predominant defect in the stoichiometric alloy is a combination of an Ni-antisite defect and two vacancies on the Ni sublattice. 2.The Al-rich alloys of composition (50 + ∆) atomic% contain 2∆% vacancies;since the alloys are almost perfectly ordered, these vacancies predominantly occupy the Ni sublattice. Similarly, the Ni-rich alloys of composition (50 — ∆)atomic% contain ∆% Ni antisites. 3.Both the vacancies on the Ni sublattice (in Al-rich alloys) and Ni-antisites (in Ni-rich alloys) show negligible temperature dependence, and hence owe their origin to the off-stoichiometry. 4.In all the alloys, the Al-antisites have the lowest concentration (of the order 10-6 even at 2000 K) and the concentration of the vacancies on the β sublattice is the next lowest. Thus, our results support the view that β-NiAl is a triple defect B2 and, if we consider constitutional vacancies as those which have a little or no temperature dependence, there exist constitutional vacancies in Al-rich β-NiAl. This conclusion is in agreement with some of the experimental results. However, it must be pointed out that there is considerable disagreement among experimental results from different groups.

El CMC, tamaño y forma de micelas son características importantes en la determinación de sus principales propiedades y campos de aplicación. Esta tesis tiene dos partes, las transiciones de forma de las micelas que se trata con "Single chain Field Theory, /SCMFT)" y simulaciones de Monte Carlo. El SCMFT reveló todas las características esenciales de las transiciones de forma esférica a cilíndrica y esférica a disco de las micelas. MC muestra que las transiciones esfera a cilindro se produce a través de una región en que esferas y cilindros coexisten junto con otras formas intermedias.

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This Ph.D. thesis in mathematical physics concerns systems of interacting fermions with strong correlations. For these systems the physical properties can only be described in terms of the collective behavior of the fermions. Moreover, they are often characterized by a close competition between fermion localization versus delocalization, which can result in complex and exotic physical phenomena. Strongly correlated fermion systems are usually modelled by many-body Hamiltonians for which the kinetic- and interaction energy have the same order of magnitude. This makes them challenging to study as the application of conventional computational methods, like mean field- or perturbation theory, often gives unreliable results. Of particular interest are Hubbard-type models, which provide minimal descriptions of strongly correlated fermions. The research of this thesis focuses on such models defined on two-dimensional square lattices. One motivation for this is the so-called high-Tc problem of the cuprate superconductors. A main hypothesis is that there exists an underlying Fermi surface with nearly flat parts, i.e. regions where the surface is straight. It is shown that a particular continuum limit of the lattice system leads to an effective model amenable to computations. This limit is partial in that it only involves fermion degrees of freedom near the flat parts. The result is an effective quantum field theory that is analyzed using constructive bosonization methods. Various exactly solvable models of interacting fermions in two spatial dimensions are also derived and studied. / QC 20111207

PhD / When modeling a system as complex as the brain, considerable simplifications are inevitable. The nature of these simplifications depends on the available experimental evidence, and the desired form of model predictions. A focus on the former often inspires models of networks of individual neurons, since properties of single cells are more easily measured than those of entire populations. However, if the goal is to describe the processes responsible for the electroencephalogram (EEG), such models can become unmanageable due to the large numbers of neurons involved. Mean-field models in which assemblies of neurons are represented by their average properties allow activity underlying the EEG to be captured in a tractable manner. The starting point of the results presented here is a recent physiologically-based mean-field model of the corticothalamic system, which includes populations of excitatory and inhibitory cortical neurons, and an excitatory population representing the thalamic relay nuclei, reciprocally connected with the cortex and the inhibitory thalamic reticular nucleus. The average firing rates of these populations depend nonlinearly on their membrane potentials, which are determined by afferent inputs after axonal propagation and dendritic and synaptic delays. It has been found that neuronal activity spreads in an approximately wavelike fashion across the cortex, which is modeled as a two-dimensional surface. On the basis of the literature, the EEG signal is assumed to be roughly proportional to the activity of cortical excitatory neurons, allowing physiological parameters to be extracted by inverse modeling of empirical EEG spectra. One objective of the present work is to characterize the statistical distributions of fitted model parameters in the healthy population. Variability of model parameters within and between individuals is assessed over time scales of minutes to more than a year, and compared with the variability of classical quantitative EEG (qEEG) parameters. These parameters are generally not normally distributed, and transformations toward the normal distribution are often used to facilitate statistical analysis. However, no single optimal transformation exists to render data distributions approximately normal. A uniformly applicable solution that not only yields data following the normal distribution as closely as possible, but also increases test-retest reliability, is described in Chapter 2. Specialized versions of this transformation have been known for some time in the statistical literature, but it has not previously found its way to the empirical sciences. Chapter 3 contains the study of intra-individual and inter-individual variability in model parameters, also providing a comparison of test-retest reliability with that of commonly used EEG spectral measures such as band powers and the frequency of the alpha peak. It is found that the combined model parameters provide a reliable characterization of an individual's EEG spectrum, where some parameters are more informative than others. Classical quantitative EEG measures are found to be somewhat more reproducible than model parameters. However, the latter have the advantage of providing direct connections with the underlying physiology. In addition, model parameters are complementary to classical measures in that they capture more information about spectral structure. Another conclusion from this work was that a few minutes of alert eyes-closed EEG already contain most of the individual variability likely to occur in this state on the scale of years. In Chapter 4, age trends in model parameters are investigated for a large sample of healthy subjects aged 6-86 years. Sex differences in parameter distributions and trends are considered in three age ranges, and related to the relevant literature. We also look at changes in inter-individual variance across age, and find that subjects are in many respects maximally different around adolescence. This study forms the basis for prospective comparisons with age trends in evoked response potentials (ERPs) and alpha peak morphology, besides providing a standard for the assessment of clinical data. It is the first study to report physiologically-based parameters for such a large sample of EEG data. The second main thrust of this work is toward incorporating the thalamocortical system and the basal ganglia in a unified framework. The basal ganglia are a group of gray matter structures reciprocally connected with the thalamus and cortex, both significantly influencing, and influenced by, their activity. Abnormalities in the basal ganglia are associated with various disorders, including schizophrenia, Huntington's disease, and Parkinson's disease. A model of the basal ganglia-thalamocortical system is presented in Chapter 5, and used to investigate changes in average firing rates often measured in parkinsonian patients and animal models of Parkinson's disease. Modeling results support the hypothesis that two pathways through the basal ganglia (the so-called direct and indirect pathways) are differentially affected by the dopamine depletion that is the hallmark of Parkinson's disease. However, alterations in other components of the system are also suggested by matching model predictions to experimental data. The dynamics of the model are explored in detail in Chapter 6. Electrophysiological aspects of Parkinson's disease include frequency reduction of the alpha peak, increased relative power at lower frequencies, and abnormal synchronized fluctuations in firing rates. It is shown that the same parameter variations that reproduce realistic changes in mean firing rates can also account for EEG frequency reduction by increasing the strength of the indirect pathway, which exerts an inhibitory effect on the cortex. Furthermore, even more strongly connected subcircuits in the indirect pathway can sustain limit cycle oscillations around 5 Hz, in accord with oscillations at this frequency often observed in tremulous patients. Additionally, oscillations around 20 Hz that are normally present in corticothalamic circuits can spread to the basal ganglia when both corticothalamic and indirect circuits have large gains. The model also accounts for changes in the responsiveness of the components of the basal ganglia-thalamocortical system, and increased synchronization upon dopamine depletion, which plausibly reflect the loss of specificity of neuronal signaling pathways in the parkinsonian basal ganglia. Thus, a parsimonious explanation is provided for many electrophysiological correlates of Parkinson's disease using a single set of parameter changes with respect to the healthy state. Overall, we conclude that mean-field models of brain electrophysiology possess a versatility that allows them to be usefully applied in a variety of scenarios. Such models allow information about underlying physiology to be extracted from the experimental EEG, complementing traditional measures that may be more statistically robust but do not provide a direct link with physiology. Furthermore, there is ample opportunity for future developments, extending the basic model to encompass different neuronal systems, connections, and mechanisms. The basal ganglia are an important addition, not only leading to unified explanations for many hitherto disparate phenomena, but also contributing to the validation of this form of modeling.

Thesis (Ph. D.)--University of Texas at Austin, 2008. / Vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Washington, 1997. / Vita. Includes bibliographical references (p. [148]-178).

Thesis (Ph. D.)--University of Missouri-Columbia, 1997. / Typescript. Vita. Includes bibliographical references. Also available on the Internet.