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Mathematical modeling

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Full-Text Articles in Physical Sciences and Mathematics

Undergraduate Mathematics Students Question And Critique Society Through Mathematical Modeling, Will Tidwell, Amy Bennett Jan 2024

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 …

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Raising Student Awareness Of Environmental Issues Via Writing Assignments With Differential Equations, Michelle L. Ghrist Jan 2024

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.

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Blue Whale And Krill Populations Modeling, Li Zhang Jan 2024

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 …

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Solar Panels, Euler’S Method And Community-Based Projects: Connecting Differential Equations With Climate Change, Victor J. Donnay Jan 2024

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 …

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Numerical Study Of Highly Efficient Centrifugal Cyclones, Murodil Madaliev Mar 2022

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 …

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Three Questions From Cctm Teachers About Mathematical Modeling, Robyn Stankiewicz-Van Der Zanden, Rachel Levy Oct 2021

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.

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Optimization Of Urban Metro-Based Underground Logistics System Network With Hub-And-Spoke Layout, Ren Rui, Wanjie Hu, Jianjun Dong, Zhilong Chen Jul 2021

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 …

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Modeling The Ecological Dynamics Of A Three-Species Fish Population In The Chesapeake Bay, Iordanka N. Panayotova, Maila B. Hallare Mar 2021

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 …

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Mathematical Modeling Of Nonlinear Problem Biological Population In Not Divergent Form With Absorption, And Variable Density, Maftuha Sayfullayeva Sep 2020

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.

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Simulation And Exergy Analysis Of Aircraft Fuel System, Liu Shuang, Wanyan Xiaoru, Damin Zhuang Sep 2020

Simulation And Exergy Analysis Of Aircraft Fuel System, Liu Shuang, Wanyan Xiaoru, Damin Zhuang

Journal of System Simulation

Abstract: Based on a certain type of aircraft fuel system design for the prototype, and characterized by the self supplied fuel network, the mathematical models of the main components were built. Using the modular structure method, the Simulink/Matlab was adopted for building the simulation modules of various components and forming the whole simulation system. According to the simulation calculation, the flow, pressure and temperature for each node of the fuel system were obtained, and the effects of several parameters of heat exchangers on its exergy losses were analyzed. The present study provides a new method and idea for the modeling …

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Modeling And Simulation Of Multi-Nozzle Ejector Based On Flowmaster, Lan Jiang, Zhu Lei, Jingquan Zhao Aug 2020

Modeling And Simulation Of Multi-Nozzle Ejector Based On Flowmaster, Lan Jiang, Zhu Lei, Jingquan Zhao

Journal of System Simulation

Abstract: A mathematical model of multi-nozzle ejector was established according to the mass conservation, energy conservation and momentum conservation, and a modification was achieved with the introduction of momentum correction coefficient and discharge coefficient. On this basis, linear coefficients used in the fluid network method were determined, then a system-level simulation model of multi-nozzle ejector was first developed with C# language on the fluid system simulation software of Flowmaster. The simulation and experimental results of the multi-nozzle ejector in an aircraft environmental control system shows that the entrainment ratio decreases with the increasing pressure ratio of primary and secondary flow. …

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Going Beyond Promoting: Preparing Students To Creatively Solve Future Problems, Kristin M. Arney, Kayla K. Blyman, Jennifer D. Cepeda, Scott A. Lynch, Michael J. Prokos, Scott Warnke Jul 2020

Going Beyond Promoting: Preparing Students To Creatively Solve Future Problems, Kristin M. Arney, Kayla K. Blyman, Jennifer D. Cepeda, Scott A. Lynch, Michael J. Prokos, Scott Warnke

Journal of Humanistic Mathematics

While we cannot know what problems the future will bring, we can be almost certain that solving them will require creativity. In this article we describe how our course, a first-year undergraduate mathematics course, supports creative problem solving. Creative problem solving cannot be learned through a single experience, so we provide our students with a blend of experiences. We discuss how the course structure enables creative problem solving through class instruction, during class activities, during out of class assessments, and during in class assessments. We believe this course structure increases student comfort with solving open-ended and ill-defined problems similar to …

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Bordering Conditions Determination For Nanocomposites Special Properties, Tokhir Rakhimov, Muhtor Mukhamediev, Dilfuza Gafurova Aug 2019

Bordering Conditions Determination For Nanocomposites Special Properties, Tokhir Rakhimov, Muhtor Mukhamediev, Dilfuza Gafurova

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

The paper is devoted to determination of active nanoparticles sizes. Other particles bigger or smaller of calculated size limits are not demonstrated the special activity, on the example of catalytic elimination of environmental pollutants, namely, carbon monoxide, under ambient conditions - low temperature, high humidity, the presence of anthropotoxins. Discusses basic understanding of catalysts used in environmental pollution abatement, in particular, high activity of nanocatalysts with certain sizes and lack of activity of catalysts particles with other sizes. Nevertheless it remains unclear why massive objects containing palladium, as well as true solutions are not effective as catalysts for low-temperature carbon …

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A New Approach For Parameter Estimation Of The Single-Diode Model Forphotovoltaic Cells/Modules, Bi̇lge Kaan Atay, Ulaş Emi̇noğlu Jan 2019

A New Approach For Parameter Estimation Of The Single-Diode Model Forphotovoltaic Cells/Modules, Bi̇lge Kaan Atay, Ulaş Emi̇noğlu

Turkish Journal of Electrical Engineering and Computer Sciences

Solar energy has become a popular renewable energy source, leading to wide use of photovoltaic (PV) cells/modules in energy production. For this reason, realistic modeling of PVs and determining the equivalent circuit parameters is of great importance in terms of planning and operation. Hence, in this study, an analytical model for identifying the single-diode equivalent circuit parameters; series resistance (Rs ), shunt resistance (Rp ), diode ideality factor (a), diode reverse-saturation current (Io ), and photon current (Ipv ) for PV cells/modules is developed without neglecting any term. In order to test the accuracy of the model, a number of …

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Comparison Of Theoretical And Experimental Geometric Characteristics Of Betulin, A. Eshimbetov,, Sh Kurbanbaeva,, Sh. Turgunbaev,, A. Xaitbaev Oct 2018

Comparison Of Theoretical And Experimental Geometric Characteristics Of Betulin, A. Eshimbetov,, Sh Kurbanbaeva,, Sh. Turgunbaev,, A. Xaitbaev

Scientific journal of the Fergana State University

The study of betulin and its derivatives is of great importance, since the programs of mathematical modeling enable a qualitative study of the relationship between structure-spectrum-properties. As a result of the theoretical search, it is possible to determine still non-synthesized highly-biologically active derivatives of betulin

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Analysis And Simulation Of Temperature Control For Battery Pole Piece Electromagnetic Heating Roller, Jing Ran, Feng Hua, Yonggeng Wang, Haiping Song, Yanjun Xiao Jun 2018

Analysis And Simulation Of Temperature Control For Battery Pole Piece Electromagnetic Heating Roller, Jing Ran, Feng Hua, Yonggeng Wang, Haiping Song, Yanjun Xiao

Journal of System Simulation

Abstract: With the application of electromagnetic heating roller on battery pole piece rolling,the processing technology, quality and efficiency of the battery pole piece are improved. The special heating technology of electromagnetic heating roller which involves multi-physics coupling in the process of conversion makes it difficult to control the heating process and determine the control index. By studying the electromagnetic heating theory, the mathematical model of electromagnetic heating roller is established and the simulation and analysis of the electromagnetic heating roller using MATLAB software and the finite difference method are carried out. The distribution, change rule and influence factors of the …

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Analysis And Modeling Of Statistical Properties Of Fmdfb Subband Coefficients, E. Jebamalar Leavline, Sutha Shunmugam May 2016

Analysis And Modeling Of Statistical Properties Of Fmdfb Subband Coefficients, E. Jebamalar Leavline, Sutha Shunmugam

Journal of Modern Applied Statistical Methods

Fast Multiscale Directional Filter Bank (FMDFB) is an image representation scheme used in several image processing applications. The statistical nature of the FMDFB subbands is analyzed, and a mathematical model of FMDFB coefficients is proposed. Experimental results are justified by goodness-of-fit tests.

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Herd Immunity And The Necessity Of Vaccinations: Modeling The Effects Of Mmr Vaccinations, Caitlyn Cardetti, Katie Groskreutz, Melissa Zins Aug 2014

Herd Immunity And The Necessity Of Vaccinations: Modeling The Effects Of Mmr Vaccinations, Caitlyn Cardetti, Katie Groskreutz, Melissa Zins

Journal of Undergraduate Research at Minnesota State University, Mankato

The MMR vaccination is a two dose vaccine given to children between the ages of 12 – 15 months and the second dose between the ages of 4 – 6 years to prevent measles, mumps, and rubella. The objective was to mathematically model the effects of the MMR vaccinations in a hypothetical school through multiple compartment and spatial models. These models were based on each disease individually with their respective vaccine effectiveness and disease infection rates. These models demonstrated the limits of herd immunity. Herd immunity occurs when a high enough percentage of the population is immune or vaccinated to …

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Coexistence Of Multi-Allelic Polymorphism With Migration And Selection, Andrew Flick Aug 2014

Coexistence Of Multi-Allelic Polymorphism With Migration And Selection, Andrew Flick

Journal of Undergraduate Research at Minnesota State University, Mankato

Population ecology is concerned with the growth patterns of populations. This field has many applications, ranging from survival at the environmental level, to the spread of infectious diseases at the cellular level. Mathematical modeling and computer simulation can be powerful tools in researching this area. I will be investigating the spatial patterns in populations (or gene frequencies) due to migration and selection. My research conditions are for the maintenance of polymorphism under a variety of migration schemes in discrete-space and continuous-time mathematical models. The results will be applicable from the ecological level to the molecular level. Some species are better …

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Modeling And Simulation On Signatures Of Mars Minerals, Widad Elmahboub, Edward Yankey, Olivia Kerwin Oct 2010

Modeling And Simulation On Signatures Of Mars Minerals, Widad Elmahboub, Edward Yankey, Olivia Kerwin

Virginia Journal of Science

The objective of this study was to assess the feasibility of identifying minerals on Mars using remotely sensed data. In the process we also investigated the effect of noise of Aerosol and dust particles on the spectra of Mars minerals. The remotely sensed data was obtained through modeling and simulation and compared to the lab spectroscopy of the specific minerals in order to make an accurate identification. A linear model was developed using MATLAB Random Number Generator to obtain a simulated image. Part of the information we needed for the linear model was pure pixel information of Mars which was …

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Programmable Design And Implementation Of A Chaotic System Utilizing Multiple Nonlinear Functions, Recai̇ Kiliç, Fatma Yildirim Dalkiran Jan 2010

Programmable Design And Implementation Of A Chaotic System Utilizing Multiple Nonlinear Functions, Recai̇ Kiliç, Fatma Yildirim Dalkiran

Turkish Journal of Electrical Engineering and Computer Sciences

In addition to exhibiting a rich variety of bifurcation and chaos via tuning parameters, a chaotic system introduced by Sprott can be modeled and realized with a fixed main system block and many different changeable nonlinear function blocks such as piecewise-linear function, cubic function and other trigonometric functions. This system is very suitable for implementing a programmable chaos generator according to its changeable nonlinearity. This paper presents a FPAA (Field Programmable Analog Array)-based programmable implementation of this system. Nonlinear function blocks used in this chaotic system are modeled with FPAA programming and a model is rapidly changed for realizing other …

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