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    Potential Scenario
    182

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    49

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    2012-Transtrum-Qiu-Optimal experiment selection for parameter estimation in biological differential equation models
    We explore the question to what extent parameters can be efficiently estimated by appropriate experimental selection.
    experimental designsystems biologyAssociation & Data Fittingreaction ratesdecay rates
    Modeling Scenario
    235

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    590

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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
    Potential Scenario
    170

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    45

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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
    Modeling Scenario
    255

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    269

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    1-002-Tossing-ModelingScenario
    We offer students simulation experience or data from a simulation and ask them to model the simulation using several approaches, to include exponential decay fit, difference equation, and differential equation.
    Modeling and simulationexponentialdecaydice
    Modeling Scenario
    277

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    200

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    1-074-BottleWaterFlow-ModelingScenario
    We offer an experiment in which data is collected to ascertain a parameter in the differential equation formulation of Torricelli's Law for water flow.
    bwaterTorricelli's Lawbottle
    Potential Scenario
    155

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    87

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    0

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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
    185

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    45

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    1969-Israelsson-Johnsson-Phase-shift in Geotropic Oscillations a Theoretical and Experimental Study
    The paper studies geotropical induced phase-shifts in circumnutations (turning) of Helianthus annus hypocotlys.
    plantoscillationdelaycircumnutationturning
    Potential Scenario
    209

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    66

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    0

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    2007-Helfgott-Seier-Some Mathematical and Statistical Aspects of Enzyme Kinetics
    We will analyze some basic ideas behind enzyme kinetics, which allow us to deal with separable and linear differential equations as well as realize the need to use power series.
    kineticsEnzymeexperimental dataregresion
    Potential Scenario
    200

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    73

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    2017-D_Goulet-Modeling, Simulating, and Parameter Fitting of Biochemical Kinetic Experiments
    In many chemical and biological applications, systems of differential equations containing unknown parameters are used to explain empirical observations and experimental data. The differential equations are typically nonlinear.
    optimizationBiochemistrysensitivity analysischromatographymass actioncluster analysisconservation lawsdimerizationestrogen receptor protein
    Potential Scenario
    215

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    46

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    1980-Peastrel-Lynch-Armenti-Terminal velocity of a shuttlecock in vertical fall
    We have performed a straightforward vertical fall experiment for a case where the effects of air resistance are important and directly measurable.
    fallingterminal velocityshuttlecockvertical fall
    Article or Presentation
    842

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    410

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    0

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    2020-TeachingModule-SpringDesignToMeetSpecsAtMinimumCosts
    We discuss a Modeling Scenario in which students are asked to design a spring mass system at minimum costs give relative costs of features of the spring.
    moduleoptimizationspring massmassspring\costTeaching Moduleminimal cost
    Potential Scenario
    148

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    57

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    2017-Bonin-EtAl-Mathematical modeling based on ordinary differential equations - promising approach to vaccinology
    As a proof of concept, we developed a model of the immune response to vaccination against the yellow fever. Our simulations have shown consistent results when compared with experimental data available in the literature.
    immune systemyellow fevercomputational immunologycomputational vaccinology
    Potential Scenario
    163

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    84

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    2016-Bonin-EtAl-Mathematical modeling based on ordinary differential equations-vaccinology
    We developed a model of the immune response to vaccination against the yellow fever. Our simulations have shown consistent results when compared with experimental data available in the literature.
    Immunologyimmune systemAntigenvaccinologyyellow fever
    Potential Scenario
    129

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    48

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    0

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    2010-Shianga-EtAl-Computational model of the human glucose-insulin regulatory system
    A computational model of insulin secretion and glucose metabolism for assisting the diagnosis of diabetes mellitus in clinical research is introduced. The
    glucose tolerance testsum of squared residualsmultiple shooting methodcost function
    Potential Scenario
    128

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    69

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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
    Modeling Scenario
    242

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    166

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    0

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    3-031-SpringCost-ModelingScenario
    We assume students are familiar with overdamping and underdamping of a spring-mass-dashpot system. Students will apply this knowledge to model the interplay between spring constant, tolerance, and cost.
    designunit costspring constantstatic equilibriumspring masss dashpot
    Modeling Scenario
    299

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    406

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    1-165-FlushToilet-ModelingScenario
    This activity analyzes the spread of a technological innovation using the Bass Model from Economics. The equation is a first-order, two-parameter separable equation and the solution has a characteristic S-shaped curve or sigmoid curve.
    juliaDiffusioninnovationrate of innovationBass modelSolver
    Article or Presentation
    164

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    53

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    0

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    1980-Peastrel-Lynch-Armenti-Terminal_velocity_of_a_shuttlecock_in_vertical_fall
    This paper offers a set of data on a falling shuttlecock (the moving object in badminton) in air. How the authors collected the data is described fully and can be replicated easily by modern equipment.
    parameter estimationdata collectionresistancefallingterminal velocityNewton's Second Law of Motionshuttlecock
    Potential Scenario
    119

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    51

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    2004-Aldo_Rescigno-On the use of pharmacokinetic models
    In this paper I will define in a simple and logical way a set of useful pharmacokinetic parameters and show how their estimation depends on the assumed model.
    compartmentsteady statepharmacokineticsvolume distribution
    Potential Scenario
    199

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    57

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    2003-Yildirim-Mackey-Feedback Regulation in the Lactose Operon
    A mathematical model for the regulation of induction in the lac operon in Escherichia coli is presented.
    mRNAlactoselactose operonfeedback regulation