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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.

    Keywords: neural networksCybenko theoremdiffusion equationfluid dynamics

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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....

    Keywords: population dynamicsenergyFluid Mechanicsmfrictionroller coasterintegration by8 parts

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    2018-Winkle-Igoshin-Bennett-Josic-Ott-Modeling_Mechanical_Interactions_in_Growing_Populations_of_Rod-Shaped_Bacteria
    Here, we present an agent-based model that allows growing cells to detect and respond to mechanical interactions.

    Keywords: bacteriaagent-basedpopulationbrod-shapedcellular growth

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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...

    Keywords: resistanceprojectile motionprojectilefluidMersenne

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    Engaging Undergraduates in Mechanisms of Tubular Reabsorption and Secretion in the Mammalian Kidney
    If students fail to see the connections among physiological systems, they can become overwhelmed with the amount of information they need to learn. Some students have particular difficulty with the...

    Keywords: OsmosisActive transportMass flowRenal reabsorptionRenal secretionTransport across membranes

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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.

    Keywords: infectioncompartmenthospitalventilationairbornesthochasticWells–Riley

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    The Flight Physics Concept Inventory: Reliably Evaluating Aerodynamic Lift, Drag and Associated (Naïve) Concepts of Flight in Class and In-Game
    Students often struggle to transfer conceptual understanding from isolated instruction to a coherent mental model. This is especially true for the context of flight physics, fluid dynamics, or the...

    Keywords: active learninggamificationmisconceptionsaerodynamicsfluid dynamicsResearch-based assessment instrumentConceptual SurveyPRE-/POST-test

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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.

    Keywords: laboratoryunderdampedoverdampedcritically dampedharmonic motionimage processingviscous fluid

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    5-005-Dialysis-ModelingScenario
    We design a compartment model of a kidney dialysis machine and compare 3 and 9 compartments for the machine as well as determine the effect of change in one of the parameters in the model on the...

    Keywords: countercurrent multiplierkidneydialysisconcurrentcompartment

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    It's a bird! It's a plane! It's biomechanics!
    Biomechanics is a discipline that draws from physics and engineering principles to understand the movement and structure of living organisms. It is highly interdisciplinary in nature and can be...

    Keywords: EvolutionecologybatphysiologyAnatomybirdFlightforcesinsect

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    Nuclear and Cytoplasmic Viscosity
    This module introduces a modified Stokes-Einstein equation in the context of understanding the difference in viscosity between the nucleus and cytoplasm of cells

    Keywords: linear equationsCell StructureCell GrowthCytoplasmic Viscosity

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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.

    Keywords: population dynamicslogistic equationlocation-dependent carrying capacities

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    2008-William_Revelle-Cues Tendencies and Actions-The Dynamics of Action Revisited
    This article describes a reparameterization of the original theory of dynamics of action and applies the power of simple modeling to the study of action, emotions, and social behavior.

    Keywords: psychologytask referenceachievement motivationdynamics of action

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    MathBench Population Dynamics Module Activity
    The resource accompanies the Mystery of the Missing Housefly Population Dynamics MathBench module which explores exponential and logistic growth models. Students explore the assumptions of the...
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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.

    Keywords: cancertumor-inhibiting cytotoxic actiontumor-promoting inflammationimmune-induced tumor dormancytumor growth dynamics

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    EREN PFPP Species Composition Curriculum Module with Data
    In this lab, students will learn foundational concepts of forest community dynamics and apply quantitative skills to data analysis and interpretation activities. Students will use tree plot data...

    Keywords: forest ecologyecologydata analysisdata in the classroomCommunity Ecologyscience educationcourse-based undergraduate research experiencecurriculum materialsPlant EcologyPlant community assemblyCollaborative researcheren

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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.

    Keywords: allee_effectdelayed biological systemsfood limitperiodiciityrecruitment modelRegulation of Haematopoiesis

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    Food Chain Dynamics In A Simple Ecosystem
    In this lab, students will work with a simple algae/brine shrimp environment to learn about food chains and population dynamics. It was implemented with limited alteration for an Introductory...

    Keywords: ecologyecosystemsfood chain

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    Using Regression Models to Examine the Effect of Carbon Dioxide on Fluid pH
    In this activity students will use statistics and regression models to explore the effects of carbon dioxide on blood pH by measuring pH changes that occur over time as carbon dioxide reacts with...

    Keywords: BiochemistryphysiologyAnatomyGeneral BiologyChoosing modelsCreate graphsInterpret graphsConcepts in Statisticscreate modelsmake predictions

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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.

    Keywords: bNewton's Law of Coolingwater bottleautonomousbottle

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