Modeling new matter!
 

Hello, I am asking a vague question knowingly, please bare with me.

Firstly, I am doing my research in Computer Graphics with interest in physically based animation. I have graduation in aerospace engineering. So I am capable of digesting few things but can't think on my own. I am trying to model a "hypermatter" having some of the properties as follows.

- The matter is continuum and has notion of mass, density, pressure, viscosity so it is just as fluid. - At the same time it also constitutes a vector field. So state of of the matter's infinitesimal element will have direction as an addition. This may be similar to "liquid crystal". - The matter has strong elastic stiffness in the direction of the field described as above. But it has very small stiffness in other directions. - The matter is suspended in air having vary fuzzy boundary between it and the air. Due to this it exhibits a surface tension across the fuzzy boundary. Hence it tends to form high density regions of either it or the air under brisk dynamics.

Until now I guessed I can formulate this as

<tt>

dr/dt = - dE(r)/dr

</tt>

Where r is state of the matter including the vector field. E(r) is the energy, I have to formulate, to penalize each of the property above. (I hope even this thinking is accurate.)

As I am no expert in physics and maths, can you please advice me on what book (fluid mechanics, condensed matter physics, participating media, etc) and few papers I can refer. Any comments on the feasibility or other wise will also be of great help.

I am considering material from the following books - Computational Fluid Dynamics, Anderson - Principles of Condensed Matter Physics, Chaikin and Lubensky - Theory of Elasticity, Timoshenko and Goodier

Thank you very much

Sunil

Re: Modeling new matter!
 

You should try, maybe, something like the sticky particles methods, in which collision of particles is allow, where momentum is conserved. This can represent a flow, you need however to take a few 10,000 of particles to model a fluid. Now you can add to this method the dirction of the vector of interest of each particle (say like a kind of spin vector in physics) and add an coefficient of elasticity for the collision that depends on this vector.

So the first step would be to make a search to find out more about the sticky particle method. WIthout the spin the particles are all identical and it is known as a Boltaman gas. With the spin (or oriented vector) things are a bit different. But this does not matter since you can write your code on the microscopic scale for each particle. The results will give you the behaviour of the particles on the macroscopic scale - the flow.

Patrick

sorry for the missprint
 

Read Boltzman instead of Boltaman, sorry for the missprint(s) in the text.