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Full-Text Articles in Physical Sciences and Mathematics
Statistical Mechanics And Schramm-Loewner Evolution With Applications To Crack Propagation Processes, Christopher Borut Mesic
Statistical Mechanics And Schramm-Loewner Evolution With Applications To Crack Propagation Processes, Christopher Borut Mesic
Masters Theses
Schramm-Loewner Evolution (SLE) has both mathematical and physical roots that extend as far back as the early 20th century. We present the progression of these humble roots from the Ideal Gas Law, all the way to the renormalization group and conformal field theory, to better understand the impact SLE has had on modern statistical mechanics. We then explore the potential application of the percolation exploration process to crack propagation processes, illustrating the interplay between mathematics and physics.
An Analysis Of The Patterns Of Crime And Socioeconomic Status Visualized Through Self-Organized Maps, Jason Carlin Kaufman
An Analysis Of The Patterns Of Crime And Socioeconomic Status Visualized Through Self-Organized Maps, Jason Carlin Kaufman
Masters Theses
This work is research to explore the association of spatial patterns between crime and socioeconomic status (SES) through the use of self-organized maps (SOM). It had been found that the spatial patterns of crime could be associated with those of socioeconomic, and this work sought to further these analyses in order to better understand how crime patterns and SES were related. To explore this association, patterns of crime and SES were examined in three cities: Nashville, TN; Portland, OR; and Tucson, AZ. Three SOMs were used in each city: one to analyze the patterns of crime, a second to analyze …
The Complementing Condition In Elasticity, Lavanya Ramanan
The Complementing Condition In Elasticity, Lavanya Ramanan
Masters Theses
We consider a boundary value problem of nonlinear elasticity on a domain [omega] in R3 [3-dimensional space] and compute the Complementing Condition for the linearized equations at a point X0 [x zero] on boundary of omega. We assume a stored energy function depending on the first and third invariants of the deformation F and that the strong-ellipticity condition holds in [omega] . A surface traction boundary condition is imposed at X0.
The Complementing Condition is calculated from a system of 3 second-order ordinary differential equations (0 less than and equal to t less than infinity) with boundary …