Computer modeling of physical systems

[TheRealColbert]

I am thinking about ways to model physical systems. An example of the type of problem I want to look at would be the response of sound waves to a series of resonators. Here is a java applet of a ripple tank, which is along the lines of what I am thinking of. http://www.falstad.com/ripple/ I expect the things I would like to look at would be intractable from a differential equations approach. Maybe I could do it from a finite element analysis approach, but I think that is beyond my budget, skill and ambition.

So to simplify things, I was wondering if these types of problems can be modeled by creating a series of grids, and making a rule such that each box in the grid uses the state of its neighbors to determine it's own state. Each step in time would allow the wave to "propagate" through the system, and hopefully would exhibit characteristics of the physical system being studied. I think this is kind of like cellular automata. (maybe it IS cellular automata) In any case, what would be the best direction to take to investigate this further? What is it called, and are there key words I could use to search, etc? Is it a dead end?

Some initial problems as I begin to think about it are: How do you deal with the "directionality" of a wave? (ie. if you were modeling a moving ball, you would get stuff flying off everywhere, not a nice, contained moving shape) Also, a square grid isn't isotropic. What problems will that cause when you have a wave or something else going at an angle to the grid.

Any thoughts?

 

[Andy Resnick]

What you describe sounds a lot like "lattice" methods. Fluid flow problems can be modeled well using the lattice-boltzmann method (which is a form of computational fluid dynamics)

http://en.wikipedia.org/wiki/Lattice_Boltzmann_Method

The tricky part, AFAIK, is how to set the mesh size. There are ways to allow the mesh to dynamically adapt to the required accuracy.

http://en.wikipedia.org/wiki/Adaptive_mesh_refinement

 

[sir-pinski]

Computer modeling of physical systems is a fascinating and complex field that has numerous applications in various industries. Your idea of using a grid-based approach to model the response of sound waves to resonators is definitely a viable option. This type of modeling, also known as grid-based or lattice-based modeling, is commonly used in physics, engineering, and other scientific fields to simulate complex systems and phenomena.

One of the main advantages of this approach is that it allows for the simulation of non-linear and chaotic systems, which are often difficult to model using traditional mathematical methods. By breaking down the system into smaller grids and applying rules for interactions between neighboring grids, the overall behavior of the system can be predicted over time.

As you mentioned, this type of modeling is similar to cellular automata, which is a computational method for simulating the behavior of complex systems based on simple rules. In fact, many grid-based modeling techniques are inspired by the principles of cellular automata.

In terms of further investigation, you can search for keywords such as "grid-based modeling," "lattice-based modeling," or "cellular automata" to find more information and resources on this topic. You can also explore different software tools and programming languages used for grid-based modeling, such as MATLAB, Python, or NetLogo.

Regarding some potential challenges with this approach, you are right to consider the limitations of a square grid and the issue of directionality in wave propagation. However, these challenges can be addressed by using more advanced techniques, such as adaptive grids or non-uniform grids, and by incorporating specific rules for directional behavior in the model.

In conclusion, computer modeling of physical systems using grid-based approaches is a promising direction for your research. With the right tools and techniques, you can effectively simulate and analyze the response of sound waves to resonators, and potentially discover new insights and solutions to complex problems in this field.