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An Analysis of the Telegrapher Equation with a Bifurcation Parameter to Model Relativistic Diffusion
Get PDFIn this paper, we derive a solution to the telegrapher equation. We then apply a bifurcation parameter to the telegrapher equation in order to analyze the behavior of the solution as it changes classification. In order to obtain the solution to both the telegrapher and modified telegrapher equation, we derive the heat equation and telegrapher equation using a continuous random walk. We also solve the heat equation using invariant properties of a particular solution, a random walk analysis, and a Fourier-Laplace transform. The solution to the telegrapher equation contains modified Bessel functions, so we also derive the solutions to both the Bessel and modified Bessel equation. Lastly, we rigorously obtain a solution to the telegrapher equation with an added bifurcation parameter. This solution represents a complete distribution of the solution to the standard telegrapher equation as its solutions transition between classifications
Situating Social Sustainability on Spartanburg’s Northside: An Engaged Neighborhood Study of Community, History, and Place Making
Get PDFFrom the very beginning of my research, I have been interested in sustainability and what it means to be sustainable. I was previously partial to environmental sustainability but came to the realization that understanding social sustainability is a more relevant and important topic for the Northside at this time. When a neighborhood is socially sustainable, they are investing in the next generation, building sincere relationships founded on trust, are adaptable, and have networks with civil society organizations such as schools, churches and businesses. Saffron Woodcraft defines social sustainability as, “a process for creating sustainable, successful places that promote well-being by understanding what people need from the places in which they live and work” (Woodcraft 2015, 133). Being an outsider to the Northside neighborhood, my initial question was can being socially sustainable coexist with social inequality
