In this article we study the geometry associated with the sub-elliptic operator ½ (X²1 +X²2), where X1 = ∂x and X2 = x²/2 ∂y are vector fields on R². We show that any point can be connected with the origin by at least one geodesic and we provide an approximate formula for the number of the geodesics between the origin and the points situated outside of the y-axis. We show there are in¯nitely many geodesics between the origin and the points on the y-axis.

In the present work, we study wave phenomena in strongly nonlinear lattices. Such lattices are characterized by the absence of classical linear waves. We demonstrate that compactons – strongly localized solitary waves with tails decaying faster than exponential – exist and that they play a major role in the dynamics of the system under consideration. We investigate compactons in different physical setups. One part deals with lattices of dispersively coupled limit cycle oscillators which find various applications in natural sciences such as Josephson junction arrays or coupled Ginzburg-Landau equations. Another part deals with Hamiltonian lattices. Here, a prominent example in which compactons can be found is the granular chain. In the third part, we study systems which are related to the discrete nonlinear Schrödinger equation describing, for example, coupled optical wave-guides or the dynamics of Bose-Einstein condensates in optical lattices. Our investigations are based on a numerical method to solve the traveling wave equation. This results in a quasi-exact solution (up to numerical errors) which is the compacton. Another ansatz which is employed throughout this work is the quasi-continuous approximation where the lattice is described by a continuous medium. Here, compactons are found analytically, but they are defined on a truly compact support. Remarkably, both ways give similar qualitative and quantitative results. Additionally, we study the dynamical properties of compactons by means of numerical simulation of the lattice equations. Especially, we concentrate on their emergence from physically realizable initial conditions as well as on their stability due to collisions. We show that the collisions are not exactly elastic but that a small part of the energy remains at the location of the collision. In finite lattices, this remaining part will then trigger a multiple scattering process resulting in a chaotic state. / In der hier vorliegenden Arbeit werden Wellenphänomene in stark nichtlinearen Gittern untersucht. Diese Gitter zeichnen sich vor allem durch die Abwesenheit von klassischen linearen Wellen aus. Es wird gezeigt, dass Kompaktonen – stark lokalisierte solitäre Wellen, mit Ausläufern welche schneller als exponentiell abfallen – existieren, und dass sie eine entscheidende Rolle in der Dynamik dieser Gitter spielen. Kompaktonen treten in verschiedenen diskreten physikalischen Systemen auf. Ein Teil der Arbeit behandelt dabei Gitter von dispersiv gekoppelten Oszillatoren, welche beispielsweise Anwendung in gekoppelten Josephsonkontakten oder gekoppelten Ginzburg-Landau-Gleichungen finden. Ein weiterer Teil beschäftigt sich mit Hamiltongittern, wobei die granulare Kette das bekannteste Beispiel ist, in dem Kompaktonen beobachtet werden können. Im dritten Teil werden Systeme, welche im Zusammenhang mit der Diskreten Nichtlinearen Schrödingergleichung stehen, studiert. Diese Gleichung beschreibt beispielsweise Arrays von optischen Wellenleitern oder die Dynamik von Bose-Einstein-Kondensaten in optischen Gittern. Das Studium der Kompaktonen basiert hier hauptsächlich auf dem numerischen Lösen der dazugehörigen Wellengleichung. Dies mündet in einer quasi-exakten Lösung, dem Kompakton, welches bis auf numerische Fehler genau bestimmt werden kann. Ein anderer Ansatz, der in dieser Arbeit mehrfach verwendet wird, ist die Approximation des Gitters durch ein kontinuierliches Medium. Die daraus resultierenden Kompaktonen besitzen einen im mathematischen Sinne kompakten Definitionsbereich. Beide Methoden liefern qualitativ und quantitativ gut übereinstimmende Ergebnisse. Zusätzlich werden die dynamischen Eigenschaften von Kompaktonen mit Hilfe von direkten numerischen Simulationen der Gittergleichungen untersucht. Dabei wird ein Hauptaugenmerk auf die Entstehung von Kompaktonen unter physikalisch realisierbaren Anfangsbedingungen und ihre Kollisionen gelegt. Es wird gezeigt, dass die Wechselwirkung nicht exakt elastisch ist, sondern dass ein Teil ihrer Energie an der Position der Kollision verharrt. In endlichen Gittern führt dies zu einem multiplen Streuprozess, welcher in einem chaotischen Zustand endet.

The main focus of this thesis is on fast numerical methods, where adaptivity is an important mechanism to lowering the methods' complexity. The application of the methods are in the areas of wireless communication, antenna design, radar signature computation, noise prediction, medical ultrasonography, crystal growth, flame propagation, wave propagation, seismology, geometrical optics and image processing.   We first consider high frequency wave propagation problems with a variable speed function in one dimension, modeled by the Helmholtz equation. One significant difficulty of standard numerical methods for such problems is that the wave length is very short compared to the computational domain and many discretization points are needed to resolve the solution. The computational cost, thus grows algebraically with the frequency w. For scattering problems with impenetrable scatterer in homogeneous media, new methods have recently been derived with a provably lower cost in terms of w. In this thesis, we suggest and analyze a fast numerical method for the one dimensional Helmholtz equation with variable speed function (variable media) that is based on wave-splitting. The Helmholtz equation is split into two one-way wave equations which are then solved iteratively for a given tolerance. We show rigorously that the algorithm is convergent, and that the computational cost depends only weakly on the frequency for fixed accuracy.  We next consider interface tracking problems where the interface moves by a velocity field that does not depend on the interface itself. We derive fast adaptive  numerical methods for such problems. Adaptivity makes methods robust in the sense that they can handle a large class of problems, including problems with expanding interface and problems where the interface has corners. They are based on a multiresolution representation of the interface, i.e. the interface is represented hierarchically by wavelet vectors corresponding to increasingly detailed meshes. The complexity of standard numerical methods for interface tracking, where the interface is described by marker points, is O(N/dt), where N is the number of marker points on the interface and dt is the time step. The methods that we develop in this thesis have O(dt^(-1)log N) computational cost for the same order of accuracy in dt. In the adaptive version, the cost is O(tol^(-1/p)log N), where tol is some given tolerance and p is the order of the numerical method for ordinary differential equations that is used for time advection of the interface.   Finally, we consider time-dependent Hamilton-Jacobi equations with convex Hamiltonians. We suggest a numerical method that is computationally efficient and accurate. It is based on a reformulation of the equation as a front tracking problem, which is solved with the fast interface tracking methods together with a post-processing step.  The complexity of standard numerical methods for such problems is O(dt^(-(d+1))) in d dimensions, where dt is the time step. The complexity of our method is reduced to O(dt^(-d)|log dt|) or even to O(dt^(-d)). / <p>QC 20121116</p>

Multilayered structures have many application in industry and society: they have peculiar properties and serve a variety of purposes, like structural support, thermal insulation, vibrational and acoustic isolation. This thesis concerns the prediction of sound transmission in multilayered structures. Two problems are herein investigated: the transmission of energy through structures and the transmission of energy along structures. The focus of the analysis is on the mid to high frequency range. To predict sound transmission in these structures, statistical energy analysis (SEA) is used.SEA models are devised for the prediction of the sound reduction index for two kinds of multilayered structures, double-walls used in buildings and trim-panels in vehicles; the double-walls comprise an air cavity in between flat plasterboard or glass plates, whereas the trim-panels a porous layer in between curved aluminium and rubber layers. The SEA models are based upon the wave-types carrying energy. The novelty in these SEAs is an element describing the waves in the air cavity, or in the porous layer, fully coupled to the mass-impeded external layers. Compared to measurements, the proposed SEA performs well: for double-walls, it performs better than previous models; for trim-panels, it is an original result. The parameters of the new SEA element, such as modal density, are derived from the coupling equations describing the fully coupled waves. For double-walls, these equations are derived via Newton's laws. For trim-panels, a variational approach based upon a modified Hamilton's principle valid for non-conservative systems is preferred, because it is a powerful machinery for deriving equations of motion and coupling conditions of a medium as complex as the porous layer. The modified Hamilton's principle for non-conservative systems is based upon a self-adjoint functional analogous to the Lagrangian, inspired by Morse and Feshbach's construction. A self-adjoint variational principle for Biot's equations in the displacement formulation is devised. An equivalent mixed formulation is obtained changing the coordinates of the displacement formulation via Lagrange multipliers. From this mixed formulation, the Lagrangian for a porous material with a limp frame is derived, which yields the continuity of the total displacement of the porous layer. Lagrange multipliers help to obtain the correct coupling functionals between a porous material and a solid. The Lagrange multipliers introducing the continuity of the frame and the solid displacements equal the traction of the in-vacuo frame, thus disappearing if the latter is limp. Measurements to gather material parameters for a Biot model of the porous layer have been conducted.The effects of spatial energy decay in the transmission along structures predicted by SEA is studied: a major effect is the increased relevance of indirect coupling loss factors between SEA elements. This may jeopardize the usefulness of SEA at higher frequencies. / <p>QC 20130218</p>

ABSTRACT Dr. Alice Hamilton (1869-1970), the leading American figure in industrial medicine during the early to mid-1900s, left behind a body of rhetoric that is important in the history of American feminist discourse and American public address. Her discourse is the exemplary of feminist-pragmatist rhetoric, a genre of cross-gender communication developed by New Women associated with Hull House and the University of Chicago between 1892 and 1918. Hamilton’s rhetoric illuminates a key event in the history of the American rhetorical tradition—the emergence of the modern woman from her late-Victorian beginnings through her Progressive self-transformation. This study is approached as a rhetorical biography. It tracks Hamilton’s evolution from “reticent scientist” to outspoken feminist-pragmatist by examining family, educational, peer and social influences on her development; and through critical analysis of her speeches, technical writing, books, and popular and specialty magazine articles over a 36-year period, from 1907 to 1943.

This study examines a frontier businessman and the evolution of his business enterprises in conjunction with the emergence of northern Indiana from its frontier period to the time that it became a settled agricultural region with strong ties to the national economy. The subject is Allen Hamilton, an Irish immigrant who settled in Fort Wayne, Indiana in 1823 and remained here until his death in 18514. Hamilton's involvement with the affairs of the state government, the Miami and Potawatomi Indians, retailing, land speculation, the promotion and construction of the Wabash and Erie Canal and numerous plank road and railroad projects, the fur trade and the Indian trade, the second State Bank of Indiana and the creation of the Hamilton ink involved him deeply in the economic development and the political affairs of Indiana and, to a lesser extent, of the North.This study of Hamilton's rise to wealth parallels the development of Indiana and is intertwined with it. At nearly all points in his career Hamilton achieved financial success by meeting the needs of the developing region. He functioned at first as a fur trade .end Indian trader, meeting the needs of the Indians as well as the large Eastern fur merchants. Toward the end of his career he was primarily a banker and promoter of internal improvements, serving both his own interests and those of the expanding white population of northern Indiana for credit and adequate transportation facilities.In order to compete successfully as a businessman, Hamilton found it necessary to become involved with the politics of the region and at times was himself a successful candidate for local and state offices. Generally, however, his political activities were confined to the support of influential men from northern Indiana, several of whom were his business partners. The ability to form judicious alliances which took advantage of both political influence and entrepreneurial talent was a chief factor of Hamilton's success. His business partnerships demonstrated the evolution of his activities and his partners included the most important men in that section of the state. These partnerships were flexible, allowing for significant alteration as new opportunities (such as the milling of wheat) presented themselves and older avenues to wealth (such as the fur trade) dried up. As Hamilton outgrew the older partnerships he created others that reflected not only the need for a different type of expertise in his partner but also his own changed economic, social and political situation. One of the consistencies of Hamilton's partnerships was their diversification which made them more fluid in nature and more capable of capitalizing on new opportunities.Hamilton's rise to wealth was significant not only to himself. His wealthy Irish origins had set for him a model to which the wealthy should aspire. Correspondingly, he was a social leader in Fort Wayne and nurtured in his offspring a respect for the highest of goals in education and civic responsibility. He was a patrician and a symbol not only of the opportunities of the West, but also of the fact that the West was far from being an area inhabited by social equals. Indeed, Hamilton's extensive commitment to land speculation was more than simply a means ofachieving wealth. The possession of large tracts of land symbolized, for Hamilton, the recreation of his family's former status in Ireland, powerfully augmenting the traditional status gained through land ownership in the United States.Through Allen Hamilton one may view not only the development of Indiana in the second quarter of the nineteenth century, but also a pattern of economic maturation that was often experienced in areas far to the east and west of the state.

This study is an assessment of the archaeological resources the Strawtown Site area in northeastern Hamilton County, _ndiana. Strawtown was an intensively occupied village during the Late woodland Period (Householder, personal communication, 1986) and appears closely related to the Bowen site (Dorwin, 1971:209).This thesis documents the Strawtown Site and associated :materials through background research and collection analysis; other sites in the immediate vicinity were identified through a systematic reconnaissance of a 555.24 acre sample area. This information was combined to test both Dorwin"s (1971) Oliver Phase settlement pattern and the Woodland settlement model proposed by Stephenson (1984).In light of the information that is available, Dorwin"s and Stephenson's models of a seasonal occupation of the river valley by Late Woodland groups was argued against in favor of a model which assumes permanent Late Woodland occupation of the river valley.Ball State UniversityMuncie, IN 47306

The presented thesis project is a study on train energy consumption calculation and optimal train driving strategies for minimum energy consumption. This study is divided into three parts; the first part is a proposed model for energy consumption calculation for trains based on driving resistances. The second part is a presentation of a method based on dynamic programming and the Hamilton-Jacobi-Bellman equation (Bellman’s backward approach) for obtaining optimal speed and control profiles leading to minimum energy consumption. The third part is a case study for a Bombardier Transportation case. It includes the presentation of a preliminary algorithm developed within this thesis project; an algorithm based on the HJB equation that can be further improved in order to be used online in real-time as an advisory system for train drivers.

The Community Based Policing model has been adopted by the large majority of policing agencies as another tool on an officer’s duty belt that allows them to do their job more effectively and efficiently. The model is premised on the building and maintaining of relationships of the Police Service and the community it serves. The model argues that Services must ensure that the community is given a voice in the way police enforce the laws. The model encourages that the police and community work together in a partnership that is different from the traditional relationship shared between the two groups under the previous Professional Policing model. This working in partnership means that not only must the police become more open to the community providing direction in the way they do their job, but also that the community must take a more active role in the policing of their areas. This partnership could be considered an exchange of information from both the police and the community. As argued by Marcel Mauss in The Gift, relationships that are on-going and have elements of exchange have obligations. These obligations of giving, receiving and reciprocity ensure that the relationship between the groups is not only maintained, but strengthened. When one of these obligations is not met, however, there are often social consequences. This research attempts to understand the model of Community Based Policing in terms of how it is being applied by Canada’s second oldest police service, the Hamilton Police. With the model encouraging a relationship with the community, issues of gift exchange appear. Through interviews with staff of the Hamilton Police Service, as well as citizens from the community of Hamilton, how these obligations are being met, as well as the effectiveness of the model and its relation to Maussian theory of gift exchange are explored.

The Community Based Policing model has been adopted by the large majority of policing agencies as another tool on an officer’s duty belt that allows them to do their job more effectively and efficiently. The model is premised on the building and maintaining of relationships of the Police Service and the community it serves. The model argues that Services must ensure that the community is given a voice in the way police enforce the laws. The model encourages that the police and community work together in a partnership that is different from the traditional relationship shared between the two groups under the previous Professional Policing model. This working in partnership means that not only must the police become more open to the community providing direction in the way they do their job, but also that the community must take a more active role in the policing of their areas. This partnership could be considered an exchange of information from both the police and the community. As argued by Marcel Mauss in The Gift, relationships that are on-going and have elements of exchange have obligations. These obligations of giving, receiving and reciprocity ensure that the relationship between the groups is not only maintained, but strengthened. When one of these obligations is not met, however, there are often social consequences. This research attempts to understand the model of Community Based Policing in terms of how it is being applied by Canada’s second oldest police service, the Hamilton Police. With the model encouraging a relationship with the community, issues of gift exchange appear. Through interviews with staff of the Hamilton Police Service, as well as citizens from the community of Hamilton, how these obligations are being met, as well as the effectiveness of the model and its relation to Maussian theory of gift exchange are explored.