Matching Items (48)
Description
Prostate cancer is the second most common kind of cancer in men. Fortunately, it has a 99% survival rate. To achieve such a survival rate, a variety of aggressive therapies are used to treat prostate cancers that are caught early. Androgen deprivation therapy (ADT) is a therapy that is given in cycles to patients. This study attempted to analyze what factors in a group of 79 patients caused them to stick with or discontinue the treatment. This was done using naïve Bayes classification, a machine-learning algorithm. The usage of this algorithm identified high testosterone as an indicator of a patient persevering with the treatment, but failed to produce statistically significant high rates of prediction.
ContributorsMillea, Timothy Michael (Author) / Kostelich, Eric (Thesis director) / Kuang, Yang (Committee member) / Computer Science and Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2016-12
Description
A moving overlapping mesh methodology that achieves spectral accuracy in space and up to second-order accuracy in time is developed for solution of unsteady incompressible flow equations in three-dimensional domains. The targeted applications are in aerospace and mechanical engineering domains and involve problems in turbomachinery, rotary aircrafts, wind turbines and others. The methodology is built within the dual-session communication framework initially developed for stationary overlapping meshes. The methodology employs semi-implicit spectral element discretization of equations in each subdomain and explicit treatment of subdomain interfaces with spectrally-accurate spatial interpolation and high-order accurate temporal extrapolation, and requires few, if any, iterations, yet maintains the global accuracy and stability of the underlying flow solver. Mesh movement is enabled through the Arbitrary Lagrangian-Eulerian formulation of the governing equations, which allows for prescription of arbitrary velocity values at discrete mesh points.
The stationary and moving overlapping mesh methodologies are thoroughly validated using two- and three-dimensional benchmark problems in laminar and turbulent flows. The spatial and temporal global convergence, for both methods, is documented and is in agreement with the nominal order of accuracy of the underlying solver.
Stationary overlapping mesh methodology was validated to assess the influence of long integration times and inflow-outflow global boundary conditions on the performance. In a turbulent benchmark of fully-developed turbulent pipe flow, the turbulent statistics are validated against the available data.
Moving overlapping mesh simulations are validated on the problems of two-dimensional oscillating cylinder and a three-dimensional rotating sphere. The aerodynamic forces acting on these moving rigid bodies are determined, and all results are compared with published data. Scaling tests, with both methodologies, show near linear strong scaling, even for moderately large processor counts.
The moving overlapping mesh methodology is utilized to investigate the effect of an upstream turbulent wake on a three-dimensional oscillating NACA0012 extruded airfoil. A direct numerical simulation (DNS) at Reynolds Number 44,000 is performed for steady inflow incident upon the airfoil oscillating between angle of attack 5.6 and 25 degrees with reduced frequency k=0.16. Results are contrasted with subsequent DNS of the same oscillating airfoil in a turbulent wake generated by a stationary upstream cylinder.
The stationary and moving overlapping mesh methodologies are thoroughly validated using two- and three-dimensional benchmark problems in laminar and turbulent flows. The spatial and temporal global convergence, for both methods, is documented and is in agreement with the nominal order of accuracy of the underlying solver.
Stationary overlapping mesh methodology was validated to assess the influence of long integration times and inflow-outflow global boundary conditions on the performance. In a turbulent benchmark of fully-developed turbulent pipe flow, the turbulent statistics are validated against the available data.
Moving overlapping mesh simulations are validated on the problems of two-dimensional oscillating cylinder and a three-dimensional rotating sphere. The aerodynamic forces acting on these moving rigid bodies are determined, and all results are compared with published data. Scaling tests, with both methodologies, show near linear strong scaling, even for moderately large processor counts.
The moving overlapping mesh methodology is utilized to investigate the effect of an upstream turbulent wake on a three-dimensional oscillating NACA0012 extruded airfoil. A direct numerical simulation (DNS) at Reynolds Number 44,000 is performed for steady inflow incident upon the airfoil oscillating between angle of attack 5.6 and 25 degrees with reduced frequency k=0.16. Results are contrasted with subsequent DNS of the same oscillating airfoil in a turbulent wake generated by a stationary upstream cylinder.
ContributorsMerrill, Brandon Earl (Author) / Peet, Yulia (Thesis advisor) / Herrmann, Marcus (Committee member) / Huang, Huei-Ping (Committee member) / Kostelich, Eric (Committee member) / Calhoun, Ronald (Committee member) / Arizona State University (Publisher)
Created2016
Description
The central purpose of this work is to investigate the large-scale, coherent structures that exist in turbulent Rayleigh-Bénard convection (RBC) when the domain is large enough for the classical ”wind of turbulence” to break down. The study exclusively focuses on the structures that from when the RBC geometry is a cylinder. A series of visualization studies, Fourier analysis and proper orthogonal decomposition are employed to qualitatively and quantitatively inspect the large-scale structures’ length and time scales, spatial organization, and dynamic properties. The data in this study is generated by direct numerical simulation to resolve all the scales of turbulence in a 6.3 aspect-ratio cylinder at a Rayleigh number of 9.6 × 107 and Prandtl number of 6.7. Single and double point statistics are compared against experiments and several resolution criteria are examined to verify that the simulation has enough spatial and temporal resolution to adequately represent the physical system.
Large-scale structures are found to organize as roll-cells aligned along the cell’s side walls, with rays of vorticity pointing toward the core of the cell. Two different large- scale organizations are observed and these patterns are well described spatially and energetically by azimuthal Fourier modes with frequencies of 2 and 3. These Fourier modes are shown to be dominant throughout the entire domain, and are found to be the primary source for radial inhomogeneity by inspection of the energy spectra. The precision with which the azimuthal Fourier modes describe these large-scale structures shows that these structures influence a large range of length scales. Conversely, the smaller scale structures are found to be more sensitive to radial position within the Fourier modes showing a strong dependence on physical length scales.
Dynamics in the large-scale structures are observed including a transition in the global pattern followed by a net rotation about the central axis. The transition takes place over 10 eddy-turnover times and the subsequent rotation occurs at a rate of approximately 1.1 degrees per eddy-turnover. These time-scales are of the same order of magnitude as those seen in lower aspect-ratio RBC for similar events and suggests a similarity in dynamic events across different aspect-ratios.
Large-scale structures are found to organize as roll-cells aligned along the cell’s side walls, with rays of vorticity pointing toward the core of the cell. Two different large- scale organizations are observed and these patterns are well described spatially and energetically by azimuthal Fourier modes with frequencies of 2 and 3. These Fourier modes are shown to be dominant throughout the entire domain, and are found to be the primary source for radial inhomogeneity by inspection of the energy spectra. The precision with which the azimuthal Fourier modes describe these large-scale structures shows that these structures influence a large range of length scales. Conversely, the smaller scale structures are found to be more sensitive to radial position within the Fourier modes showing a strong dependence on physical length scales.
Dynamics in the large-scale structures are observed including a transition in the global pattern followed by a net rotation about the central axis. The transition takes place over 10 eddy-turnover times and the subsequent rotation occurs at a rate of approximately 1.1 degrees per eddy-turnover. These time-scales are of the same order of magnitude as those seen in lower aspect-ratio RBC for similar events and suggests a similarity in dynamic events across different aspect-ratios.
ContributorsSakievich, Philip Sakievich (Author) / Peet, Yulia (Thesis advisor) / Adrian, Ronald (Committee member) / Squires, Kyle (Committee member) / Herrmann, Marcus (Committee member) / Kostelich, Eric (Committee member) / Arizona State University (Publisher)
Created2017
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
Description
A general continuum model for simulating the flow of ions in the salt baths that surround and fill excitable neurons is developed and presented. The ion densities and electric potential are computed using the drift-diffusion equations. In addition, a detailed model is given for handling the electrical dynamics on interior membrane boundaries, including a model for ion channels in the membranes that facilitate the transfer of ions in and out of cells. The model is applied to the triad synapse found in the outer plexiform layer of the retina in most species. Experimental evidence suggests the existence of a negative feedback pathway between horizontal cells and cone photoreceptors that modulates the flow of calcium ions into the synaptic terminals of cones. However, the underlying mechanism for this feedback is controversial and there are currently three competing hypotheses: the ephaptic hypothesis, the pH hypothesis and the GABA hypothesis. The goal of this work is to test some features of the ephaptic hypothesis using detailed simulations that employ rigorous numerical methods. The model is first applied in a simple rectangular geometry to demonstrate the effects of feedback for different extracellular gap widths. The model is then applied to a more complex and realistic geometry to demonstrate the existence of strictly electrical feedback, as predicted by the ephaptic hypothesis. Lastly, the effects of electrical feedback in regards to the behavior of the bipolar cell membrane potential is explored. Figures for the ion densities and electric potential are presented to verify key features of the model. The computed steady state IV curves for several cases are presented, which can be compared to experimental data. The results provide convincing evidence in favor of the ephaptic hypothesis since the existence of feedback that is strictly electrical in nature is shown, without any dependence on pH effects or chemical transmitters.
ContributorsJones, Jeremiah (Author) / Gardner, Carl (Committee member) / Baer, Steven (Committee member) / Crook, Sharon (Committee member) / Kostelich, Eric (Committee member) / Ringhofer, Christian (Committee member) / Arizona State University (Publisher)
Created2013
Description
This thesis shows analyses of mixing and transport patterns associated with Hurricane Katrina as it hit the United States in August of 2005. Specifically, by applying atmospheric velocity information from the Weather Research and Forecasting System, finite-time Lyapunov exponents have been computed and the Lagrangian Coherent Structures have been identified. The chaotic dynamics of material transport induced by the hurricane are results from these structures within the flow. Boundaries of the coherent structures are highlighted by the FTLE field. Individual particle transport within the hurricane is affected by the location of these boundaries. In addition to idealized fluid particles, we also studied inertial particles which have finite size and inertia. Basing on established Maxey-Riley equations of the dynamics of particles of finite size, we obtain a reduced equation governing the position process. Using methods derived from computer graphics, we identify maximizers of the FTLE field. Following and applying these ideas, we analyze the dynamics of inertial particle transport within Hurricane Katrina, through comparison of trajectories of dierent sized particles and by pinpointing the location of the Lagrangian Coherent Structures.
ContributorsWake, Christian (Author) / Tang, Wenbo (Thesis director) / Moustaoui, Mohamed (Committee member) / Kostelich, Eric (Committee member) / Barrett, The Honors College (Contributor) / College of Liberal Arts and Sciences (Contributor)
Created2012-12
Description
Glioblastoma multiforme (GBMs) is the most prevalent brain tumor type and causes approximately 40% of all non-metastic primary tumors in adult patients [1]. GBMs are malignant, grade-4 brain tumors, the most aggressive classication as established by the World Health Organization and are marked by their low survival rate; the median survival time is only twelve months from initial diagnosis: Patients who live more than three years are considered long-term survivors [2]. GBMs are highly invasive and their diffusive growth pattern makes it impossible to remove the tumors by surgery alone [3]. The purpose of this paper is to use individual patient data to parameterize a model of GBMs that allows for data on tumor growth and development to be captured on a clinically relevant time scale. Such an endeavor is the rst step to a clinically applicable predictions of GBMs. Previous research has yielded models that adequately represent the development of GBMs, but they have not attempted to follow specic patient cases through the entire tumor process. Using the model utilized by Kostelich et al. [4], I will attempt to redress this deciency. In doing so, I will improve upon a family of models that can be used to approximate the time of development and/or structure evolution in GBMs. The eventual goal is to incorporate Magnetic Resonance Imaging (MRI) data into a parameterized model of GBMs in such a way that it can be used clinically to predict tumor growth and behavior. Furthermore, I hope to come to a denitive conclusion as to the accuracy of the Koteslich et al. model throughout the development of GBMs tumors.
ContributorsManning, Miles (Author) / Kostelich, Eric (Thesis director) / Kuang, Yang (Committee member) / Preul, Mark (Committee member) / Barrett, The Honors College (Contributor) / College of Liberal Arts and Sciences (Contributor)
Created2012-12
Description
Dividing the plane in half leaves every border point of one region a border point of both regions. Can we divide up the plane into three or more regions such that any point on the boundary of at least one region is on the border of all the regions? In fact, it is possible to design a dynamical system for which the basins of attractions have this Wada property. In certain circumstances, both the Hénon map, a simple system, and the forced damped pendulum, a physical model, produce Wada basins.
ContributorsWhitehurst, Ryan David (Author) / Kostelich, Eric (Thesis director) / Jones, Donald (Committee member) / Armbruster, Dieter (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Chemistry and Biochemistry (Contributor)
Created2013-05
Description
This project aims to better understand aggression in a cooperative social system, specifically within the ant species Pogonomyrmex Californicus. The queens of some populations of these ants form cooperative associations of unrelated queens during nest foundation, while others prefer to form solitary nests and may show aggression towards unwanted nest mates. Because it is difficult to collect large amounts of data from a wild population and laboratory environments cannot capture the scale of nature, we created a computer simulation based on data collected in the lab and the field that emulates the life cycle of this species of ants. By manipulating behavioral and environmental conditions and observing the results we were able to better understand the advantages and disadvantages of showing aggression in this cooperative social system.
ContributorsScolaro, Jared Anthony (Author) / Kostelich, Eric (Thesis director) / Fewell, Jennifer (Committee member) / School of International Letters and Cultures (Contributor) / W. P. Carey School of Business (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Over time, tumor treatment resistance inadvertently develops when androgen de-privation therapy (ADT) is applied to metastasized prostate cancer (PCa). To combat tumor resistance, while reducing the harsh side effects of hormone therapy, the clinician may opt to cyclically alternates the patient’s treatment on and off. This method,known as intermittent ADT, is an alternative to continuous ADT that improves the patient’s quality of life while testosterone levels recover between cycles. In this paper,we explore the response of intermittent ADT to metastasized prostate cancer by employing a previously clinical data validated mathematical model to new clinical data from patients undergoing Abiraterone therapy. This cell quota model, a system of ordinary differential equations constructed using Droop’s nutrient limiting theory, assumes the tumor comprises of castration-sensitive (CS) and castration-resistant (CR)cancer sub-populations. The two sub-populations rely on varying levels of intracellular androgen for growth, death and transformation. Due to the complexity of the model,we carry out sensitivity analyses to study the effect of certain parameters on their outputs, and to increase the identifiability of each patient’s unique parameter set. The model’s forecasting results show consistent accuracy for patients with sufficient data,which means the model could give useful information in practice, especially to decide whether an additional round of treatment would be effective.
ContributorsBennett, Justin Klark (Author) / Kuang, Yang (Thesis director) / Kostelich, Eric (Committee member) / Phan, Tin (Committee member) / School of Mathematical and Statistical Sciences (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2021-05