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    Potential Scenario
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    2017-Alex_Honchar-Neural Networks For Solving Differential Equations
    In this post I want to show how I applied simple feed-forward NNs to different differential equations with increasing complexity: ODEs, second order ODEs, and, finally, PDEs.
    neural networksCybenko theoremdiffusion equationfluid dynamics
    Modeling Scenario
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    1-120-CircularRollerCoaster-ModelingScenario
    Students study the dynamics of a circular roller coaster and work out the equations of motion in the ideal case as well as considering the interesting complication of including kinetic friction. This problem is an excellent introduction for students
    population dynamicsenergyFluid Mechanicsmfrictionroller coasterintegration by8 parts
    Article or Presentation
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    2014-C_W_Groetsch-S_A_ Yost-Vertical Projection_in_a_Resisting_Medium_Revelations_on_Observations_of_Mersenne
    This article, inspired by a 17th-century woodcut, validates empirical observations of Marin Mersenne (1588–1648) on timing of vertically-launched projectiles for a general mathematical model of resistance.
    resistanceprojectile motionprojectilefluidMersenne
    Potential Scenario
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    2009-Noakes-Sleigh-Mathematical models for assessing the role of airflow on the risk of airborne infection in hospital wards
    Understanding the risk of airborne transmission can provide important information for designing safe healthcare environments with an appropriate level of environmental control for mitigating risks.
    infectioncompartmenthospitalventilationairbornesthochasticWells–Riley
    Potential Scenario
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    2009-Shamim-EtAl-Investigating viscous damping using a webcam
    We describe an experiment involving a mass oscillating in a viscous fluid and analyze overdamped, critically damped and underdamped regimes of harmonic motion.
    laboratoryunderdampedoverdampedcritically dampedharmonic motionimage processingviscous fluid
    Potential Scenario
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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
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    2016-Wilkie-EtAl-Using ODEs to Explore Cancer-Immune Dynamics and Tumor Dormancy
    Here we present a general method using ordinary differential equations (ODEs) to model and analyze cancer-immune interactions, and in particular, immune-induced tumor dormancy.
    cancertumor-inhibiting cytotoxic actiontumor-promoting inflammationimmune-induced tumor dormancytumor growth dynamics
    Potential Scenario
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    2006-Shigui_Ruan-Delay differential equations in single species dynamics
    In this survey, we shall review various delay differential equations models arising from studying single species dynamics.
    allee_effectdelayed biological systemsfood limitperiodiciityrecruitment modelRegulation of Haematopoiesis
    Modeling Scenario
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    1-068-WaterBottleCooling-ModelingScenario
    Students create of a differential equation describing how fluid in a water bottle will change its temperature to approach the ambient temperature in a room.
    bNewton's Law of Coolingwater bottleautonomousbottle
    Modeling Scenario
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    1-090-EmptySphericalTank-ModelingScenario
    We model the emptying of water from a spherical tank. First, we pump out water at a constant rate. Second, we allow the water to exit through a small hole in the bottom of the tank. We seek to determine how fast the water level is falling in both...
    VolumesphereTorricelli's Lawtimingspherical tankfluidempty
    Modeling Scenario
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    7-020-ThermometerInVaryingTempStream-ModelingScenario
    We present a first order differential equation model for the temperature of a mercury thermometer which is sitting in a stream of water whose temperature oscillates. We suggest a solving strategy which uses Laplace Transforms.
    temperaturesteady statethermometerheat exchangetransfer functionphase lagInvers Laplace Transform
    Potential Scenario
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    2008-Huangi-Lu-Modeling long-term longitudinal HIV dynamics with applications to an AIDS clinical study 
    To better understand the factors responsible for the virological failure, this paper develops the mechanism-based nonlinear differential equation models for characterizing long-term viral dynamics with ARV therapy.
    longitudinal dataAIDSantiretroviral drug therapyBayesian nonlinear mixed-effectstime-varying drug efficacyHIV dynamics
    Potential Scenario
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    2007-I-Liang_Chern-Mathematical Modeling and Differential Equations
    In this course, I will mainly focus on, but not limited to, two important classes of mathematical models by ordinary differential equations: • population dynamics in biology • dynamics in classical mechanics.
    population dynamicsecologydynamicsclassical mechanicschemical reaction
    Potential Scenario
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    2009-Marten-EtAl-Derivation and analysis of an ordinary differential equation for epilepsy dynamics
    In this paper we describe how an ordinary differential equation model of corticothalamic interactions may be obtained from a more general system of delay differential equations.
    delayepilepsy dynamicsepilepsybistabilityseizure activity
    Potential Scenario
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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
    Free Online Textbook
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    2014-Andre_De Ross-Modeling Population Dynamics
    This course is intended as an introduction to the formulation, analysis and application of mathematical models that describe the dynamics of biological populations.
    predator-preycompetitionpopulationgrowthbifrucationtext
    Potential Scenario
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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
    Modeling Scenario
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    1-135-FishHarvesting-ModelingScenario
    This short activity will walk students through a guided list of questions to help them to understand how the stability of equilibrium changes with changes in a model parameter, in this case the rate of harvesting fish.
    population dynamicsfishstabilitybifurcationharvest
    Potential Scenario
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    2006-Loyd-Wodarz-Drug Resistance in Acute Viral Infections-Rhinovirus as a Case Study
    We develop an epidemiological model that can be used to address the spread of resistance at the population level, and a virus dynamics model that can be used to study the dynamics of virus over the time course of an individual’s infection.
    stabilityresistancevirusdrugepidemic competitionimmune responserhinovirus
    Potential Scenario
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    2005-P_Howard-Modeling with ODE
    In these notes we consider three critical aspects in the theory of ordinary differential equations: developing models of physical phenomena, mathematically well-posed, solving ODE numerically .
    Fluid Mechanicscompartmentpopulationsvariational methodsHamiltonian mechanics