Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 5 of 5
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 …
Adaptive Wavelet Discretization Of Tensor Products In H-Tucker Format, Mazen Ali
Adaptive Wavelet Discretization Of Tensor Products In H-Tucker Format, Mazen Ali
Masters Theses
"In previous work, the solution to a system of coupled parabolic PDEs, modeling the price of a CDO, was approximated numerically. Due to the nature of the problem, the system involved a large number of equations such that the parameters cannot be stored explicitly. The authors combined the data sparse H-Tucker storage format with the Galerkin method to approximate the solution, using wavelets for the space discretization together with time stepping (Method of Lines). The aforementioned approximation is of the linear kind, i.e., using a nonadaptive method. In this work, three methods for solving such systems adaptively are presented, together …
An Iterative Algorithm For Variational Data Assimilation Problems, Xin Shen
An Iterative Algorithm For Variational Data Assimilation Problems, Xin Shen
Masters Theses
"Data assimilation is a very powerful and efficient tool to use collected raw data for improving model prediction in numerical weather forecasting, hydrology, and many other areas of geosciences. In this thesis, an iterative algorithm [23] of variational data assimilation with finite element method is utilized to study different models. One motivation for this fundamental mathematical study is to provide a potential tool for simulation of CO2 sequestration by extending it to more realistic and sophisticated models in the future. The basic idea of variational data assimilation is to utilize the framework of optimal control problems. We apply the …