Thursday, September 8, 2011

Simulation Modeling Exercises Module 1

Exercise 1.1

Can you think of 3 other examples of models? What is the spatial/ temporal resolution in your models?

1. An engineer’s diagram of a circuit board. Spatial resolution is on the order of microns, no temporal resolution.

2. An architect’s blueprint. Spatial resolution is on the order of cm, no temporal resolution.

3. A timeline of the history of an invasion. Spatial resolution is on the order of km, temporal resolution on the order of months.
Model of Napoleon’s ill-fated 1812 invasion of Russia. Thickness of the line represents troop numbers, brown on the advance, black on the retreat. Troop size, location, date, and temperature are all captured in the model. Edward Tufte called this “probably the best statistical graphic ever drawn.”
Can you use an electric lamp as a model of the sun? What goals could such a model meet?

You could use a lamp as a model of the sun to show how light radiates out from a sphere. If your goal were to demonstrate how eclipses are generated by different states of the sun-earth-moon system, this would make an excellent model.

Exercise 1.2

Think of examples of 3 systems. How would you describe these systems?

The human body is a complex system made up of scores of organs, each of which with unique and interacting functions. An organ is a system composed of one or more types of cellular tissue. Cells within tissue interact to produce a function such as nutrient absorption or hormone secretion. Cells are complex systems comprised of proteins, membranes, and genetic material, each of which could again be described as a system.

Describe chicken noodle soup as a system. What are the elements? What is the function? What makes it a system?

Chicken noodle soup could be thought of a system comprised of water, soluble chicken elements, chicken meat, noodles, and spices. My functions for chicken soup are warmth, nourishment, and feelings of comfort, but the function of chicken soup for a chicken may be quite different, and the function for, say, Lipton, different still. It can be thought of as a system because it has multiple components which, when combined, produce a function greater than the sum of its parts. I would not derive the same satisfaction as from eating  a bowl of chicken soup by eating a chicken, drinking a glass of water, swallowing a bunch of garlic and black pepper, and then sitting on the stove for an hour.

Exercise 1.3

List five elements for each of the following systems:

I.        steam engine
1.       Fuel
2.       Combustion chamber
3.       Boiler
4.       Water pump
5.       Water

II.      oak tree
1.       Roots
2.       Xylem
3.       Phloem
4.       Leaves
5.       Acorns

III.    Thanksgiving turkey
1.       Skin
2.       Flesh
3.       Bones
4.       Gravy
5.       Stuffing

IV.    city
1.       Roads
2.       Buildings
3.       Public officials
4.       Merchants
5.       Sewers

What is the system that has the following elements: water, gravel, 3 fish, fish feed, aquatic plants?

One such system is an aquarium.

What if we add a scuba diver to this list? Can elements entirely describe a system?

Then it’s either an ecologically poor lake or sea or a very large aquarium with a scuba diver that needs a new hobby.

Elements cannot describe a system completely for at least two reasons; one is that we have defined a system as having emergent properties that are greater than the sum of its components, and another is that we cannot ever fully describe the elements of a system; there is always another level of detail to which we could appeal (eg., human body, organs, tissues, cells, proteins, atoms, quarks, strings…).

Exercise 1.4

Look at a tree in a forest and describe the relevant hierarchy.

The immediate super-system of the tree is the forest ecosystem, composed of a population of that species of tree, a community of trees and other plants, a collection of animals, fungi, etc.. Moving further up the hierarchy, the forest ecosystem fits within the global ecosystem. In the other direction, the tree’s organs—leaves, xylem, roots, etc.—are subsystems of the tree. Each of those contain tissues and within those cells, proteins, atoms, etc..

Think of an example when a system is affected by a system 3 levels above in the hierarchy, but is not affected by the system 2 levels above in the hierarchy. Is this possible?

I am going to assume that the question intends the meaning “is not being affected by the system 2 levels above in the hierarchy at the moment” because, by definition, a system can be affected by any super-system. With that caveat, using Alexi’s example of a student as a system and the class as the immediate supersystem, the department could be a system 2 levels up, and the university a system 3 levels up. If the university instituted new degree requirements, that could affect the student directly, while the interaction between the student and the department remained the same.

If a system collapses (dies off) can subsystems survive?

Sure. When an animal dies, the proteins within them survive for a time. They will eventually decay, but the sub-er-system of atoms will ultimately survive.

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