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    Potential Scenario
    189

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    2017-Jean-Roux-Mathematical Models in Air Quality Problems
    Presents many models with analysis in air quality control. Starts with chemical kinetics models and builds complexity to PDE models.
    air pollution effects on forest ecosystemsfinite volume methodboundary layerchemical kineticsfinite differenceemissionsdepositionsadvection
    Technique Narrative
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    201

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    9-001-SkinBurnModelNumericalMethods-TechniqueNarrative
    The heat equation is an important partial differential equation (PDE) which describes the distribution of heat in a given region over time. Numerical methods play an important role in solving these.
    Maternal-Fetal interfaceheat equationConservation of Energytheat fluxEuler's forward methodcentral differenceskin burnhyperthermiathermal conductivitylayers
    Potential Scenario
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    40

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    2014-Brun-EtAl-An introduction to the mechanics of the lasso
    Here, we study the mechanics of the simplest rope trick, the Flat Loop, in which the rope is driven by the steady circular motion of the roper’s hand in a horizontal plane.
    bifurcationmotionlassorod modelrodeo
    Potential Scenario
    134

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    47

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    2012-Nokkaew-EtAl-Estimation of Algae Growth Model Parameters by a Double Layer Genetic Algorithm
    This paper presents a double layer genetic algorithm (DLGA) to improve performance of the information-constrained parameter estimations.
    optimizationalgae growthgenetic algorithmssimulated dataconvergence of parameters
    Modeling Scenario
    172

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    164

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    9-152-HorizontalBeam-ModelingScenario
    This scenario is designed to lead students to discover a differential equation that models the vertical deflection of a horizontal beam under different boundary conditions.
    Polynomial dynamical systembeamcantilever
    Modeling Scenario
    227

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    518

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    9-020-HeatDiffusion-ModelingScenario
    This project guides students through experimental, analytical, and numerical techniques for understanding the heat (diffusion) equation with nonhomogeneous boundary conditions. In particular, students collect data and model a physical scenario.
    laboratoryDiffusionheat
    Modeling Scenario
    215

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    230

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    3-069-HeatInBar-ModelingScenario
    The temperature distribution along a uniform slender bar due to conduction and convection is investigated through experimental, analytical, and numerical approaches.
    heat transferexperimentconductionconvectionboundary conditionsfinite volume method
    Modeling Scenario
    220

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    324

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    9-015-UnearthingTruth-ModelingScenario
    This project introduces \textit{electrical resistivity tomography}, a technique of interest for geophysical imaging, used to produce images of underground features or structures by using electrical current.
    geophysicalImagingStatistical inverse problemtunnelconductionHolocaustVilniusDivergence TheoremfluxLaplace's equationimpedanceelectrical resistivity tomographytomographyresistivity
    Potential Scenario
    156

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    46

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    1969-Carl_Metzler-A mathematical model for the pharmacokinetics of LSD effect
    Contains data on performance scores vs. plasma levels of LSD in human tissues.
    LSDtestingpharmacokineticsperformanceplasma level
    Potential Scenario
    125

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    37

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    1992-CHF_Bulte-The differential equation of the deflection curve
    This paper presents the derivation and physical meaning of the general fourth-order linear differential equation (with sectionally continuous derivatives) of the deflection curve and its general formulation and solution as a multipoint BVP.
    beamdeflectionshear forcebending momentcritical loadnatural frequency
    Modeling Scenario
    225

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    328

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    9-125-BeamModeling-ModelingScenario
    This modeling scenario examines the deflection of a cantilever beam under two different distributed loads. Students will have the opportunity to conduct experiments with their own cantilever beam or use data provided to build a model.
    Fluid MechanicsbeamcantileverimpulseLaplace transformboundary conditionfourth order
    Free Online Textbook
    161

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    47

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    2014-Jiri_Lebl-Notes_on_Diffy_Qs_Differential_Equations_for_Engineers
    There is a pdf and html version of the text as well as a purchasable paperback version. The text has pretty much all the basics, but has only a few exercises and there is very little modeling.
    differential equationstextbookengineering
    Modeling Scenario
    193

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    147

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    9-030-WaterHammer-ModelingScenario
    We develop and apply a numerical algorithm that solves a system of two nonlinear partial differential equations (PDEs) that describes the time evolution of the water hammer phenomenon.
    Stock and Flow modelhyperbolic equationsfinite differenceswater hammerhydrodynamicscompressibilitywave celerity
    Modeling Scenario
    217

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    228

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    6-029-TumorGrowth-ModelingScenario
    This modeling scenario guides a student familiar with single ordinary differential equation (ODE) models towards the development of a more complex system of two ODEs for describing the evolution of tumor growth over time.
    Pop_Growth Pilotlogisticcomparmenttumorsynthetic datasum of squares error
    Potential Scenario
    125

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    59

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    2015-Erzo-Luttmer-Four Models of Knowledge Diffusion and Growth
    This paper describes how long-run growth emerges in four closely related models that combine individual discovery with some form of social learning.
    knowledge diffusionstationary distributionsproductivity distributionreaction-diffusion equationsquasi-stationary distributions
    Potential Scenario
    208

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    42

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    2012-Michael_Kerckhove-From Population Dynamics to Partial Differential Equations
    This article illustrates PDE models for location-dependent carrying capacities, migrations, and the dispersion of a population.
    population dynamicslogistic equationlocation-dependent carrying capacities
    Potential Scenario
    234

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    79

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    2012-Bech-EtAl-Resources For Engineering Applications Of Math
    Illustrations of applied mathematics including statics, truss, heat equation, column analysis, coupled oscillators, feedback control, AC circuit, chemical reactions, kinetics.
    kineticsheat equationcolumn analysiscoupled oscillatorsfeedback controlAC circuitchemical reactions
    Potential Scenario
    104

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    38

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    2011-Therese-Keane-Combat modelling with partial differential equations
    We present work seeking to more realistically represent troop dynamics and to enable a deeper understanding of the nature of conflict.
    Lanchester modeltroop dynamicsswarming behaviortroop regroupinglossesnon-local termslocal terms
    Potential Scenario
    200

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    87

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    1971-Carl_Metzler-Usefulness Of Two Compartment Open Model In Pharmacokinetics
    Compartment models are widely used in pharmaceutical research to quantitate the kinetics of absorption, distribution, metabolism and excretion of a drug. In this article two applications of the two compartment open model are discussed.
    LSDcompartmentpharmacokinetics
    Potential Scenario
    165

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    51

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    1988-Michael Intriligator-Dagobert Brito-A Predator-Prey Model of Guerrilla Warfare
    The authors present a three variable: numbers of guerrillas, numbers of regular (government) soldiers, and size of population controlled by the guerrillas, at time t), nonlinear system of three differential equations.
    combat modelguerrilla warfaregovernment