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Articles 1 - 30 of 125
Full-Text Articles in Physical Sciences and Mathematics
Applying Mathematical Modeling To The Study Of Family Systems, Dahlia Maxwell
Applying Mathematical Modeling To The Study Of Family Systems, Dahlia Maxwell
Theses and Dissertations
Mathematical modeling provides a powerful framework for insight into current scientific theories as well as hypothesis generation for further research. Despite its undeniable potential to enrich scientific advancement, the application of mathematical modeling remains conspicuously scarce in the field of family science. The complexity inherent in family dynamics, coupled with the intricate interplay of emotions in the individual, underscores the necessity of a robust analytical approach. Addressing this critical gap in the literature, this thesis introduces a sophisticated mathematical model of family dynamics integrating essential elements from family systems theory, emotion dynamics, and appraisal theory. The model is implemented as …
Undergraduate Mathematics Students Question And Critique Society Through Mathematical Modeling, Will Tidwell, Amy Bennett
Undergraduate Mathematics Students Question And Critique Society Through Mathematical Modeling, Will Tidwell, Amy Bennett
Journal of Humanistic Mathematics
Mathematics can be used as a tool to question and critique society and, in doing so, give us more information about the world around us and how it operates. This however, is not a common perspective that is conveyed to students during their undergraduate mathematics coursework. This paper contributes to the understanding of how undergraduate mathematics students question and critique society via mathematical modeling tasks. In two courses at two universities, 27 mathematics majors and secondary preservice teachers engaged in the modeling process situated in authentic contexts to learn specific concepts and make mathematical connections across domains and disciplines. Both …
Blue Whale And Krill Populations Modeling, Li Zhang
Blue Whale And Krill Populations Modeling, Li Zhang
CODEE Journal
We present an intriguing topic in an undergraduate mathematical modeling course where predator-prey models are taught to our students. We describe modeling activities and the use of technology that can be implemented in teaching this topic. Through modeling activities, students are expected to use the numerical and graphical methods to observe the qualitative long-term behavior of predator and prey populations. Although there are other choices of predators and prey, we find that using blue whales and krill as predator and prey, respectively, would be most beneficial in strengthening our students' awareness of protecting endangered species and its impact on climate …
Raising Student Awareness Of Environmental Issues Via Writing Assignments With Differential Equations, Michelle L. Ghrist
Raising Student Awareness Of Environmental Issues Via Writing Assignments With Differential Equations, Michelle L. Ghrist
CODEE Journal
In this paper, I discuss two environmentally-focused writing assignments that I developed and implemented in recent integral calculus and differential equations courses. These models of carbon storage and PCB’s in a river provide interesting applications of one-compartment mixing problems. The assignments were intended to focus student attention on sustainability concerns while also developing other essential skills. I discuss these assignments and their effect on my students’ technical writing and environmental awareness. Detailed introductory instructions and mostly complete solutions to these assignments appear in the appendices, to include sample student work.
Solar Panels, Euler’S Method And Community-Based Projects: Connecting Differential Equations With Climate Change, Victor J. Donnay
Solar Panels, Euler’S Method And Community-Based Projects: Connecting Differential Equations With Climate Change, Victor J. Donnay
CODEE Journal
How does mathematics connect with the search for solutions to the climate emergency? One simple connection, which can be explored in an introductory differential equations course, can be found by analyzing the energy generated by solar panels or wind turbines. The power generated by these devices is typically recorded at standard time intervals producing a data set which gives a discrete approximation to the power function $P(t)$. Using numerical techniques such as Euler’s method, one can determine the energy generated. Here we describe how we introduce the topic of solar power, apply Euler’s method to determine the energy generated, and …
An Integrated Experimental And Modeling Approach To Design Rotating Algae Biofilm Reactors (Rabrs) Via Optimizing Algae Biofilm Productivity, Nutrient Recovery, And Energy Efficiency, Gerald Benjamin Jones
An Integrated Experimental And Modeling Approach To Design Rotating Algae Biofilm Reactors (Rabrs) Via Optimizing Algae Biofilm Productivity, Nutrient Recovery, And Energy Efficiency, Gerald Benjamin Jones
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
Microalgae biofilms have been demonstrated to recover nutrients from wastewater and serve as biomass feedstock for bioproducts. However, there is a need to develop a platform to quantitatively describe microalgae biofilm production, which can provide guidance and insights for improving biomass areal productivity and nutrient uptake efficiency. This paper proposes a unified experimental and theoretical framework to investigate algae biofilm growth on a rotating algae biofilm reactor (RABR). The experimental laboratory setups are used to conduct controlled experiments on testing environmental and operational factors for RABRs. We propose a differential-integral equation-based mathematical model for microalgae biofilm cultivation guided by laboratory …
Conversion Of Fat To Cellular Fuel—Fatty Acids 𝛽-Oxidation Model, Sylwester M. Kloska, Krzysztof Pałczyński, Tomasz Marciniak, Tomasz Talaśka, Marissa Miller, Beata J. Wysocki, Paul Davis, Tadeusz A. Wysocki
Conversion Of Fat To Cellular Fuel—Fatty Acids 𝛽-Oxidation Model, Sylwester M. Kloska, Krzysztof Pałczyński, Tomasz Marciniak, Tomasz Talaśka, Marissa Miller, Beata J. Wysocki, Paul Davis, Tadeusz A. Wysocki
School of Computing: Faculty Publications
𝛽-oxidation of fatty acids plays a significant role in the energy metabolism of the cell. This paper presents a 𝛽-oxidation model of fatty acids based on queueing theory. It uses Michaelis–Menten enzyme kinetics, and literature data on metabolites’ concentration and enzymatic constants. A genetic algorithm was used to optimize the parameters for the pathway reactions. The model enables real-time tracking of changes in the concentrations of metabolites with different carbon chain lengths. Another application of the presented model is to predict the changes caused by system disturbance, such as altered enzyme activity or abnormal fatty acid concentration. The model has …
Linking Mathematical Models And Trap Data To Infer The Proliferation, Abundance, And Control Of Aedes Aegypti, Jing Chen, Xi Huo, Andre B. B. Wilke, John C. Beier, Chalmers Vasquez, William Petrie, Robert Stephen Cantrell, Chris Cosner, Shigui Ruan
Linking Mathematical Models And Trap Data To Infer The Proliferation, Abundance, And Control Of Aedes Aegypti, Jing Chen, Xi Huo, Andre B. B. Wilke, John C. Beier, Chalmers Vasquez, William Petrie, Robert Stephen Cantrell, Chris Cosner, Shigui Ruan
Mathematics Faculty Articles
Aedes aegypti is one of the most dominant mosquito species in the urban areas of Miami-Dade County, Florida, and is responsible for the local arbovirus transmissions. Since August 2016, mosquito traps have been placed throughout the county to improve surveillance and guide mosquito control and arbovirus outbreak response. In this paper, we develop a deterministic mosquito population model, estimate model parameters by using local entomological and temperature data, and use the model to calibrate the mosquito trap data from 2017 to 2019. We further use the model to compare the Ae. aegypti population and evaluate the impact of rainfall intensity …
Stochastic Modeling Of Flows In Membrane Pore Networks, Binan Gu
Stochastic Modeling Of Flows In Membrane Pore Networks, Binan Gu
Dissertations
Membrane filters provide immediate solutions to many urgent problems such as water purification, and effective remedies to pressing environmental concerns such as waste and air treatment. The ubiquity of applications gives rise to a significant amount of research in membrane material selection and structural design to optimize filter efficiency. As physical experiments tend to be costly, numerical simulation and analysis of fluid flow, foulant transport and geometric evolution due to foulant deposition in complex geometries become particularly relevant. In this dissertation, several mathematical modeling and analytical aspects of the industrial membrane filtration process are investigated. A first-principles mathematical model for …
A New Sir Model With Mobility., Ciana Applegate
A New Sir Model With Mobility., Ciana Applegate
Electronic Theses and Dissertations
In this paper, a mobility-based SIR model is built to understand the spread of the pandemic. A traditional SIR model used in epidemiology describes the transition of particles among states, such as susceptible, infected, and recovered states. However, the traditional model has no movement of particles. There are many variations of SIR models when it comes to the factor of mobility, the majority of studies use mobility intensity or population density as a measure of mobility. In this paper, a new dynamical SIR model, including the spatial motion of three-type particles, is constructed and the long-time behavior of the first …
Developing Confidence And Interest In Teaching Relevant Mathematical Modeling Lessons, Jacy Beck
Developing Confidence And Interest In Teaching Relevant Mathematical Modeling Lessons, Jacy Beck
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
What is mathematical modeling and how can inservice and pre-service teachers develop the skills and competencies necessary to increase confidence and interest in teaching relevant mathematical modeling lessons? Mathematical modeling is “the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions” (CSSM, 2010, p. 72). By providing students with an opportunity to engage in relevant mathematical modeling prompts, we provide them with transferable skills and knowledge. The aim of this paper will be to provide insight into the relevance of teaching mathematical modeling, provide resources for integrating modeling …
Mentoring Undergraduate Research In Mathematical Modeling, Glenn Ledder
Mentoring Undergraduate Research In Mathematical Modeling, Glenn Ledder
Department of Mathematics: Faculty Publications
In writing about undergraduate research in mathematical modeling, I draw on my 31 years as a mathematics professor at the University of Nebraska–Lincoln, where I mentored students in honors’ theses, REU groups, and research done in a classroom setting, as well as my prior experience. I share my views on the differences between research at the undergraduate and professional levels, offer advice for undergraduate mentoring, provide suggestions for a variety of ways that students can disseminate their research, offer some thoughts on mathematical modeling and how to explain it to undergraduates, and discuss the challenges involved in broadening research participation …
Mentoring Undergraduate Research In Mathematical Modeling, Glenn Ledder
Mentoring Undergraduate Research In Mathematical Modeling, Glenn Ledder
Department of Mathematics: Faculty Publications
In writing about undergraduate research in mathematical modeling, I draw on my 31 years as a mathematics professor at the University of Nebraska–Lincoln, where I mentored students in honors’ theses, REU groups, and research done in a classroom setting, as well as my prior experience. I share my views on the differences between research at the undergraduate and professional levels, offer advice for undergraduate mentoring, provide suggestions for a variety of ways that students can disseminate their research, offer some thoughts on mathematical modeling and how to explain it to undergraduates, and discuss the challenges involved in broadening research participation …
Modeling The Effect Of Human Behavior On Disease Transmission, Katie Yan
Modeling The Effect Of Human Behavior On Disease Transmission, Katie Yan
Mathematics and Statistics Theses
Many infectious disease models build upon the classical Susceptible-Infected-Recovered (SIR) model. The SIR model is a compartmental model that is used to model disease transmission throughout a population. The SIR model and its variations often focus on the transmission of disease but rarely include behavioral or informational components that explore how the perception of a disease influences transmission. In this thesis we propose a six compartment SIR model that segments the classical SIR model based on knowledge of information to explore the sharing of information and its ability to increase and decrease transmission. We designate these two model states as …
Stabilizing Controlled Systems In The Presence Of Time-Delays, Isaac Becker Pardo
Stabilizing Controlled Systems In The Presence Of Time-Delays, Isaac Becker Pardo
Theses and Dissertations
A dynamical system's state evolves over time, and when the system stays near a particular state this state is known as a stable state of the system. Through control methods, dynamical systems can be manipulated such that virtually any state can be made stable. Although most real systems evolve continuously in time the application of digital control methods to these systems is inherently discrete. States are sampled (with sensors) and fed back into the system in discrete-time to determine the input needed to control the continuous system. Additionally, dynamical systems often experience time delays. Some examples of time delays are …
A Mathematical Model For The Adoption Of Information And Communication Technology In School Libraries In Nigeria, Helen Olubunmi Jaiyeola Akinade, Jeremiah Ademola Balogun, Peter Adebayo Idowu
A Mathematical Model For The Adoption Of Information And Communication Technology In School Libraries In Nigeria, Helen Olubunmi Jaiyeola Akinade, Jeremiah Ademola Balogun, Peter Adebayo Idowu
Library Philosophy and Practice (e-journal)
This study focused on the development of a mathematical model required for estimating the number of adopters of ICT devices among libraries located in Nigeria. Data for this study was collected from 121 respondents selected based on a research survey approach using simple random sampling. 9 ICT devices were identified, namely: PCs, printers/fax machines, search engines, e-library systems, bulk SMS services, library management systems, bar/QR code readers, projectors and video conferencing. The results showed that the earliest ICT devices were adopted for use in 1997, such as: PCs, printers/fax machines and search engines. The remaining ICT devices were adopted in …
Numerical Study Of Highly Efficient Centrifugal Cyclones, Murodil Madaliev
Numerical Study Of Highly Efficient Centrifugal Cyclones, Murodil Madaliev
Scientific-technical journal
Centrifugal cyclones have been developing for 100 years, while the efficiency of all cyclones for fine dust does not increase by 80%. The widespread use of cyclones in all branches of industrial production is determined by the simplicity of the design and sufficient reliability in operation. Along with this, the process carried out in a cyclone presents a complex scientific problem that has not been solved from the standpoint of aerohydromechanics. This is confirmed by various cyclone designs. Currently, the efficiency of cyclone cleaning of technological flows does not meet the requirements of sanitary standards and largely determines the level …
Mathematical Models Of Infection Prevention Programs In Hospital Settings, Kelly A. Reagan
Mathematical Models Of Infection Prevention Programs In Hospital Settings, Kelly A. Reagan
Theses and Dissertations
Hospitals play a vital role in providing for the healthcare needs of a community. Patients can develop hospital-acquired infections (HAIs) during their hospitalization due to exposure to foreign bacteria, viruses, and fungi. Infection prevention programs target and reduce HAIs, but implementing the infection prevention programs often comes with a cost. The goal of my research is to use mathematical models to quantify the impact of infection prevention programs on cases of HAIs and total healthcare costs. First, I use a Markov chain model to quantify how one infection prevention program reduces general HAIs in the hospital. Then, I calculate the …
Three Questions From Cctm Teachers About Mathematical Modeling, Robyn Stankiewicz-Van Der Zanden, Rachel Levy
Three Questions From Cctm Teachers About Mathematical Modeling, Robyn Stankiewicz-Van Der Zanden, Rachel Levy
Colorado Mathematics Teacher
This article shares three questions and answers about mathematical modeling in the classroom from an April 2020 online conversation with participants of a CCTM webinar. We hope that the answers to these questions will motivate teachers to embrace the value of implementing math modeling tasks, help students see the math all around them in the world, and empower future professionals to reach for the mathematical tools in their pockets to make data-driven decisions.
Modeling Dewetting, Demixing, And Thermal Effects In Nanoscale Metal Films, Ryan Howard Allaire
Modeling Dewetting, Demixing, And Thermal Effects In Nanoscale Metal Films, Ryan Howard Allaire
Dissertations
Thin film dynamics, particularly on the nanoscale, is a topic of extensive interest. The process by which thin liquids evolve is far from trivial and can lead to dewetting and drop formation. Understanding this process involves not only resolving the fluid mechanical aspects of the problem, but also requires the coupling of other physical processes, including liquid-solid interactions, thermal transport, and dependence of material parameters on temperature and material composition. The focus of this dissertation is on the mathematical modeling and simulation of nanoscale liquid metal films, which are deposited on thermally conductive substrates, liquefied by laser heating, and subsequently …
Modeling And Design Optimization For Membrane Filters, Yixuan Sun
Modeling And Design Optimization For Membrane Filters, Yixuan Sun
Dissertations
Membrane filtration is widely used in many applications, ranging from industrial processes to everyday living activities. With growing interest from both industrial and academic sectors in understanding the various types of filtration processes in use, and in improving filter performance, the past few decades have seen significant research activity in this area. Experimental studies can be very valuable, but are expensive and time-consuming, therefore theoretical studies offer potential as a cost-effective and predictive way to improve on current filter designs. In this work, mathematical models, derived from first principles and simplified using asymptotic analysis, are proposed for: (1) pleated membrane …
Optimization Of Urban Metro-Based Underground Logistics System Network With Hub-And-Spoke Layout, Ren Rui, Wanjie Hu, Jianjun Dong, Zhilong Chen
Optimization Of Urban Metro-Based Underground Logistics System Network With Hub-And-Spoke Layout, Ren Rui, Wanjie Hu, Jianjun Dong, Zhilong Chen
Journal of System Simulation
Abstract: Dual application of passenger commuting and underground logistics based on urban metro (M-ULS) provides a solution for traffic congestion. A three-stage optimization approach for the hub-and-spoke M-ULS network is proposed. An Entropy-TOPSIS model for underground flow screening was established based on indicators of freight flows unity, order priority and regional accessibility, considering facility capacity constraints, a location-allocation-routing combinatorial model with construction and operation costs objectives is proposed, Set Coverage Exact Algorithm, Adaptive Immunity Clone Selection Algorithm and Floyd-Warshall Algorithm are developed. Geographic information statistics of Nanjing is applied as the benchmark for real-world simulation. Results show that the modeling …
Social Distancing And Testing As Optimal Strategies Against The Spread Of Covid-19 In The Rio Grande Valley Of Texas, Kristina P. Vatcheva, Josef A. Sifuentes, Tamer Oraby, Jose Campo Maldonado, Timothy Huber, Cristina Villalobos
Social Distancing And Testing As Optimal Strategies Against The Spread Of Covid-19 In The Rio Grande Valley Of Texas, Kristina P. Vatcheva, Josef A. Sifuentes, Tamer Oraby, Jose Campo Maldonado, Timothy Huber, Cristina Villalobos
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
At the beginning of August 2020, the Rio Grande Valley (RGV) of Texas experienced a rapid increase of coronavirus disease 2019 (abbreviated as COVID-19) cases and deaths. This study aims to determine the optimal levels of effective social distancing and testing to slow the virus spread at the outset of the pandemic. We use an age-stratified eight compartment epidemiological model to depict COVID-19 transmission in the community and within households. With a simulated 120-day outbreak period data we obtain a post 180-days period optimal control strategy solution. Our results show that easing social distancing between adults by the end of …
Mathematical Modeling In Finance, Owen Sweeney
Mathematical Modeling In Finance, Owen Sweeney
Honors Projects
Financial tools play an integral role in the day-to-day lives of individuals and businesses. Many of these tools use predefined formulas to calculate items such as loan payments, interest and capital structure components. These tools do not usually provide the flexibility needed when new parameters are introduced. By utilizing mathematical modeling, these standard formulas can be derived and even improved to provide the needed flexibility.
Mathematical Modeling Of The Candida Albicans Yeast To Hyphal Transition Reveals Novel Control Strategies, David J. Wooten, Jorge Gómez Tejeda Zañudo, David Murrugarra, Austin M. Perry, Anna Dongari-Bagtzoglou, Reinhard Laubenbacher, Clarissa J. Nobile, Réka Albert
Mathematical Modeling Of The Candida Albicans Yeast To Hyphal Transition Reveals Novel Control Strategies, David J. Wooten, Jorge Gómez Tejeda Zañudo, David Murrugarra, Austin M. Perry, Anna Dongari-Bagtzoglou, Reinhard Laubenbacher, Clarissa J. Nobile, Réka Albert
Mathematics Faculty Publications
Candida albicans, an opportunistic fungal pathogen, is a significant cause of human infections, particularly in immunocompromised individuals. Phenotypic plasticity between two morphological phenotypes, yeast and hyphae, is a key mechanism by which C. albicans can thrive in many microenvironments and cause disease in the host. Understanding the decision points and key driver genes controlling this important transition and how these genes respond to different environmental signals is critical to understanding how C. albicans causes infections in the host. Here we build and analyze a Boolean dynamical model of the C. albicans yeast to hyphal transition, integrating …
A Computational Investigation Of The Biophysical Mechanisms Underlying Thermotaxis In The Afd Neurons Of Caenorhabditis Elegans, Zachary Mobille
A Computational Investigation Of The Biophysical Mechanisms Underlying Thermotaxis In The Afd Neurons Of Caenorhabditis Elegans, Zachary Mobille
Theses and Dissertations
Thermotaxis in the nematode Caenorhabditis elegans (C. elegans) is studied at the cellular scale of the amphid finger-like ciliated (AFD) neurons, which have previously been shown to be essential for thermoreception. The voltage and calcium signals of AFD during temperature stimuli are described with ordinary differential equations. The primary calcium model is a modified version of that published by Kuramochi and Doi in 2017 to explain the calcium responses of the chemosensitive amphid single-ciliated right (ASER) neuron to fluctuations in extracellular salt concentration. To account for the effects of temperature, changes to the stimuli conditions under which inactivation takes place …
Modeling The Ecological Dynamics Of A Three-Species Fish Population In The Chesapeake Bay, Iordanka N. Panayotova, Maila B. Hallare
Modeling The Ecological Dynamics Of A Three-Species Fish Population In The Chesapeake Bay, Iordanka N. Panayotova, Maila B. Hallare
CODEE Journal
We present an inquiry-based project that is designed for a mathematical modeling class of undergraduate junior or senior students. It discusses a three-species mathematical model that simulates the biological interactions among three important fish species in the Chesapeake Bay: the prey Atlantic menhaden and its two competing predators, the striped bass and the non-native blue catfish. The model also considers the following ecological issues related to these three species: the overfishing of menhaden, the invasiveness of the blue catfish, and the harvesting of blue catfish as a method to control the population. A series of modeling scenarios are considered based …
Modeling The Bidirectional Glutamine/ Ammonium Conversion Between Cancer Cells And Cancer-Associated Fibroblasts, Peter Hinow, Gabriella Pinter, Wei Yan, Shizhen Emily Wang
Modeling The Bidirectional Glutamine/ Ammonium Conversion Between Cancer Cells And Cancer-Associated Fibroblasts, Peter Hinow, Gabriella Pinter, Wei Yan, Shizhen Emily Wang
Mathematical Sciences Faculty Articles
Like in an ecosystem, cancer and other cells residing in the tumor microenvironment engage in various modes of interactions to buffer the negative effects of environmental changes. One such change is the consumption of common nutrients (such as glutamine/Gln) and the consequent accumulation of toxic metabolic byproducts (such as ammonium/NH4). Ammonium is a waste product of cellular metabolism whose accumulation causes cell stress. In tumors, it is known that it can be recycled into nutrients by cancer associated fibroblasts (CAFs). Here we present monoculture and coculture growth of cancer cells and CAFs on different substrates: glutamine and ammonium. …
Explicit Tight Frames For Simulating A New System Of Fractional Nonlinear Partial Differential Equation Model Of Alzheimer Disease, Mutaz Mohammad, Alexander Trounev
Explicit Tight Frames For Simulating A New System Of Fractional Nonlinear Partial Differential Equation Model Of Alzheimer Disease, Mutaz Mohammad, Alexander Trounev
All Works
This paper is devoted to develop a new mathematical model for Alzheimer disease based on a system of fractional-order partial differential equations. The system of Alzheimer disease includes neurons, astrocytes, microglias and peripheral macrophages, as well as amyloid β aggregation and hyperphosphorylated tau proteins. We consider the Caputo fractional derivative definition to analyze the formulated system by simulating the effect of drugs that either failed or currently in clinical trials. To simulate the model, we use tight frame (framelet) systems generated using the unitaryand oblique extension principle. According to the simulation results, and based on using such new direction of …
Mathematical Modeling Of Nonlinear Problem Biological Population In Not Divergent Form With Absorption, And Variable Density, Maftuha Sayfullayeva
Mathematical Modeling Of Nonlinear Problem Biological Population In Not Divergent Form With Absorption, And Variable Density, Maftuha Sayfullayeva
Acta of Turin Polytechnic University in Tashkent
В работе установлены критические и двойные критические случаи, обусловленные представлением двойного нелинейного параболического уравнения с переменной плотностью с поглощением в "радиально-симметричной" форме.Такое представление исходного уравнения дало возможность легко построить решения типа Зельдовоч-Баренбатт-Паттл для критических случаев в виде функций сравнения.