General
In general, I spend time from Friday - Monday for each week on the project. The other days I spend
my time looking at other modules. 1 hour supervisions with Gareth are on Tuesdays from midday.
Notes are typically taken on paper
This week was 'background reading' on Liquid Crystals.
Additional Notes:
Progress could have been better, 'freshers flue' caused issues
Week 1 Page 1
The Physics of Liquid Crystals 4h
The Physics of Liquid Crystals Second Edition, P.G. De Gennes and J. Prost
- Read Chapter 1 (p1 - 34) and took notes on most relevant info
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- Brief reading on Chapter 2, (p41-92) although didn’t take any notes
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Risk Assessment 1h
Risk assessment, completed risk assessment form for theory project. Spent approx. 1h of time say
due to confusion of what was expected.
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Supervision 1h
Looked at different liquid crystal states, i.e nematic, smectic, etc. Looked at some simple models.
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Principles of Condensed Matter Physics 4h
Principles of Condensed Matter Physics, P. M. Chaikin
Read Chapter 1, chapter 2, some notes taken from chapter 2.
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General
Progress again was not as much as I would have liked, freshers flue again reduced productivity.
Mostly focused on elasticity of liquid crystals. Also did some reading in other areas.
Week2 Page 12
Supervision 1h
Looked at elasticity of liquid crystals, mostly nematic.
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PX366 4h
Revised some material from PX366 Statistical mechanics. Looked at Landau theory and some
simple phase transitions for liquid crystals. Also went through the problem sheets.
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The Physics of Liquid Crystals 3h
Read Chapter 2 in much more depth, wasn't certain how relevant each section was so didn’t take
much notes. Some notes taken included in previous page.
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Read an article on
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Tensor Calculus 1h30
Revised ideas on tensors, multivariable / tensor calculus. Didn’t feel like reading too much at the
time so skipped through Youtube series by 'Eigenchris' on tensor calculus. Looked at Jacobian.
Jacobian matrix and determinant - Wikipedia
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General
07 December 2021
03:04
Revised again more through theory of liquid crystals. Looked at splay, bend and twist. Looked at
modelling nematics and smectics. Looked at different properties of nematics/smectics from Physics
of Liquid Crystals.
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Supervision
Looked at elasticity of smectics, went through questions from other areas, started to talk about
resolving some problems of systems. Got a good idea of what to look at over the week. Start to look
at active systems.
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General
06 December 2021
17:34
Further looked at elasticity of nematics. Started to Look at elasticity of smectics and Helfric Hurault
Instability.
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Gareth Chapter
07 December 2021
02:15
Went through the chapter and its exercises provided by our Supervisor.
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General
06 December 2021
17:34
Finished looking at Helfric Hurault stability. Started looking at stability of Smectics & additional
active matter term in the N.S. equation.
Week 5 Page 24
Hydrostatics of Nematics
Went through Chapter 3.5 of Physics of Liquid Crystals and took notes.
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Dynamical Properties of Nematics
07 December 2021
02:20
Went through Chapter 5 of Physics of Liquid Crystals. Took Notes
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Gareth Chapter Hydronematics
07 December 2021
02:21
Took notes from the section on Hydronematics discussed in Gareth's Chapter.
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PX366 Problem Week 2 Q1
07 December 2021
02:39
Looked at problem from PX366 module on linearising a pde followed by Fourier analysis to find
when the pde has stable/unstable solutions.
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General
06 December 2021
17:34
Added the chiral term to the N.S equation to see how that affects the stability of the solutions.
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Tensor Calculus Revision
07 December 2021
02:23
Went through definition of outer product. Then various identities in vector/tensor calculus and some
of their derivations. For example looked at by parts in 3d. Mostly sourced from Wikipedia. Cleared
up understanding of various terms in N-S equation such as outer product of the gradient of order
parameter with itself.
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PX440 Variational Principles
07 December 2021
02:32
Revised/notes on variational principles from PX440 and the meaning of the functional derivative.
Looked at deriving functional derivative i.e. in derivation of 1d/nd Euler-Lagrange equations. Looked
at finding functional derivative by considering a small change in the path on the case by case basis
for the free energy rather than using a formula. Also looked at constrained systems briefly as well.
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General
06 December 2021
17:34
Looked at perturbations caused by mechanical strain in combination with active & chiral active
terms in N.S equations. Used Free energy from Helfric-Hurault instability and that linearisation of the
order parameter. Also considered case where temporal changes in velocity field are non-zero/nonnegligible. Started looking at non-uniform density but got stuck.
Week 7 Page 32
07 December 2021
02:46
Also derived Helfric Hurault instability now instead using the system of equations (order parameter,
N.S. and fluid mass conservation) without the active term, instead with the linearised order
parameter as before.
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General
06 December 2021
17:41
Didn't do much work towards project this week due to workload with assignments due and other
external factors. Resolved issue with non-uniform density by linearisation. Removed issue altogether
with needing to take convolution in Fourier transform of the system of equations.
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Supervision 1h
06 December 2021
17:34
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Pressure 2h
06 December 2021
17:45
Considered the form of the pressure within the liquid crystal. Found the appropriate form to be
adiabatic pressure.
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2h
06 December 2021
18:01
Effectively revision, went through solving the system of equations with the chiral and active terms in
the N.S. equations again with project partner. Was able to check for mistakes, etc. with signs and
check our understanding.
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General
07 December 2021
02:02
Work done still to be updated for this week.
Week 9 Page 38
Supervision 1h
Discussed stability of linearised equations and Fourier wavevectors.
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Pressure 2h
Considered the form of the pressure for
Week 9 Page 40
More generalised
06 December 2021
17:40
Linearised the N.S., order parameters and mass conservation equations. This time non-constant
(linear approx.) in density. I.e. considering sound waves. Lead to a 5x5 matrix equation with
corresponding eigenvalues and eigenvectors that show conditions for stability.
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06 December 2021
17:35
TBC
Week 10 Page 42