sheng/Introduction
From CDS 130
Introduction to Computing for Scientists
Contents |
1. Why Computing For Scientists?
1.1. Approaches to solving science problems
- Scope of sciences
- Scientific research modes
- Experiment (before 1600)
- Quote: "Experimental science is queen of sciences" by Roger Bacon
- Theory/Math
- Quote: "Math is the queen of sciences" by Carl Friedrich Gauss
- Computing
1.2. Theory, Experiment and computation
- Using computers to solve science problems is as important as
- Using a microscope or a telescope to solve science problems
- Using math to solve science problems
- With Computers, we can study problems that previously would have been
- too difficult, time consuming, or hazardous
- Important: "Computers are used to generate insight, not just numbers"
2. What is Computing for Scientists?
2.1. Computing
- Computing allows us to
- Balance your account
- Find directions on Google maps
- Purchase books on amazon.com
- Play games on smart phones
- Create presentations
2.2. Scientific Computing
- Scientific Computing allows us to
- Obtain genome information
- Understand how the universe was formed
- Design new drugs to cure diseases
- Take the temperature of the Earth's core
- Find the toughest material in the world
2.3. Scientific Computing requires
- A Scientific Model (A description of the system)
- A Mathematical Model (A translation of the description to a set of mathematical equations)
- Computation (Solving the mathematical equations with a computer)
- Science Analysis, Interpretation and Verification
3. Relationship to Other Fields
Computational Science
4. Example I of Scientific Computing
The predator-prey problem is a simulation that attempts to predict the relationship in populations between a population of foxes and rabbits isolated on an island.
4.1. Science Model
Make the following Assumptions:
- Rabbits only die by being eaten by foxes
- Foxes only die from natural causes.
- The interaction between Foxes and Rabbits can be described by a function.
In other words, we have the following scientific model.
A closed system (Rabbits and Foxes on an island, for example)
- Change in number of rabbits per year
- increases in proportion to the number of rabbits (breeding like rabbits!)
- decreases in proportion to (the number of rabbits) x (number of foxes)
- Does not depend on rabbits dying of natural death
- Change in number of foxes per year
- decreases in proportion to the number of foxes (more competition for food)
- increases in proportion to (the number of rabbits) x (the number of foxes)
4.2. Mathematical Model
The science model can be written in terms of equations that can be solved using a computer. A mathematical model is [1]
R = Number of Rabbits
F = Number of Foxes
where a, c, b, and e are numbers such as (1.2, 0.5, etc.) and have meaning of
- a is the natural growth rate of rabbits in the absence of predation,
- c is the natural death rate of foxes in the absence of food (rabbits),
- b is the death rate per encounter of rabbits due to predation,
- e is the efficiency of turning predated rabbits into foxes.
4.2.1. Notes
What you will need to know for this course is that a mathematical model exists, not have a complete understanding of the math involved in solving the problem. After taking this course you will not be able to solve these equations by hand, but you will be able to understand what it means and how to solve it on a computer.
4.3. Computation
Online: http://home.messiah.edu/~deroos/CSC171/PredPrey/PRED.htm
Vensim: http://www.shodor.org/talks/ncsi/vensim/
4.4. Science Analysis and Interpretation
- How much of real measurements does simulation explain?
- What are the appropriate values for those constants?
- How are they determined?
- What is their uncertainty?
- What features on the plot can't the model explain?
- Can the model be improved?
5. Example II of Scientific Computing
Galaxy Collisions
5.1. Science Model
- An initial configuration of galaxy particles
- Newton's law of gravity
5.2. Mathematical Model
Need to do this calculation for every combination of mass 1 and mass 2!
5.3. Computation
- Example of only three particles: [2]
- Example of many particles:
5.4. Science Analysis and Interpretation
Do simulations explain telescope observations?
6. Example III of Scientific Computing
Molecular Dynamics of Biomolecules
6.1. Science Model
- An initial configuration of molecules
- Newton's second law of motion
6.2. Mathematical Model
Need to do this calculation for all interactions on each particle
6.3. Computation
- Example of molecular dynamics simulation [3]
- Example of a protein:
6.4. Science Analysis and Interpretation
Do simulations explain real properties?
- NMR spectroscopy
- X-ray diffraction data
7. Emerging Fields
Informatics is the study of information science (turning data into science) and information technology (developing tools that enable information science)
All require core competencies in computing: