Matching Items (13)
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- All Subjects: Mathematical Modeling
- All Subjects: Gas Dynamics
- Creators: Gardner, Carl
- Creators: Armbruster, Dieter
- Creators: Jones, Jeremiah
- Status: Published
Description
This project discusses simulation results of star formation by Active Galactic Nuclei (AGN) jets using the WENO method. A typical AGN jet with velocity uj=0.3c, density ρj=10^(-2) H/cm3, and temperature Tj=10^(7) K was injected into a 425 light years square region. The jet passes through a stationary inhomogeneous ambient background of temperature Ta=5x10^4 K and density ρa= 2 H/cm^3 to test if AGN jets, by creating bow shocks propagating through the interstellar medium and molecular clouds, can form stars in the densest regions. According to the star formation criteria for gravitational collapse of Cen and Ostriker, the resulting simulations indicate the presence of star formation via AGN jets (1992). The parameters are tuned to match Centaurs A to identify star formation in this galaxy. The simulations will also be run in three dimensions in the future and for longer time intervals to gain a better understanding of the star formation process via AGN jets.
ContributorsFindley, Christina Marie (Author) / Gardner, Carl (Thesis director) / Scannapieco, Evan (Committee member) / Barrett, The Honors College (Contributor) / School of Earth and Space Exploration (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2015-05
Description
The purpose of this thesis is to accurately simulate the surface brightness in various spectral emission lines of the HH 901 jets in the Mystic Mountain Formation of the Carina Nebula. To accomplish this goal, we gathered relevant spectral emission line data for [Fe II] 12660 Å, Hα 6563 Å, and [S II] 6720 Å to compare with Hubble Space Telescope observations of the HH 901 jets presented in Reiter et al. (2016). We derived the emissivities for these lines from the spectral synthesis code Cloudy by Ferland et al. (2017). In addition, we used WENO simulations of density, temperature, and radiative cooling to model the jet. We found that the computed surface brightness values agreed with most of the observational surface brightness values. Thus, the 3D cylindrically symmetric simulations of surface brightness using the WENO code and Cloudy spectral emission models are accurate for jets like HH 901. After detailing these agreements, we discuss the next steps for the project, like adding an external ambient wind and performing the simulations in full 3D.
ContributorsMohan, Arun (Author) / Gardner, Carl (Thesis director) / Jones, Jeremiah (Committee member) / Computer Science and Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2020-05
Description
Pogonomyrmex californicus (a species of harvester ant) colonies typically have anywhere from one to five queens. A queen can control the ratio of female to male offspring she produces, field research indicating that this ratio is genetically hardwired and does not change over time relative to other queens. Further, a queen has an individual reproductive advantage if she has a small reproductive ratio. A colony, however, has a reproductive advantage if it has queens with large ratios, as these queens produce many female workers to further colony success. We have developed an agent-based model to analyze the "cheating" phenotype observed in field research, in which queens extend their lifespans by producing disproportionately many male offspring. The model generates phenotypes and simulates years of reproductive cycles. The results allow us to examine the surviving phenotypes and determine conditions under which a cheating phenotype has an evolutionary advantage. Conditions generating a bimodal steady state solution would indicate a cheating phenotype's ability to invade a cooperative population.
ContributorsEngel, Lauren Marie Agnes (Author) / Armbruster, Dieter (Thesis director) / Fewell, Jennifer (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2017-05
ContributorsPowell, Devon (Author) / Gardner, Carl (Thesis director) / Scannapieco, Evan (Committee member) / Windhorst, Rogier (Committee member) / Barrett, The Honors College (Contributor)
Created2012-05
Description
The purpose of this thesis is to accurately simulate in 3D the HH901 jet in the Mystic Mountain Formation of the Carina Nebula. Astronomers present a narrow-band Wide Field Camera image of Carina and the morphology of some astrophysical jets, including HH901. The simulation attempts to replicate features of the jet, among which are pulses, bow shock, terminal Mach disk, and Kelvin-Helmholtz rollup. We use the gas dynamical equations to solve for density, velocity, and temperature. The numerical methods used to solve the equations are third-order WENO (weighted essentially non-oscillatory) and third-order Runge-Kutta. Graphs of density and radiative cooling demonstrate the effect of adding wind (nonzero ambient velocity). The paper discusses the altering of the ambient velocity and final time to fit the shape of the jet in the Hubble image. The suggested next steps are simulating the other HH901 jet and comparing the jets’ atomic makeups to advance understanding of astrophysical jets.
ContributorsBuyer, Michael (Author) / Gardner, Carl (Thesis director) / Jones, Jeremiah (Committee member) / Barrett, The Honors College (Contributor) / Computer Science and Engineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2022-05
DescriptionUnderstanding the evolution of opinions is a delicate task as the dynamics of how one changes their opinion based on their interactions with others are unclear.
ContributorsWeber, Dylan (Author) / Motsch, Sebastien (Thesis advisor) / Lanchier, Nicolas (Committee member) / Platte, Rodrigo (Committee member) / Armbruster, Dieter (Committee member) / Fricks, John (Committee member) / Arizona State University (Publisher)
Created2021
Description
A description of numerical and analytical work pertaining to models that describe the growth and progression of glioblastoma multiforme (GBM), an aggressive form of primary brain cancer. Two reaction-diffusion models are used: the Fisher-Kolmogorov-Petrovsky-Piskunov equation and a 2-population model that divides the tumor into actively proliferating and quiescent (or necrotic) cells. The numerical portion of this work (chapter 2) focuses on simulating GBM expansion in patients undergoing treatment for recurrence of tumor following initial surgery. The models are simulated on 3-dimensional brain geometries derived from magnetic resonance imaging (MRI) scans provided by the Barrow Neurological Institute. The study consists of 17 clinical time intervals across 10 patients that have been followed in detail, each of whom shows significant progression of tumor over a period of 1 to 3 months on sequential follow up scans. A Taguchi sampling design is implemented to estimate the variability of the predicted tumors to using 144 different choices of model parameters. In 9 cases, model parameters can be identified such that the simulated tumor contains at least 40 percent of the volume of the observed tumor. In the analytical portion of the paper (chapters 3 and 4), a positively invariant region for our 2-population model is identified. Then, a rigorous derivation of the critical patch size associated with the model is performed. The critical patch (KISS) size is the minimum habitat size needed for a population to survive in a region. Habitats larger than the critical patch size allow a population to persist, while smaller habitats lead to extinction. The critical patch size of the 2-population model is consistent with that of the Fisher-Kolmogorov-Petrovsky-Piskunov equation, one of the first reaction-diffusion models proposed for GBM. The critical patch size may indicate that GBM tumors have a minimum size depending on the location in the brain. A theoretical relationship between the size of a GBM tumor at steady-state and its maximum cell density is also derived, which has potential applications for patient-specific parameter estimation based on magnetic resonance imaging data.
ContributorsHarris, Duane C. (Author) / Kuang, Yang (Thesis advisor) / Kostelich, Eric J. (Thesis advisor) / Preul, Mark C. (Committee member) / Crook, Sharon (Committee member) / Gardner, Carl (Committee member) / Arizona State University (Publisher)
Created2023
Description
Modern measurement schemes for linear dynamical systems are typically designed so that different sensors can be scheduled to be used at each time step. To determine which sensors to use, various metrics have been suggested. One possible such metric is the observability of the system. Observability is a binary condition determining whether a finite number of measurements suffice to recover the initial state. However to employ observability for sensor scheduling, the binary definition needs to be expanded so that one can measure how observable a system is with a particular measurement scheme, i.e. one needs a metric of observability. Most methods utilizing an observability metric are about sensor selection and not for sensor scheduling. In this dissertation we present a new approach to utilize the observability for sensor scheduling by employing the condition number of the observability matrix as the metric and using column subset selection to create an algorithm to choose which sensors to use at each time step. To this end we use a rank revealing QR factorization algorithm to select sensors. Several numerical experiments are used to demonstrate the performance of the proposed scheme.
ContributorsIlkturk, Utku (Author) / Gelb, Anne (Thesis advisor) / Platte, Rodrigo (Thesis advisor) / Cochran, Douglas (Committee member) / Renaut, Rosemary (Committee member) / Armbruster, Dieter (Committee member) / Arizona State University (Publisher)
Created2015
Description
Cancer is a major health problem in the world today and is expected to become an even larger one in the future. Although cancer therapy has improved for many cancers in the last several decades, there is much room for further improvement. Mathematical modeling has the advantage of being able to test many theoretical therapies without having to perform clinical trials and experiments. Mathematical oncology will continue to be an important tool in the future regarding cancer therapies and management.
This dissertation is structured as a growing tumor. Chapters 2 and 3 consider spheroid models. These models are adept at describing 'early-time' tumors, before the tumor needs to co-opt blood vessels to continue sustained growth. I consider two partial differential equation (PDE) models for spheroid growth of glioblastoma. I compare these models to in vitro experimental data for glioblastoma tumor cell lines and other proposed models. Further, I investigate the conditions under which traveling wave solutions exist and confirm numerically.
As a tumor grows, it can no longer be approximated by a spheroid, and it becomes necessary to use in vivo data and more sophisticated modeling to model the growth and diffusion. In Chapter 4, I explore experimental data and computational models for describing growth and diffusion of glioblastoma in murine brains. I discuss not only how the data was obtained, but how the 3D brain geometry is created from Magnetic Resonance (MR) images. A 3D finite-difference code is used to model tumor growth using a basic reaction-diffusion equation. I formulate and test hypotheses as to why there are large differences between the final tumor sizes between the mice.
Once a tumor has reached a detectable size, it is diagnosed, and treatment begins. Chapter 5 considers modeling the treatment of prostate cancer. I consider a joint model with hormonal therapy as well as immunotherapy. I consider a timing study to determine whether changing the vaccine timing has any effect on the outcome of the patient. In addition, I perform basic analysis on the six-dimensional ordinary differential equation (ODE). I also consider the limiting case, and perform a full global analysis.
This dissertation is structured as a growing tumor. Chapters 2 and 3 consider spheroid models. These models are adept at describing 'early-time' tumors, before the tumor needs to co-opt blood vessels to continue sustained growth. I consider two partial differential equation (PDE) models for spheroid growth of glioblastoma. I compare these models to in vitro experimental data for glioblastoma tumor cell lines and other proposed models. Further, I investigate the conditions under which traveling wave solutions exist and confirm numerically.
As a tumor grows, it can no longer be approximated by a spheroid, and it becomes necessary to use in vivo data and more sophisticated modeling to model the growth and diffusion. In Chapter 4, I explore experimental data and computational models for describing growth and diffusion of glioblastoma in murine brains. I discuss not only how the data was obtained, but how the 3D brain geometry is created from Magnetic Resonance (MR) images. A 3D finite-difference code is used to model tumor growth using a basic reaction-diffusion equation. I formulate and test hypotheses as to why there are large differences between the final tumor sizes between the mice.
Once a tumor has reached a detectable size, it is diagnosed, and treatment begins. Chapter 5 considers modeling the treatment of prostate cancer. I consider a joint model with hormonal therapy as well as immunotherapy. I consider a timing study to determine whether changing the vaccine timing has any effect on the outcome of the patient. In addition, I perform basic analysis on the six-dimensional ordinary differential equation (ODE). I also consider the limiting case, and perform a full global analysis.
ContributorsRutter, Erica Marie (Author) / Kuang, Yang (Thesis advisor) / Kostelich, Eric J (Thesis advisor) / Frakes, David (Committee member) / Gardner, Carl (Committee member) / Jackiewicz, Zdzislaw (Committee member) / Arizona State University (Publisher)
Created2016
Description
The increased number of novel pathogens that potentially threaten the human population has motivated the development of mathematical and computational modeling approaches for forecasting epidemic impact and understanding key environmental characteristics that influence the spread of diseases. Yet, in the case that substantial uncertainty surrounds the transmission process during a rapidly developing infectious disease outbreak, complex mechanistic models may be too difficult to be calibrated quick enough for policy makers to make informed decisions. Simple phenomenological models that rely on a small number of parameters can provide an initial platform for assessing the epidemic trajectory, estimating the reproduction number and quantifying the disease burden from the early epidemic phase.
Chapter 1 provides background information and motivation for infectious disease forecasting and outlines the rest of the thesis.
In chapter 2, logistic patch models are used to assess and forecast the 2013-2015 West Africa Zaire ebolavirus epidemic. In particular, this chapter is concerned with comparing and contrasting the effects that spatial heterogeneity has on the forecasting performance of the cumulative infected case counts reported during the epidemic.
In chapter 3, two simple phenomenological models inspired from population biology are used to assess the Research and Policy for Infectious Disease Dynamics (RAPIDD) Ebola Challenge; a simulated epidemic that generated 4 infectious disease scenarios. Because of the nature of the synthetically generated data, model predictions are compared to exact epidemiological quantities used in the simulation.
In chapter 4, these models are applied to the 1904 Plague epidemic that occurred in Bombay. This chapter provides evidence that these simple models may be applicable to infectious diseases no matter the disease transmission mechanism.
Chapter 5, uses the patch models from chapter 2 to explore how migration in the 1904 Plague epidemic changes the final epidemic size.
The final chapter is an interdisciplinary project concerning within-host dynamics of cereal yellow dwarf virus-RPV, a plant pathogen from a virus group that infects over 150 grass species. Motivated by environmental nutrient enrichment due to anthropological activities, mathematical models are employed to investigate the relevance of resource competition to pathogen and host dynamics.
Chapter 1 provides background information and motivation for infectious disease forecasting and outlines the rest of the thesis.
In chapter 2, logistic patch models are used to assess and forecast the 2013-2015 West Africa Zaire ebolavirus epidemic. In particular, this chapter is concerned with comparing and contrasting the effects that spatial heterogeneity has on the forecasting performance of the cumulative infected case counts reported during the epidemic.
In chapter 3, two simple phenomenological models inspired from population biology are used to assess the Research and Policy for Infectious Disease Dynamics (RAPIDD) Ebola Challenge; a simulated epidemic that generated 4 infectious disease scenarios. Because of the nature of the synthetically generated data, model predictions are compared to exact epidemiological quantities used in the simulation.
In chapter 4, these models are applied to the 1904 Plague epidemic that occurred in Bombay. This chapter provides evidence that these simple models may be applicable to infectious diseases no matter the disease transmission mechanism.
Chapter 5, uses the patch models from chapter 2 to explore how migration in the 1904 Plague epidemic changes the final epidemic size.
The final chapter is an interdisciplinary project concerning within-host dynamics of cereal yellow dwarf virus-RPV, a plant pathogen from a virus group that infects over 150 grass species. Motivated by environmental nutrient enrichment due to anthropological activities, mathematical models are employed to investigate the relevance of resource competition to pathogen and host dynamics.
ContributorsPell, Bruce (Author) / Kuang, Yang (Thesis advisor) / Chowell-Puente, Gerardo (Committee member) / Nagy, John (Committee member) / Kostelich, Eric (Committee member) / Gardner, Carl (Committee member) / Arizona State University (Publisher)
Created2016