Matching Items (6)

Application of Individual Based Models in Modeding Brain Tumor

Description

Cancer modeling has brought a lot of attention in recent years. It had been proven to be a difficult task to model the behavior of cancer cells, since little about

Cancer modeling has brought a lot of attention in recent years. It had been proven to be a difficult task to model the behavior of cancer cells, since little about the "rules" a cell follows has been known. Existing models for cancer cells can be generalized into two categories: macroscopic models which studies the tumor structure as a whole, and microscopic models which focus on the behavior of individual cells. Both modeling strategies strive the same goal of creating a model that can be validated with experimental data, and is reliable for predicting tumor growth. In order to achieve this goal, models must be developed based on certain rules that tumor structures follow. This paper will introduce how such rules can be implemented in a mathematical model, with the example of individual based modeling.

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Date Created
  • 2016-12

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An l1 Regularization Algorithm for Reconstructing Piecewise Smooth Functions from Fourier Data Using Wavelet Projection

Description

Imaging technologies such as Magnetic Resonance Imaging (MRI) and Synthetic Aperture Radar (SAR) collect Fourier data and then process the data to form images. Because images are piecewise smooth, the

Imaging technologies such as Magnetic Resonance Imaging (MRI) and Synthetic Aperture Radar (SAR) collect Fourier data and then process the data to form images. Because images are piecewise smooth, the Fourier partial sum (i.e. direct inversion of the Fourier data) yields a poor approximation, with spurious oscillations forming at the interior edges of the image and reduced accuracy overall. This is the well known Gibbs phenomenon and many attempts have been made to rectify its effects. Previous algorithms exploited the sparsity of edges in the underlying image as a constraint with which to optimize for a solution with reduced spurious oscillations. While the sparsity enforcing algorithms are fairly effective, they are sensitive to several issues, including undersampling and noise. Because of the piecewise nature of the underlying image, we theorize that projecting the solution onto the wavelet basis would increase the overall accuracy. Thus in this investigation we develop an algorithm that continues to exploit the sparsity of edges in the underlying image while also seeking to represent the solution using the wavelet rather than Fourier basis. Our method successfully decreases the effect of the Gibbs phenomenon and provides a good approximation for the underlying image. The primary advantages of our method is its robustness to undersampling and perturbations in the optimization parameters.

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Date Created
  • 2015-12

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FOURFUN: A new system for automatic computations using Fourier expansions

Description

Using object-oriented programming in MATLAB, a collection of functions, named Fourfun, has been created to allow quick and accurate approximations of periodic functions with Fourier expansions. To increase efficiency and

Using object-oriented programming in MATLAB, a collection of functions, named Fourfun, has been created to allow quick and accurate approximations of periodic functions with Fourier expansions. To increase efficiency and reduce the number of computations of the Fourier transform, Fourfun automatically determines the number of nodes necessary for representations that are accurate to close to machine precision. Common MATLAB functions have been overloaded to keep the syntax of the Fourfun class as consistent as possible with the general MATLAB syntax. We show that the system can be used to efficiently solve several differential equations. Comparisons with Chebfun, a similar system based on Chebyshev polynomial approximations, are provided.

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Date Created
  • 2014-05

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Numerical Simulation of the Surface Brightness of Astrophysical Jets

Description

The goal of this thesis is to extend the astrophysical jet model created by Dr.
Gardner and Dr. Jones to model the surface brightness of astrophysical jets. We attempt to

The goal of this thesis is to extend the astrophysical jet model created by Dr.
Gardner and Dr. Jones to model the surface brightness of astrophysical jets. We attempt to accomplish this goal by modeling the astrophysical jet HH30 in the spectral emission lines [SII] 6716Å, [OI] 6300Å, and [NII] 6583Å. In order to do so, we used the jet model to simulate the temperature and density of the jet to match observational data by Hartigan and Morse (2007). From these results, we derived the emissivities in these emission lines using Cloudy by Ferland et al. (2013). Then we used the emissivities to determine the surface brightness of the jet in these lines. We found that the simulated surface brightness agreed with the observational surface brightness and we conclude that the model could successfully be extended to model the surface brightness of a jet.

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Created

Date Created
  • 2016-12

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Lagrangian Transport of Inertial Particles in Hurricane Katrina

Description

Using weather data from the Weather Research and Forecasting model (WRF), we analyze the transport of inertial particles in Hurricane Katrina in order to identify coherent patterns of motion. For

Using weather data from the Weather Research and Forecasting model (WRF), we analyze the transport of inertial particles in Hurricane Katrina in order to identify coherent patterns of motion. For our analysis, we choose a Lagrangian approach instead of an Eulerian approach because the Lagrangian approach is objective and frame-independent, and gives results which are better defined. In particular, we locate Lagrangian Coherent Structures (LCS), which are smooth sets of fluid particles which are locally most hyperbolic (either attracting or repelling). We implement a variational method for locating LCS and compare the results to previous computation of LCS using Finite-Time Lyapunov Exponents (FTLE) to identify regions of high stretching in the fluid flow.

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Date Created
  • 2013-05

Parametric Forcing of Confined and Stratified Flows

Description

A continuously and stably stratified fluid contained in a square cavity subjected to harmonic body forcing is studied numerically by solving the Navier-Stokes equations under the Boussinesq approximation. Complex dynamics

A continuously and stably stratified fluid contained in a square cavity subjected to harmonic body forcing is studied numerically by solving the Navier-Stokes equations under the Boussinesq approximation. Complex dynamics are observed near the onset of instability of the basic state, which is a flow configuration that is always an exact analytical solution of the governing equations. The instability of the basic state to perturbations is first studied with linear stability analysis (Floquet analysis), revealing a multitude of intersecting synchronous and subharmonic resonance tongues in parameter space. A modal reduction method for determining the locus of basic state instability is also shown, greatly simplifying the computational overhead normally required by a Floquet study. Then, a study of the nonlinear governing equations determines the criticality of the basic state's instability, and ultimately characterizes the dynamics of the lowest order spatial mode by the three discovered codimension-two bifurcation points within the resonance tongue. The rich dynamics include a homoclinic doubling cascade that resembles the logistic map and a multitude of gluing bifurcations.

The numerical techniques and methodologies are first demonstrated on a homogeneous fluid contained within a three-dimensional lid-driven cavity. The edge state technique and linear stability analysis through Arnoldi iteration are used to resolve the complex dynamics of the canonical shear-driven benchmark problem. The techniques here lead to a dynamical description of an instability mechanism, and the work serves as a basis for the remainder of the dissertation.

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Created

Date Created
  • 2019