Matching Items (16)
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- All Subjects: Mathematics
- Creators: Kostelich, Eric
Description
In 1968, phycologist M.R. Droop published his famous discovery on the functional relationship between growth rate and internal nutrient status of algae in chemostat culture. The simple notion that growth is directly dependent on intracellular nutrient concentration is useful for understanding the dynamics in many ecological systems. The cell quota in particular lends itself to ecological stoichiometry, which is a powerful framework for mathematical ecology. Three models are developed based on the cell quota principal in order to demonstrate its applications beyond chemostat culture.
First, a data-driven model is derived for neutral lipid synthesis in green microalgae with respect to nitrogen limitation. This model synthesizes several established frameworks in phycology and ecological stoichiometry. The model demonstrates how the cell quota is a useful abstraction for understanding the metabolic shift to neutral lipid production that is observed in certain oleaginous species.
Next a producer-grazer model is developed based on the cell quota model and nutrient recycling. The model incorporates a novel feedback loop to account for animal toxicity due to accumulation of nitrogen waste. The model exhibits rich, complex dynamics which leave several open mathematical questions.
Lastly, disease dynamics in vivo are in many ways analogous to those of an ecosystem, giving natural extensions of the cell quota concept to disease modeling. Prostate cancer can be modeled within this framework, with androgen the limiting nutrient and the prostate and cancer cells as competing species. Here the cell quota model provides a useful abstraction for the dependence of cellular proliferation and apoptosis on androgen and the androgen receptor. Androgen ablation therapy is often used for patients in biochemical recurrence or late-stage disease progression and is in general initially effective. However, for many patients the cancer eventually develops resistance months to years after treatment begins. Understanding how and predicting when hormone therapy facilitates evolution of resistant phenotypes has immediate implications for treatment. Cell quota models for prostate cancer can be useful tools for this purpose and motivate applications to other diseases.
First, a data-driven model is derived for neutral lipid synthesis in green microalgae with respect to nitrogen limitation. This model synthesizes several established frameworks in phycology and ecological stoichiometry. The model demonstrates how the cell quota is a useful abstraction for understanding the metabolic shift to neutral lipid production that is observed in certain oleaginous species.
Next a producer-grazer model is developed based on the cell quota model and nutrient recycling. The model incorporates a novel feedback loop to account for animal toxicity due to accumulation of nitrogen waste. The model exhibits rich, complex dynamics which leave several open mathematical questions.
Lastly, disease dynamics in vivo are in many ways analogous to those of an ecosystem, giving natural extensions of the cell quota concept to disease modeling. Prostate cancer can be modeled within this framework, with androgen the limiting nutrient and the prostate and cancer cells as competing species. Here the cell quota model provides a useful abstraction for the dependence of cellular proliferation and apoptosis on androgen and the androgen receptor. Androgen ablation therapy is often used for patients in biochemical recurrence or late-stage disease progression and is in general initially effective. However, for many patients the cancer eventually develops resistance months to years after treatment begins. Understanding how and predicting when hormone therapy facilitates evolution of resistant phenotypes has immediate implications for treatment. Cell quota models for prostate cancer can be useful tools for this purpose and motivate applications to other diseases.
ContributorsPacker, Aaron (Author) / Kuang, Yang (Thesis advisor) / Nagy, John (Committee member) / Smith, Hal (Committee member) / Kostelich, Eric (Committee member) / Kang, Yun (Committee member) / Arizona State University (Publisher)
Created2014
Description
I investigate two models interacting agent systems: the first is motivated by the flocking and swarming behaviors in biological systems, while the second models opinion formation in social networks. In each setting, I define natural notions of convergence (to a ``flock" and to a ``consensus'', respectively), and study the convergence properties of each in the limit as $t \rightarrow \infty$. Specifically, I provide sufficient conditions for the convergence of both of the models, and conduct numerical experiments to study the resulting solutions.
ContributorsTheisen, Ryan (Author) / Motsch, Sebastien (Thesis advisor) / Lanchier, Nicholas (Committee member) / Kostelich, Eric (Committee member) / Arizona State University (Publisher)
Created2018
Description
A semi-implicit, fourth-order time-filtered leapfrog numerical scheme is investigated for accuracy and stability, and applied to several test cases, including one-dimensional advection and diffusion, the anelastic equations to simulate the Kelvin-Helmholtz instability, and the global shallow water spectral model to simulate the nonlinear evolution of twin tropical cyclones. The leapfrog scheme leads to computational modes in the solutions to highly nonlinear systems, and time-filters are often used to damp these modes. The proposed filter damps the computational modes without appreciably degrading the physical mode. Its performance in these metrics is superior to the second-order time-filtered leapfrog scheme developed by Robert and Asselin.
ContributorsBurke, Lee Matthew Moore (Author) / Moustaoui, Mohamed (Thesis director) / Kostelich, Eric (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Mechanical and Aerospace Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Coherent vortices are ubiquitous structures in natural flows that affect mixing and transport of substances and momentum/energy. Being able to detect these coherent structures is important for pollutant mitigation, ecological conservation and many other aspects. In recent years, mathematical criteria and algorithms have been developed to extract these coherent structures in turbulent flows. In this study, we will apply these tools to extract important coherent structures and analyze their statistical properties as well as their implications on kinematics and dynamics of the flow. Such information will aide representation of small-scale nonlinear processes that large-scale models of natural processes may not be able to resolve.
ContributorsCass, Brentlee Jerry (Author) / Tang, Wenbo (Thesis director) / Kostelich, Eric (Committee member) / Department of Information Systems (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
Description
Much research has been devoted to identifying trends in either convergence upon a neoliberal model or divergence among welfare states in connection to globalization, but most research has focused on advanced industrialized countries. This has limited our understanding of the current state of convergence or divergence, especially among welfare states in developing regions. To address this research gap and contribute to the broader convergence vs. divergence debate, this research explores welfare state variation found within Latin America, in terms of the health policy domain, through the use of cross-national data from 18 countries collected between the period of 1995 to 2010 and the application of a series of descriptive and regression analysis techniques. Analyses revealed divergence within Latin America in the form of three distinct welfare states, and that among these welfare states income inequality, trust in traditional public institutions, and democratization, are significantly related to welfare state type and health performance.
ContributorsJohnson, Kory Alfred (Author) / Martin, Nathan (Thesis director) / Gonzales, Vanna (Committee member) / Barrett, The Honors College (Contributor) / School of Social Transformation (Contributor) / School of Politics and Global Studies (Contributor)
Created2014-05
Description
A numerical study of wave-induced momentum transport across the tropopause in the presence of a stably stratified thin inversion layer is presented and discussed. This layer consists of a sharp increase in static stability within the tropopause. The wave propagation is modeled by numerically solving the Taylor-Goldstein equation, which governs the dynamics of internal waves in stably stratified shear flows. The waves are forced by a flow over a bell shaped mountain placed at the lower boundary of the domain. A perfectly radiating condition based on the group velocity of mountain waves is imposed at the top to avoid artificial wave reflection. A validation for the numerical method through comparisons with the corresponding analytical solutions will be provided. Then, the method is applied to more realistic profiles of the stability to study the impact of these profiles on wave propagation through the tropopause.
ContributorsCole, Alexandra Shea (Author) / Moustaoui, Mohamed (Thesis director) / Kostelich, Eric (Committee member) / Mahalov, Alex (Committee member) / School of International Letters and Cultures (Contributor) / School of Geographical Sciences and Urban Planning (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2017-05
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 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.
ContributorsHan, Zimo (Author) / Motsch, Sebastien (Thesis director) / Moustaoui, Mohamed (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-12
Description
There are multiple mathematical models for alignment of individuals moving within a group. In a first class of models, individuals tend to relax their velocity toward the average velocity of other nearby neighbors. These types of models are motivated by the flocking behavior exhibited by birds. Another class of models have been introduced to describe rapid changes of individual velocity, referred to as jump, which better describes behavior of smaller agents (e.g. locusts, ants). In the second class of model, individuals will randomly choose to align with another nearby individual, matching velocities. There are several open questions concerning these two type of behavior: which behavior is the most efficient to create a flock (i.e. to converge toward the same velocity)? Will flocking still emerge when the number of individuals approach infinity? Analysis of these models show that, in the homogeneous case where all individuals are capable of interacting with each other, the variance of the velocities in both the jump model and the relaxation model decays to 0 exponentially for any nonzero number of individuals. This implies the individuals in the system converge to an absorbing state where all individuals share the same velocity, therefore individuals converge to a flock even as the number of individuals approach infinity. Further analysis focused on the case where interactions between individuals were determined by an adjacency matrix. The second eigenvalues of the Laplacian of this adjacency matrix (denoted ƛ2) provided a lower bound on the rate of decay of the variance. When ƛ2 is nonzero, the system is said to converge to a flock almost surely. Furthermore, when the adjacency matrix is generated by a random graph, such that connections between individuals are formed with probability p (where 0
1/N. ƛ2 is a good estimator of the rate of convergence of the system, in comparison to the value of p used to generate the adjacency matrix..
ContributorsTrent, Austin L. (Author) / Motsch, Sebastien (Thesis director) / Lanchier, Nicolas (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-05
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
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