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  1. 9-015-S-UnearthingTruth

    28 Aug 2019 | Modeling Scenarios | Contributor(s):: Kurt Bryan

    This project introduces electrical resistivity tomography, a technique of interest for geophysical imaging, used to produce images of underground features or structures by using electrical current. Specifically, a known electrical current is injected into an object (for example, the earth) and...

  2. 1-083-S-FallingMeteorites

    24 Aug 2019 | Modeling Scenarios | Contributor(s):: Lyle Clifford Smith

    After introducing the solution to the ordinary differential equation which models a falling object with drag (first-order, non-linear, separable), students will consider generalizing the model to a falling and disintegrating meteorite. The focus is on creative identification of factors. Students...

  3. 1-082-S-MirrorMirror

    21 Aug 2019 | Modeling Scenarios | Contributor(s):: Kurt Bryan

    This project models the ``Foucault Knife Edge Test,'' an optical test commonly used by amateur astronomers who make their own mirrors for reflecting telescopes. The goal of the test is to estimate the shape of the surface of a mirror from optical reflection data. The model results in a...

  4. 9-010-S-TravelingWaves

    21 Aug 2019 | Modeling Scenarios | Contributor(s):: Eric Stachura

    In this scenario, students will be taken through a traveling wave analysis of a porous medium model. While the starting point is a nonlinear partial differential equation (PDE) model, after a change of variables, students are led quickly to an ordinary differential equation (ODE) model....

  5. 3-011-S-EulerBallThrowing

    19 Aug 2019 | Modeling Scenarios | Contributor(s):: Chris McCarthy

    If a tennis ball is thrown through the air it will eventually hit the ground due to gravity. Using Euler's method, write a short script (Python, Matlab, R, etc.) to find the trajectory of the ball which will maximize the distance the ball lands from the thrower taking into account air...

  6. 5-002-S-PhasePortraitForRelationshipDynamics

    15 Aug 2019 | Modeling Scenarios | Contributor(s):: Lawrence C Udeigwe

    The different possible dynamics of a two-person romantic relationship are modeled -- as a linear two dimensional system of equations -- and analyzed. Students are guided to explore how the mathematical model of one relationship type can be obtained by modifying the mathematical model of another....

  7. 1-068-S-WaterBottleCooling

    14 Aug 2019 | Modeling Scenarios | Contributor(s):: Eli E Goldwyn

    The scenario uses an Inquiry Based Learning approach to walk the students through the creation and understanding of a differential equation describing how fluid in a water bottle will change its temperature to approach the ambient temperature in a room. The goal is for the students to understand...

  8. 3-150-S-ItsABlastFurnace

    13 Aug 2019 | Modeling Scenarios | Contributor(s):: Kurt Bryan

    This project uses the steady-state heat equation to model the temperature distribution in an industrial furnace used for metal production, for example, a blast furnace.The heat flow is assumed to be steady-state, so that only an elementary ordinary differential equation (ODE) is needed, and...

  9. 1-076-S-ClimateBifurcation

    08 Aug 2019 | Modeling Scenarios | Contributor(s):: Mayer Humi

    In this paper we present (for educational purposes) simple zero and one dimensional models for the mean temperature of the Earth. These models can exhibit bifurcations from the present Earth climate to an ice age or a ``Venus type of climate.'' The models are accompanied by Matlab.

  10. 9-005-S-InvasiveSpeciesModel

    08 Aug 2019 | Modeling Scenarios | Contributor(s):: Eric Stachura

    This scenario takes students through the development of an invasive species partial differential equation model. Basic models are discussed first, which lead students to eventually develop their own model which takes into account dispersion. Students will explore various Mathematica modules...

  11. 3-130-S-MatterOfSomeGravity

    07 Aug 2019 | Modeling Scenarios | Contributor(s):: Kurt Bryan

    This project introduces the concept of an inverse problem (or parameter estimation), in the context of the simple linearized pendulum ordinary differential equation. The theme of the project is that one often has a physical model for a system but in which the model contains unknown parameters or...

  12. 5-025-S-SaltCompatments

    19 Jul 2019 | Modeling Scenarios | Contributor(s):: Brian Winkel

    Model a phenomena in which salt mixtures from two tanks are mixed using several strategies.

  13. 1-001d-S-HotelPopulationDecay

    03 Jul 2019 | Modeling Scenarios | Contributor(s):: Dina Yagodich

    We offer students an opportunity to create a simulation model a hotel population with clients checking in and checking out according to two different disciplines as well as a number of different starting populations in the hotel.

  14. 1-001c-S-PopulationDecayThenSome

    18 Jun 2019 | Modeling Scenarios | Contributor(s):: Dina Yagodich

    This is an adaption of Modeling Scenario 1-001-S-MandMDeathAndImmigration  in which death and immigration of m&m's is replaced by check outs and arrivals in a hotel and makes specific use of MatLab coding.

  15. 3-067-S-RLCSeriesCircuit

    28 Apr 2019 | Modeling Scenarios | Contributor(s):: Virgil Ganescu

    In this validation-oriented setup, the second order linear ordinary differential governing equation of a small signal RLC series AC circuit is solved analytically, and the results are compared with the data acquired from analyzing the numerical model (using Multisim).

  16. 1-107-S-ClothDry

    27 Apr 2019 | Modeling Scenarios | Contributor(s):: Brian Winkel

    We build a mathematical model for the rate at which drying takes place in a cloth wet with water while hanging in air. A model can be based on underlying physical principles. Such a model is called an analytic model. Or your model could be based on observations and reasoned terms in your...

  17. 5-090-S-SolidParticleErosion

    27 Mar 2019 | Modeling Scenarios | Contributor(s):: Rich Laverty

    By applying Newton's second law, and making a collection of reasonable assumptions, students will derive a system of differential equations that model the path of a rigid particle as it gouges material from a more ductile surface. Examination of the solution will yield a formula for the...

  18. 1-109-S-EmployeeAttrition

    25 Mar 2019 | Modeling Scenarios | Contributor(s):: Lyle Clifford Smith

    This scenario models the loss of employees and the employer's attempt to retain them through stock options. This is intended for introductory students and is paired well with exponential growth/decay material. We also introduce the 5% rule to sort possible factors into assumptions and...

  19. 1-125-S-DiceyPopulations

    04 Mar 2019 | Modeling Scenarios | Contributor(s):: Brian Winkel

    We offer students an opportunity to generate unique data for their team on a death and immigration model using 12 and 20 sided dice and then pass on the data to another student team for analysis with a model they built. The key is to recover the parameters and try to explain how the simulation...

  20. 1-077-S-RLMSimSeriesCircuit

    03 Mar 2019 | Modeling Scenarios | Contributor(s):: Virgil Ganescu

    In this validation-oriented setup, the first order linear ordinary differential equation governing a small signal RL series AC circuit is solved analytically and the results are compared with the data acquired from analyzing the numerical model (using Multisim) of the circuit. This is compared to...