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Downloads
Views
Date
Relevance
Potential Scenario
106
views
41
downloads
0
comments
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 Law
Conservation of Energyt
Conservation of Mass
Bernoulli’s Theorem
Potential Scenario
118
views
48
downloads
0
comments
2017-Adolfo_Rumbos-Differential Equations and modeling
The study of any phenomenon in the physical or biological sciences, in which continuity and differentiability assumptions about the quantities in question can be made, invariably leads to a differential equation, or a system of differential...
pendulum
Lotka Volterra equations
existence
uniqueness
Modeling Scenario
203
views
96
downloads
0
comments
3-085-SimplePendulum-ModelingScenario
Thestudent is asked to derive and solve a differential equation that gives the position (angle
Newton's Second Law of Motion
pendulum
kinetic energy
potential energy
Conservation of Energyt
initial conditions
small angle approximation
Taylor polynomial
percent error
Modeling Scenario
254
views
173
downloads
0
comments
3-010-EnergyInSpringMassSystem-ModlingScenario
As a way to synthesize the effects of damping and forcing terms, this activity is meant to encourage students to explore how different forcing terms will change the total energy in a mass-spring system.
energy
mass-spring system
kinetic energy
potential energy
total energy
Modeling Scenario
219
views
149
downloads
0
comments
1-057-FiguringFluidFlow-ModelingScenario
We propose three differential equations models for the height of a column of falling water as the water exits a small bore hole at the bottom of the cylinder and ask students to determine which model is the best of the three.
discharge
tank
Torricelli's Law
Conservation of Energy
fluid flow
height
liquid
Modeling Scenario
187
views
167
downloads
0
comments
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 transfer
experiment
conduction
convection
boundary conditions
finite volume method
Modeling Scenario
254
views
248
downloads
0
comments
1-114-EarthClimate-ModelingScenario
In this modeling scenario, we investigate the Earth's climate using a zero-dimensional energy balance model. Energy balance models are climate models that try to predict the average surface temperature of the Earth.
climate
energy
temperature
linearization
phase lines
energy balance model
root finding
Potential Scenario
128
views
41
downloads
0
comments
2009-James_May-Nonlinear vibration control of long flexible structures
An automated, non-linear control scheme was developed to transfer energy from the fundamental vibration mode, where most vibration energy of the structures of interest resides, to higher order modes where vibration impedance was shown to be...
vibration
damping
tuned mass damper
viscous
nodal
model damping
flexible structure
energy transfer
Modeling Scenario
470
views
255
downloads
0
comments
1-050-BargingAhead-ModelingScenario
As captain of a barge, you need to determine how fast to transport your barge up river against the current in order to minimize the expended energy.
optimization
kinetics
energy
trophic efficiency
work
river
terminal velocity
friction
current
force
barge
worlk
speed
Potential Scenario
104
views
36
downloads
0
comments
2017-Ben_Finio-Science Buddies – Linear & Nonlinear Springs Tutorial
This tutorial provides a basic summary of linear and nonlinear springs and their associated equations for force, stiffness, and potential energy.
spring mass
stiffness
springs
potential energy
force
nonlinear spring
linear spring
Potential Scenario
261
views
33
downloads
0
comments
2008-Claire_Vailance-Reaction_Kinetics-Course_Notes
This is but one of several set of notes which may interest the reader on chemical kinetics.
kinetics
parameters
rate constant
chemical kinetics
reactions
Potential Scenario
144
views
49
downloads
0
comments
2013-Kose-Kunze-Climate Modeling in the Calculus and Differential Equations Classroom
We introduce here the basic principles of climate science for a one-dimensional Energy Balance Model (EBM),
climate change
Energy Balance Models
ice albedo
Potential Scenario
176
views
26
downloads
0
comments
2014-John_Cain-Chemical Reaction Kinetics Mathematical Underpinnings
The usual way of deriving kinetic equations involves application of the principle of conservation of mass in conjunction with the law of mass action. Here, examples of kinetic models for several basic processes are discussed.
kinetics
biochemical reaction
reactants
products
Modeling Scenario
383
views
200
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
Modeling Scenario
337
views
548
downloads
0
comments
1-076-ClimateBifurcation-ModelingScenario
We cover simple zero and one dimensional models for the mean temperature of the Earth. These models can exhibit bifurcations.
energy balance
climate
energy
albedo
Hysteresis
bifurcation
ice-age
greenhouse
balance
Stefan Boltzmann Law
Modeling Scenario
358
views
400
downloads
0
comments
1-047a-CondensationOptimization-ModelingScenario
We seek to optimize a condensation process which is modeled by a simulation using the random motion of 200 particles in a 50 by 50 square in which a particle bounces off the two vertical and top walls and condenses on the bottom wall.
simulation
data
optimization
energy
condensation
best fit
cost
sum of scquare errors
Article or Presentation
117
views
40
downloads
0
comments
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.
resistance
projectile motion
projectile
fluid
Mersenne
Potential Scenario
128
views
51
downloads
0
comments
1989-R_Blickhan-Spring Mass Model For Running-Hopping
A simple spring—mass model consisting of a massless spring attached to a point mass describes the interdependency of mechanical parameters characterizing running and hopping of humans as a function of speed.
spring mass
jump
jumping
Modeling Scenario
213
views
338
downloads
0
comments
3-073-EarthQuakePartII-ModelingScenario
Your goal here is to determine how much friction/damping should be designed into a building to keep the roof from moving too far (which would result in the entire building collapsing) when it undergoes minor vibrations from a small earthquake.
earthquake
vibration
damping
amplitude
spring-mass system
steady-state solution
underdamped
Potential Scenario
161
views
60
downloads
0
comments
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.
optimization
Biochemistry
sensitivity analysis
chromatography
mass action
cluster analysis
conservation laws
dimerization
estrogen receptor protein
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