"Crack" patterns in nature.

[Daecon]

I wasn't sure whether this should be in mathematics or physics, but as I'm speculating, it's probably better here.

 

Is there any mathematical association between various crack-based patterns in nature, for example with earthquake fault lines, broken glass, etc? I was curious if the distribution of galaxies throughout the observable Universe follow a similar pattern?

 

I'm sure there must be more accurate terminology to describe it other than "fractal", which seems too broad.

[ajb]

It has been observed for a long time that these patterns are pseudo-fractals. I have myself observed some great patterns in drying mud on coast.

 

The very large scale distribution of matter does indeed show a similar pseudo-fractal structure. These patterns can also be created using computer simulations based on the Lambda CDM model.

 

As for the general mathematics, I guess that fractals is the word.

[studiot]

This can be a fascinating subject that is about far more than fractals, and can draw in many important parts of Physics and Maths, Chemistry, and Biology.

 

There is also a very good book about this, that is not highly mathematical;

 

The Self-Made Tapestry

Pattern formation in nature

By Philip Ball

 

I once gave a lecture to the Concrete Society about cracks in concrete, and compared them with cracks in wood and elsewhere, with lots of powerpoint pictures.

Edited April 20, 2016 by studiot

[ajb]

I once gave a lecture to the Concrete Society...

I bet that was a hard audience.

[studiot]

 

ajb

I bet that was a hard audience.

 

 

Excellent riposte. +1

 

I like to end a talk with this slide, and then declare the bar open, though for some audiences I might substitute a cup of tea.

 

 

On a more serious note, photoelasticity of cracks produces some wonderful images, and some great mathematical physics.

 

https://www.google.co.uk/search?q=photoelasticity&hl=en-GB&gbv=2&prmd=ivns&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiDtLCa55zMAhVpJMAKHUe4DHcQ_AUIBQ

 

Another hugely important mathematical aspect of cracks in materials is called dislocation theory.

 

https://www.google.co.uk/search?q=dislocation+theory&hl=en-GB&gbv=2&prmd=ivns&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjeuP_C8pzMAhXkDsAKHYoyC6wQ_AUIBQ

 

 

Cracks are serious business.

Edited April 20, 2016 by studiot

[Bill Angel]

On a more serious note, photoelasticity of cracks produces some wonderful images, and some great mathematical physics.

 

https://www.google.co.uk/search?q=photoelasticity&hl=en-GB&gbv=2&prmd=ivns&source=lnms&tbm=isch&sa=X&ved=0ahUKEwiDtLCa55zMAhVpJMAKHUe4DHcQ_AUIBQ

 

The image below was created by photographing the ice on the surface of a pond with the camera's lens equipped with a polarizing filter.

A good review article discussing elasticity and crack formation in ice is "The Structure and Mechanical Behavior of Ice" http://www.tms.org/pubs/journals/JOM/9902/Schulson-9902.html

[Daecon]

I was wondering if there was any connection with Brane cosmology, the Big Bang, and (possibly) the Ekpyrotic model?

 

For example, a collision between two branes with such energy that caused the inflationary epoch and established the crack-style pattern for the layout of matter as it condensed out of that energy.

 

Or is it just my ignorance showing?

[ajb]

For example, a collision between two branes with such energy that caused the inflationary epoch and established the crack-style pattern for the layout of matter as it condensed out of that energy. ?

The Ekpyrotic model quickly becomes the Lambda CDM model. Ekpyrotic models remove the intial singularity from big bang type cosmologies, but they do not replace these cosmologies.

Edited April 21, 2016 by ajb