Physics stuff

This page hosts all of my documents that are not from my degree specifically. That is, set of notes I have produced on my own, or are taught from a non-university academic (not saying anything about the level of difficulty!). Also, at the bottom, are the reports I produced whilst during a couple of summer projects.

I have now added a section at the bottom of the page with my publications and talks.

By way of "right of use", if you use any of my work, please reference me. Preferably, ask me first. Do not copy any of my reports for your own use.

Publications

These are my publications

R.A.Battye, J.A.Pearson, P.M.Sutcliffe and S.Pike 13/08/09 We present field theory simulations of a model with Z_2xU(1) symmetry in (2+1)-dimensions. This model has two discrete vacua, allowing for domain walls, and also a conserved Noether charge. For initial conditions in which the field is placed in one of the vacua and given a homogeneous background charge, we find that the number of walls does not scale in the standard way. We argue that the Noether charge and current become localized on the walls, forming kinky vortons, (2+1) dimensional analogues of cosmic vortons. These loops of wall can be long-lived, or even stable, depending on the precise characteristics. We suggest that our simulations illustrate a possible mechanism for dynamical frustration of domain wall networks and that cosmic vortons will form naturally in U(1)xU(1) models.
  • Download and view here from arXiv.
    JournalRef: JCAP09 (2009) 039 arXivRef: 0908.1865
Talks

These are talks I have given (postgrad)

See also my PhD literature review: field theoretic models of dark energy.

Index notation style stuff
  • Matrices: This is a "textbook chapter" style document, which I wrote, to explain matrices. Its only quite basic stuff: algebra, and basic operations.
  • Matrix Notation: This is a document I wrote to summarise some of the research I had been doing into matrix notations.
  • Index Notation: This is a "new" document, that is all my own work. It explains the usage of index notation, in a way which is rarely found in a single book/course. It is also a work in progress, so will be added to!
Lagrangian dynamics: mathematically
  • Lagrange Equations (1/3): This is the first in a series of documents which I typed out, when I learnt the actual maths & proofs & derivations behind Lagrangian Mechanics. This first chapter derives the lagrange equations. Most of these are written with conservative systems in mind. This particular version is written using LaTeX.
  • Calculus of Variations (2/3): This is the second chapter, and it is on the Calculus of Variations.
  • Hamiltonian Mechanics (3/3): This is the final chapter, on the Hamiltonian method.
Tensor calculus & general relativity
  • Tensor Calculus 1: This is the first in a series on tensor calculus. It introduces tensors (covariant & contravariant), geodesics, and begins on general relativity.
  • Tensor Calculus 2: This chapter discusses differentiation of tensors.
    • Appended versions in "Index Notation".... these ones have a lot of mistakes!
  • Notes on Special and General Relativity: Does what it says on the tin. Given by Dr.P.Dale. This is a work in progress, so will be added to.

    • A word of warning: the above set of notes have been given by Dr.P.Dale; they use un-conventional notation, so should be used with care. However, they do provide a very good aid on tensor manipulations.
Misc
  • Symmetry: This is an (incomplete) set of notes I have written out on the basics in group theory, symmetries; and proofs in group theory. Taken from a course I did with the Open University a few years ago.
  • Function Decomposition: This is a very informal look at function decompositions, using an analogy to paying for things.
Degree reports
Theory project 2007

This is a report/project on the Physics of Neutron Stars. In the report we discuss equations of state, equations of equilibrium & the origin of neutron stars. As well as results obtained & their errors.
Below are copies of the report handed in, report with all derivations & a copy of the full code:

This is all done in collaboration with S.Pike

PPARC IUSS07: quintessence models of dark energy

This is a report on the work done at the PPARC International Summer School, Sheffield, 2007.
The report contains all the maths done, and results obtained for my project:

This report looks at the expotential scalar potential of the quintessence scalar field, as a model of dark energy. Power law solutions to the scale factor are investigated. Autonomous solution equations are plotted, which describe the evolution of various species. Phases of universal acceleration are looked at, and the roles of varies species discussed.

Summer project 2008: cosmic texture

This is the report I produced during a summer project, 2008, at the University of Manchester, supervised by Dr.R.Battye.

We discuss a possible explanation of the observed 5degree cold spot in the CMB as being an unwound topological defect known as texture. We briefly discuss the nature of texture. We then discuss numerical simulations of texture populated skies, and numerically find their power spectrum. We then discuss the covariance matrices of texture only skies, finding that textures are non-Gaussian distributes, with zero bispectrum. We also derive the distribution of textures, extending the approximation of Cruz. We derive analytic expressions for the power spectrum of both a single spot & whole sky, and numerically evaluate them; thus providing previously unused computationally trivial methods for finding such spectra.

MPhys project 2008/9: The dynamics of charged domain walls

This the MPhys report that I produced during my fourth year 2008/9, at the University of Manchester, supervised by Dr.R.Battye.

We investigate the dynamics of a class topological defects known as domain walls. We consider models with interacting fields with junctions and charge, possessing a O(N)xU(1) symmetry with cubic anisotropy terms. We find that a phase separation is possible, between domain and charge, and that if phase separation occurs, domain walls do not scale. This is a more general case of our finding that kinky vortons form from random initial conditions, preventing walls from scaling, in the regime where symmetry currents associate with domain walls.
  • Download here. This is a very low quality version of the report. Contact me if you want better quality images and videos.