M635 PATTERN FORMATION

SYLLABUS

POLICIES

ASSIGNMENTS

FINAL PROJECTS

COURSE MATERIAL


       M635 Pattern Formation / Projects



SUGGESTED TOPICS

Symmetry-Breaking as an Origin of Species.
Ian Stewart, Toby Elmhirst and Jack Cohen.
Bifurcation, Symmetry and Patterns, J. Buescu, S. Castro, A.P. Dias and I. Labouriau. Eds., pp 3-54.		 ODEs: SN-Symmetry
Bifurcation and Planar Pattern Formation for a Liquid Crystal.
M. Golubitsky and D. Chillingworth.
Bifurcation, Symmetry and Patterns, J. Buescu, S. Castro, A.P. Dias and I. Labouriau. Eds., pp 55-66 		PDEs and Lattice Symmetry
Secondary Instabilities of Hexagons: A Bifurcation Analysis of Experimentally Observed Faraday Wave Patterns.
A.M. Rucklidge, M. Silber, and J. Fineberg.
Bifurcation, Symmetry and Patterns, J. Buescu, S. Castro, A.P. Dias and I. Labouriau. Eds., pp 101-114 		PDEs and Lattice Symmetry
Models of Central Pattern Genrators for Quadruped Locomotion: I. Primary Gaits.
P.L. Buono and M. Golubitsky.
J. Math. Biology 42, 291-326 (2001). 		ODEs: Z4 x Z2 Symmetry
A model for fast computer simulations of waves in excitable media.
Dwight Barkley.
Physica D, 49, 61-70 (1991). 		PDEs and Numerics.
Modelling Travelling Waves of Spatial Patterning in Morphogenesis.
G.C. Cruywagen.
Pattern Formation: Symmetry Methods and Applications.
J. Chadam, M. Golubitsky, W. Langford, and B. Wetton. Eds. 125-141.
PDEs and Numerics.



GENERAL GUIDELINES FOR WRITING A REPORT

1. Goal: The goal of this work is to provide an objective written review of the technical merits of a research paper or project. The main discoveries, the contribution to a particular field of science or to industry, and the relevance of the work to the principles and methods discussed in the M636 Mathematical Modeling course. Rule of thumbs: (1) USE YOUR OWN WORDS and (2) assume a minimum background for the reader.

2. Format: Maximum 5 one-side pages (including pictures, references, appendices, etc.), type font size 12. Failure to follow this format may result in loss of partial credit.

3. Suggested Outline.

Introduction
In a leading paragraph, briefly describe the aim of the paper. For instance, the aim could consist of a new idea, methodology, algorithm, or discovery. Typically, you can get a good idea of what the paper is all about by reading the abstract. Then you could write a more detail description of the relevance of the work to science or industry, those aspects that make the paper interesting, discuss previous work or any other work related to this paper. Make sure to include citations and references. A final paragraph in the introduction should include a brief overviewed of how the paper is organized and its overall contribution to advance the scientific knowledge.

Methodology or Technical Section
In this section, you would want to expand the technical aspects of the paper. If experimental data is employed, then you could begin with a description of the experiment and the data collection process. If a mathematical model is employed, then begin with a derivation or description of the model and a description of each term. In either case, make sure to give credit to those authors who contributed to the experiment or the model. Then you can focus on specific technical aspects and discuss any interesting results that were observed in the analysis. For instance, a description of the dynamics in phase space, derivation of a particular algorithm, derivation of a particular technique, and predictions that can infered from the model. If the emphasis of the paperis on an algorithm, then a description of the algorithm should be followed by a discussion of applications or examples.

Conclusions
Summarize the main ideas and results of the work. Objectively, indicate the stregnths and weaknesses of the work. For instance, if the authors make oversimplified or vague assumptions then criticise them in a constructive way.

Bibliography
Make sure to include a list of relevant references.



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