Physical modelling

Question 1

How is a diffusion model implemented with CA?

Answer 1

1. Compare each cell with the average of its neighbours.
2. If the concentration of the centre cell exceeds the neighbourhood average, the chemical flows from the centre to the neighbours.
3. If its lower, the chemical flows the other way.

Question 2

What are the parameters of a diffusion model?

Answer 2

r = rate of flow
c = concentration

Question 3

What are the parameters of a reaction-diffusion model?

Answer 3

A,B = diffusion rate
feed rate = how quickly A is added to the system
kill rate = how quickly B is removed from the system

Question 4

How do we implement a percolation model?

Answer 4

1. Initialise each cell with p prob of being porous, or 1-p non-porous
2. All cells are considered dry except the top row
3. During each time step, if a porous cell has at least one wet neighbour, it becomes wet. Non-porous cells stay dry
4. The simulation ends when no more cells change state

Question 5

How do we see if a percolating cluster exists?

Answer 5

If there are any cells on the bottom layer that are wet.

Question 6

What are the various p values and associated percolating clusters? Where is the critical value?

Answer 6

at p=0.55, near 0
at p=0.60, around 70%
at p=0.65, near 1

So critical value around 0.6

Question 7

How can we determine if a fractal exists?

Answer 7

Plot number of cells vs time steps.
If on a log scale, the constant is not an integer, it may be a fractal.

Question 8

What is self-organised criticality?

Answer 8

Self-organised criticality means from any initial condition, the system moves towards a critical state and stays there, without external control.

Question 9

What is a critical value?

Answer 9

Rapid change of behaviour called a phase change.

Question 10

What are properties of critical systems?

Answer 10

Fractal geometry
Heavy-tailed distributions
Pink noise

Question 11

Describe a sand pile model.

Answer 11

1. 2D ca where the state of each cell represents the slope of a sand pile.
2. Each cell is checked whether it exceeds a critical value K (usually 3).
3. If it exceeds, the cell topples and transfers sand to the four neighbouring cells (i.e. if Slope is 4, each neighbour increases to 1)
4. Excess is spilt over the edge.

Run the simulation until the pile stabilises.
At this point a single grain can topple the sand pile, implying it is at a critical state.

Question 12

How to tell if a distribution is heavy tailed?

Answer 12

Plot log-log slope, if the distribution is straight, its heavy tailed.

Question 13

How to test for fractals in sand pile model?

Answer 13

Take each level, then plot log-log distribution. See if fractal dimensions is non integer

Question 14

What is signal, power spectrum and noise?

Answer 14

Signal - quantity that varies in time
Power spectrum - a signal that can be decomposed into different levels of power. The power spectrum of a signal is a function that shows the power of each component
Noise - signal that contains many frequency components

Question 15

What is pink noise?

Answer 15

Power(f) = 1/frequency^Beta where beta is between 0 and 2.

Question 16

How is sand pile pink noise?

Answer 16

Because Beta = 1.5

Question 17

What is the difference between a reductionist model and a holistic model?

Answer 17

Reductionist = Describe a system by its parts and their interactions
Holistic = More focused on similarities between systems and less interested in analogous parts.

Question 18

How would you model a holistic model?

Answer 18

Observe a behaviour that appears in a variety of systems.
Find a simple model that demonstrates that behaviour.
Identify the elements of the model that are necessary to produce the behaviour.

Question 19

How are earthquakes self organised criticality?

Answer 19

They are always in state of self organised criticality.

It only takes one small adjustment to the system to cause an earthquake.