PHYS220: Scientific Modelling

Macquarie University 2009

Description

1st Semester 2009, 3 credit points.

This unit introduces students to scientific modeling and applications in a wide range of topics. Students will learn to apply computer modeling and simulation packages and be introduced to a variety of techniques such as matrix methods, finite differencing and the numerical solution of ordinary differential equations. The emphasis is on learning through examples which encompass topics such as discrete simulations of physical systems (chaos and percolation), optimization in physical problems (minimum energy configurations), simulation of systems using ordinary differential equations (projectile motion with drag, predator-prey), and also using partial differential equations (heat equations, fluid flow, Poisson’s equation and solitons).

Aims

Students will learn the principles of scientific modeling. Students will be gradually introduced to a variety of techniques used to model phenomena on the computer. The aim will be that at the completion of the course students will have good capabilities to use their acquired skills to model a variety of complex systems ranging from biology, chemistry, physics through to complex models in social, economic and financial sciences. 

Objectives (and generic skills)

• To develop familiarity with principles of scientific computer modelling;
• To develop good skills in programming with Matlab (Matrix Laboratory computer language)
• To connect phenomenology with mathematical modelling;
• To develop skills in scientific computer modelling techniques;
• To develop report writing skills;
• To develop problem-solving skills and techniques.
• To develop independent thought in the formulation and analysis of complex systems through scientific computer modeling

Prerequisites

MATH132(P) or MATH133 or MATH135(P) or MATH 136; and any 100-level COMP or ISYS unit(P); and any 100-level PHYS, CBMS, CHEM, BIOL, GEOS or STAT unit(P)

Lecturers

Laboratory Demonstrator

Lectures/tutorials

• Lecture: Monday 2pm E7B 163
• Lecture: Monday 3pm E7B 163
• Lecture: Wednesday 1pm C4A 320
• Laboratory: Friday 2pm-5pm E7B209

Tentative Syllabus

• Part 0: Introduction to scientific computer modeling and the Matlab computer language
• Part 1: Modeling nature using discrete systems: Random Numbers and Percolation, Sandpiles and Critical Phenomena, Fractals and Diffusion Limited Aggregation
• Part 2: Optimization and Chaos in computer models in science: numerical root finding (solutions to sets of equations), numerical minimum/maximum find or optimization, simulated annealing and genetic optimization methods. Modeling chaotic systems in nature.
• Part 3: Computational modeling of scientific systems using differential equations: using ordinary differential equations, damped projectile motion, gravitational pendulum, driven pendulum. Solving boundary value problems: damped projectile motion with given range.
• Part 4: Computational modeling using partial differential equations

Assessment

Assignments	20%	Four assignments
Practical	20%	Nine on-line lab reports
Modelling Project	30%	Report due Final Week (Thursday 5th June 2008)
In Lab Examination	30%	To be examined in the lab on Friday 5 June

Laboratory Classes (Friday 2-5 pm E7B 209)

Project Due: WED 3 June

Notes and report templates are available on-line as Word documents. Access to these notes is password-restricted. Completion of lab work is mandatory, but lab work may be done at home or outside lab session times. It should, however, be handed in for marking by the end of the lab session for the relevant week. Attending the labs does give students opportunities to ask questions and get help with the lab tasks. The 3-hour lab sessions allow sufficient time to complete the lab work and write the report.

A report on each lab session will be submitted by the end of the class in weeks 1-9. The template report provided is to be filled in on-line and printed out at completion of the lab. These nine reports are assessed and each counts towards the final mark for the unit for a total of 20%. Backing up of files is the student's responsibility and it is advisable to bring a USB memory stick to the lab for this purpose. Also note that food and drinks are not allowed in the lab.

Students will undertake a project for weeks 10-13. Students are encouraged to attend the Friday lab times as the demonstrator will be present (as well as the odd lecturer), to help with the projects. A number of project themes will be presented by the course lecturers by week 6. Students are free to choose alternative projects after discussion and agreement by  the course convenor. Students will be asked to write up their project both as a written report but also as a website report. The written and website report will be assessed and counts for 20% of the final mark for the unit. The web reports of the projects will be uploaded to this website for general viewing

Resources

Suggested Reading: (books and video are available in the library)

Computational physics : problem solving with computers / Rubin H. Landau, et al, QC20.82 .L36/1997
 Introduction to computational physics / Tao Pang. QC20.7.E4 .P36/1997  
Elementary Mathematical Models, D. Kalman, QA401.K24 1997
The Beauty of Fractals: Images of complex dynamical systems, Peitgen & Richter, QA447.P45/1986
Complexity: The emerging science at the edge of order and chaos, M.M. Waldrop, Q175.W35
Chaos and Fractals: New frontiers of science, H-O. Peitgen, QA614.86.P43/1992
Chaos: Making a new science, J. Gleick, Q172.5.C45.G54/1987
A New Kind of Science, S. Wolfram, QA267.5.C45.W67/2002

An overview of chaos is given in the video:
Chaos, Q172.5.C45.C45

Plagiarism

"Plagiarism involves using the work of another person and presenting it as one's own. Any of the following acts constitutes plagiarism unless the source of each quotation or piece of borrowed material is clearly acknowledged:

• copying out part(s) of any document or audio-visual material (including computer-based material);
• using or extracting another person's concepts, experimental results, or conclusions;
• summarising another person's work;
• in an assignment where there was collaborative preparatory work, submitting substantially the same final version of any material as another student.

A general discussion of plagiarism, definitions, examples, procedures that will be followed by the University in cases of plagiarism, and recommended penalties are available from the Student@Macquarie website at http://www.student.mq.edu.au/plagiarism/. The University expects students to familiarise themselves with the website.

Special Consideration

Information about special considerations and student services is available at http://www.physics.mq.edu.au/undergrad/services/.

Student Liaison Committee

The Physics Department values quality teaching and engages in periodic student evaluations of its units, external review of its programs and course units, and seeks formal feedback from students via focus groups and the Student Liaison Committee. The Physics Department Student Liaison Committee meets once each semester, and lunch is provided. Two students should be elected/nominated to represent this unit at the student Liaison Committee meeting. Minutes of the meetings are reported at subsequent Student Liaison Committee meetings and to the Physics Department Committee for action. Please consider being a member of this committee.

Scientific Computer Modeling Images