sheng/Introduction

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Introduction to Computing for Scientists

Contents

  1. Why Computing For Scientists?
    1. Approaches to solving science problems
    2. Theory, Experiment and computation
  2. What is Computing for Scientists?
    1. Computing
    2. Scientific Computing
    3. Scientific Computing requires
  3. Relationship to Other Fields
  4. Example I of Scientific Computing
    1. Science Model
    2. Mathematical Model
      1. Notes
    3. Computation
    4. Science Analysis and Interpretation
  5. Example II of Scientific Computing
    1. Science Model
    2. Mathematical Model
    3. Computation
    4. Science Analysis and Interpretation
  6. Example III of Scientific Computing
    1. Science Model
    2. Mathematical Model
    3. Computation
    4. Science Analysis and Interpretation
  7. Emerging Fields

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

This diagram shows the relationship between different research modes - experimentation, theory and computation. The three research modes interact with and complement each other, commonly involved in modern scientific researches.

  • 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"
    • (The quote appears in Section 1.1 of a book by Hamming)


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
[SciDAC project] [UK supercomputing projects]

2.3. Scientific Computing requires

  1. A Scientific Model (A description of the system)
  2. A Mathematical Model (A translation of the description to a set of mathematical equations)
  3. Computation (Solving the mathematical equations with a computer)
  4. Science Analysis, Interpretation and Verification

3. Relationship to Other Fields

Computational Science

Image:Venn_SVG.svg




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.

From www.globalchange.umich.edu on June 23 2017 00:10:37.

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


\frac{dR}{dt} = aR - bRF


\frac{dF}{dt} = ebRF - cF

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

From www.globalchange.umich.edu on June 23 2017 00:10:37.
  • 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


F_{m_1 \mbox{ on } m_2} = \frac{Gm_1m_2}{(\mbox{distance between } m_1 \mbox{ and } m_2)^2}



\frac{}{}F_{m_1 \mbox{ on } m_2} = -F_{m_2 \mbox{ on } m_1}



\frac{}{}F_{\mbox{Total on } m_1} = m_1a_1

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?

From science.nationalgeographic.com on June 25 2017 03:35:17.

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


F_{m_1 \mbox{ on } m_2} =\mbox{ Obtained from force-field tables }



\frac{}{}F_{m_1 \mbox{ on } m_2} = -F_{m_2 \mbox{ on } m_1}



\frac{}{}F_{\mbox{Total on } m_1} = m_1a_1

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:

  • Astroinformatics
  • Bioinformatics [4]
  • Cheminformatics/Computational Chemistry [5]
  • Helioinformatics
  • Heath informatics (Medical, Nursing, Biomedical)
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