A Part III Essay

A. PartIIIStudent

March 19, 2004

1 Introduction

This is LaTeX template constructed very quickly by Peter Haynes from John Rudge’s Part III essay submitted in 2003.

2 Approach

Here is a second section and some equations (taken at random from the Rudge Part III essay).

Non-dimensionalise all lengths on the gap thickness. Let h(θ) = 1+ϵ cos θ, where ϵ gives the eccentricity of the annulus.

Introduce the dynamic pressure p_{dyn} = p − ρgz. Henceforth drop the dyn suffix and work with dynamic pressure. The thin layer approximations give

μ\frac{∂^{2}u_{θ}}{∂r^{2}} = \frac{1}{a} \frac{∂p}{∂θ}

μ\frac{∂^{2}u_{z}}{∂r^{2}} = \frac{∂p}{∂z}

That’s enough equations.

3 Results and Conclusions

Not every Part III essay will have a Results or Conclusions section.

Here is an example of the use of a Figure. 1 shows a picture of something. The figure is taken from the file picture.eps.

Here is an example of how to cite a book [1] or a paper [2] using BibTeX. The relevant information is stored in the file bibfile.bib. Note use of Figure 1: Figure showing a graph of something.

2

bibliographystyle and bibliography commands below. To make this

work you need to run latex, then bibtex, then latex twice more.

A more straightforward option is simply to insert a list of references directly into the .tex file.

References

[1] G.K. Batchelor. An Introduction to Fluid Dynamics. Cambridge University Press, first edition, 1967.

[2] R.H. Kraichnan. Convection of a passive scalar by a quasi-uniform random straining field. J. Fluid Mech., 64:737–762, 1974.