this is for holding javascript data
Luke Carlson edited Method.tex
about 11 years ago
Commit id: 3c244e521d5bbc335079dcc1bc438003a1eabdef
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I began constructing my simulation with '3D Balls Bouncing', a project from Open Processing, as a base. Starting off with a system that could already handle 3D collisions of small objects inside a container was necessary [see Failed Methods]. From there, I created small spheres with the properties of an ideal gas. Their speed was roughly determined on a Maxwell-Boltzman distribution and assuming that the most probable speed ($V_{p}$) would occur the most often (calculated using the formula $V_{p} = \sqrt{\frac{2kT}{m}}$. Next, I focused on one wall in the container and tracked each time a particle collided with the area. I could then compute the change in momentum over the area since I had the masses and velocities of the particles. The simulation did not keep track of total time since initiation, which is equivalent to \Delta time, but I knew that aspects of the code were executed every frame. The project ran at a fixed number of frames per second (60) so I designed this formula to figured out the change in time: $total\ time (seconds) = \frac{total\ frames}{frames\ per\ second}$.
I inserted that data into this formula $F = \frac{2m *
\displaystyle\sum\limits_{0}^n \displaystyle\sum\limits_{i=0}^n v}{\Delta t}$ (see Introduction) to find the total force on the wall. To obtain the pressure, I just divided the answer by the area of the wall.