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    Potential Scenario
    107

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    42

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    2001-Edwards-Buckmire-A differential equation model of North American cinematic box-office dynamics
    A new mathematical model is presented for the box-office dynamics of a motion picture released in North America.
    cinemamoviesbox-office
    Potential Scenario
    159

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    76

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    2014-Do-Lee-A Differential Equation Model for the Dynamics of Youth Gambling
    We examine the dynamics of gambling among young people aged 16–24 years, how prevalence rates of at-risk gambling and problem gambling change as adolescents enter young adulthood, and prevention and control strategies.
    reproductive numberGamblingepidemicsensitivity indexyouth gambling
    Modeling Scenario
    310

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    329

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    0

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    5-024-PhGreatLakes
    In this teaching modeling scenario, we demonstrate how lessons on salt-tank compartmental modeling can be used to predict phosphorus levels in the Great Lakes.
    Great Lakeslimnologycomparmentpollutioncompartmental modelsphosphorous
    Potential Scenario
    125

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    67

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    2000-deOlivera-Delfino-Costa-Leite-Pinhole Water Flow From Cylindrical Bottles
    The water flowing from the first bottle feeds the second one located below it. The same concepts of mass and energy conservation now lead to a non-trivial differential equation for the lowest bottle dynamics.
    Torricelli's LawConservation of EnergytConservation of MassBernoulli’s Theorem
    Potential Scenario
    149

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    85

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    2015-Heiko_Enderling-Integrating experimental data to calibrate quantitative cancer models
    For quantitative cancer models to be meaningful and interpretable the number of unknown parameters must be kept minimal. We focus on a tumor hierarchy of cancer stem and progenitor non-stem cancer cells.
    cancertumorfittingagent-based
    Potential Scenario
    184

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    41

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    2000-Dwayne-Anderson-Estimates of the future membership of the Church of Jesus Christ of Latter-Day Saints
    Thus, the purpose of this paper is to model the membership of the Church of the Latter Day Saints from the available data on membership from 1844 to 2000.
    population dynamicslogisticLatter-Day Saints
    Modeling Scenario
    393

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    373

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    0

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    3-100-Ripcord-Toys-ModelingScenario
    This modeling scenario examines the motion of a ripcord-powered toy with the goal of using real data to estimate parameters in a first-order model of the velocity of the toy. Students may conduct experiments or use videos to collect data.
    dataphysicsdynamicsdata collectionrollingslippingripcordtoy
    Potential Scenario
    126

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    91

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    2015-Liang-EtAl-Advanced ordinary differential equation based head modelling for Chinese marionette art preservation
    This paper addresses the heritage preservation of the marionette head carving by digitalizing the head models with a novel modelling technique using ordinary differential equations (ODEs).
    digitizationcontrolmarionetteChinese marionettehead carving
    Potential Scenario
    159

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    40

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    2013-Boscolo-Stellato-Undergraduate study of harmonic and parametric motion of a simple spring-mass system from motion waveforms
    In this paper, we describe a laboratory exercise that caters to beginning students while giving those with more background an opportunity to explore more complex aspects of the motion.
    laboratoryexperimentspring massair frictionapparatuswaveforms
    Potential Scenario
    121

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    56

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    2007-Choisy-Guégan-Rohani-Mathematical Modeling of Infectious Diseases Dynamics
    After presenting general notions of mathematical modeling (Section 22.2) and the nature of epidemiological data available to the modeler (Section 22.3), we detail the very basic SIR epidemiological model (Section 22.5).
    stochasticSIR modeldeterministicincubationinfectives
    Modeling Scenario
    245

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    473

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    0

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    3-004-VanderPol-ModelingScenario
    This paper presents an electronic spreadsheet model of the Van der Pol oscillator, a well-known nonlinear second-order ordinary differential equation.
    phase planeVan der Pol oscillatorlimit cycleRunge-Kutta methodLienard equation
    Potential Scenario
    156

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    44

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    0

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    2013-Clarke-Skirba-Rationale and resources for teaching the mathematical modeling of athletic training and performance
    It is advisable that the professionals involved learn the various tools available for designing effective training programs.
    fitnessexercise physiologycritical power modelBanister impulse-response modelcoaching educationphysical fitnessperformance modeling
    Potential Scenario
    273

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    93

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    2006-Wilensky-Reisman-Thinking Like a Wolf a Sheep or a Firefly
    We describe a computation-based approach that enables students to investigate the connections between different biological levels using agent-based, embodied modeling tools.
    simulationNetLogopredator-preyagent-basedwolffox
    Modeling Scenario
    349

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    542

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    0

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    3-103-PullBackCars-ModelingScenario
    This activity offers analysis of a toy pull-back car: solution of a differential equation from model; data collection and parameter estimation; and adapting the model to predict maximum speed and distance traveled for a new pull-back distance.
    modelingdynamicshands-ontoypull-back carpullback