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Downloads
Views
Date
Relevance
Modeling Scenario
419
views
826
downloads
0
comments
9-002-GroundWaterFlow-ModelingScenario
The goals of this project are to compare a conceptual one-dimensional groundwater flow model to observations made in a laboratory setting, and to discuss the differences.
s
groundwater flow
Darcy's Law
heat equation
aquifer
hydraulic head
Fourier's Law
sand tank
Modeling Scenario
338
views
266
downloads
0
comments
1-026-Evaporation-ModelingScenario
We provide data on evaporation of 91% isopropyl alcohol in six different Petri dishes and one conical funnel and on evaporation of water in one Petri dish. We ask students to develop a mathematical model for the rate of change in the respective...
evaporation
cone
alcohol
Petri dish
Article or Presentation
826
views
366
downloads
0
comments
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.
module
optimization
spring mass
mass
spring\
cost
Teaching Module
minimal cost
Article or Presentation
223
views
508
downloads
0
comments
2020-TeachingModule-ModelingNonlethalInfluenzaEpidemic
We discuss the modeling efforts and tools for success in modeling the spread of nonlethal influenza in an English boarding school
module
epidemic
boarding school
Teaching Module
Article or Presentation
229
views
568
downloads
0
comments
2020-TeachingModule-ModelingSpreadOfOilSlick
This is support material and video for teaching a Modeling Scenario using a first order ODE to model the spread of an oilslick with incomplete data.
module
oil slick
Teaching Module
Article or Presentation
183
views
539
downloads
1
comments
2020-TeachingModule-ModelingFallingColumnOfWater
We discuss how to model a falling column of water empirically and analytically from first principles in physics laws.
module
column of water
Torricelli's Law
Torricelli
Teaching Module
Article or Presentation
278
views
809
downloads
0
comments
2020-TeachingModule-SpreadOfCommonColdSimulation
This simulation is meant to introduce the idea of a differential equation model and investigate the impact of heightened hygiene and decreased interactions on the spread of an infectious disease. The focus of this simulation is on the common cold.
simulation
module
infectious disease
disease
spread
Teaching Module
spread of disease
Modeling Scenario
314
views
476
downloads
0
comments
1-132-DigoxinElimination-ModelingScenario
We model the concentration of digoxin eliminated from the human body at a rate proportional to the concentration. This is a ``first-order reaction'' in the language of pharmacokinetics -- the study of how drugs move in the body.
nullclines
pharmacokinetics
digoxin
drug elimination
two compartment
Article or Presentation
5839
views
713
downloads
0
comments
2020-TeachingModule-GeometricBehaviorOfLinearSysteModeling
This module concentrates on the geometric properties of a system of 2 linear, homogeneous first order differential equations in 2 variables as dictated by the corresponding eigenvalues. Students should be familiar with using eigenvalues.
module
linear systems
digoxin
Teaching Module
Article or Presentation
264
views
527
downloads
0
comments
2020-Teaching Module-Applying Separation Of Variables
This is one of several Teaching Modules prepare by the Principal Investigates of SIMIODE’s National Science Foundation grant and offered in 2020. The material offered is a complete narrative of how a modeling activity can be offered including...
modules
Ebola
separation of variables
Teaching Modules
Separation
Modeling Scenario
336
views
586
downloads
0
comments
1-155-CruiseControl-ModelingScenario
In this project we illustrate the design of a proportional-integral-derivative (PID) cruise control algorithm for an automobile. PID control is one of the most common techniques in control engineering.
PID controller
feedback control
Control theory
cruise control
automobile
closed-loop control
input-ouput
block diagram
Technique Narrative
160
views
276
downloads
0
comments
1-061-SingularPerturbation-TechniqueNarrative
This paper introduces the basics of singular perturbation methods for solving ordinary differential equations. Interactive examples will show how the smallness of physical parameters can drastically change the nature of the solutions.
perturbation
singular perturbation
Technique Narrative
198
views
324
downloads
0
comments
1-060-RegularPerturbation-TechniqueNarrative
This paper presents an introduction to a set of analytical approximations referred to as regular perturbation. This is a particular mathematical tool within the broader set of perturbation methods.
perturbation
regular perturbation
asymptotic expansions
analytical approximation
Bernoulli equation
Modeling Scenario
524
views
260
downloads
0
comments
1-104A-T-InfectionRisk-ModelingScenario
This project is designed to examine differences between the exponential and logistic growth models in biology and how to apply these models in solving epidemic questions and comparing to actual disease data sets.
regression
infection
COVID19
carrying capacity
logistic equation
exponential model
Modeling Scenario
367
views
317
downloads
0
comments
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.
data
physics
dynamics
data collection
rolling
slipping
ripcord
toy
Modeling Scenario
261
views
178
downloads
0
comments
3-130-MatterOfSomeGravity-ModelingScenario
This project introduces the concept of an inverse problem (or parameter estimation), in the context of the simple linearized pendulum ordinary differential equation.
gravity
inverse problem
acceleration
Modeling Scenario
401
views
1003
downloads
0
comments
1-015-Torricelli-ModelingScenario
We help students develop a model (Torricelli's Law) for the height of a falling column of water with a small hole in the container at the bottom of the column of water through which water exits the column.
data
Spanish
tank
column of water
aperture
Torricelli's Law
Conservation of Energyt
Solver
water flow
Excel Solver
Technique Narrative
217
views
242
downloads
0
comments
1-015-DimensionlessVariables-TechniqueNarrative
This material introduces the idea of ``rescaling'' for ordinary differential equations (ODE's) by the use of dimensionless variables. In practice this is an extremely common and useful prelude to the analysis and solution of ODE's.
linearization
dimensional analysis
time scale
scaling
dimensionless variables
spatial scale
Modeling Scenario
422
views
213
downloads
0
comments
6-005-InsectColonySurvivalOpt-ModelingScenario
We present a system of nonlinear differential equations to model the control of energy flow into producing workers or reproducers in an insect colony, using a set of given parameters and a number of different energy functions.
optimization
Optimal Control Theory
insect colony
optimal control
natural resources
Pointryagin's Maximum Principle
control variable
Potential Scenario
249
views
84
downloads
0
comments
2023-Roberto_Camassaa-Richard_McLaughlina-Tauberian identities and the connection to Wile E Coyote physics
The application of the motion of a vertically suspended mass-spring system released under tension is studied focusing upon the delay timescale for the bottom mass as a function of the spring constants and masses.
Hangtime
Tauberian Identities
Road Runner
Wile E. Coyote
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