Physics - Particle Gravity Simulation - part 1

[Qasimbajwaa]

It would be cool to set all the gravities to the same number and then wait until they line up in a grid

[coldironhands1]

I detected some colisions!

[EngineeringFun]

Very well suited music...

[javier07b9]

what kind of equations using?

[particlefun]

The Inverse Square Law.

f = G ( (m1 m2) / d squared )

[CACBCCCU]

I notice the particles seem to have a radius or at least seem to behave inelastically like ball-bearings upon collisions.

I'm not sure why the illumination level around each particle is not more symmetrical if it's supposed to match gravitational field potentials, there seems to be a bias to illumination pointing away from the center, as if there is some sort of gravitational potential well fixed in the center.

[particlefun]

The intensity of each pixel is determined by calculating the change in velocity of a single point with a mass of one due to the influence of all of the other particles. At the center of mass for the entire system there is little or no acceleration and this creates the "bias" you mention, or darkness.

There are actually no collisions in this calculation, see comments below.

I love thinking about these comments keep them coming.

[CACBCCCU]

Thank you. Thinking about it a little more, I might have compared the illumination level's appearance to gravitational potential gradient instead, which is the rate of change of gravitational potential. I was also thinking the contribution of each particle to the local field is strongest on the side away from the center of mass of all the particles. Another thought was that maybe the way the brain's visual system handles contrasts is having an effect on the appearance of things here.

[EngineeringFun]

The not so curved trajectories actually make sense for a low density cloud of particle like this case. And of course computing the field in each point at every moment can increase the simulation time by orders of magnitude.

[circle559]

why are the particles bouncing of each other

[particlefun]

The particles do not actually bounce off one another, they accelerate past each other very quickly. Because of the Inverse-square law the closer two particles are to each other the faster they accelerate toward each other. When two particles come very close together, their relative speed increases exponentially and they fly past each other. If we zoomed in enough on the part of the animation in question, this would be evident.

[edm279]

so how is this calculated?

for every particle x for every other particle y that is not x add the force that y exerts on x to total force vector

??? this seems like an awful lot of number crunching, is there a better way to calculate this??

[particlefun]

The calculation is basically this: m1 m2

F = ----- r^2

where: F is the magnitude of the gravitational force between the two particles, m1 is the mass of the first particle, m2 is the mass of the second particle, r is the distance between the two particles.

The calculation above is performed on every point in the matrix. The intensity of the light assigned to each pixel represents the strength of gravity at that point in space.

[particlefun]

This IS a lot of number crunching and it takes several hours to render a movie. I have made a few clever optimizations but I'm open to suggestions for a faster approach.

[bobbybodickerson]

i've done similar modeling in matlab and have found that by using berghoff's interpolation with intermediate time scale you can effectively reduce the number of iterations required for convergence. i did run into some problems with determination of real vs complex results but by following the step rules it's not too bad

[TheReasonWhyGuy]

"The intensity of the light assigned to each pixel represents the strength of gravity at that point in space."

Kind of like the overused grid bending except a little more eye appealing.

I like it, I tried the grid bending effect a while back and it took along time to record.

I may do another 2d grid one soon.

Grid meaning a visual representation of the space time grid.

[TheReasonWhyGuy]

Is this 2d or 3d

[particlefun]

I ignored perspective in the movie but the simulation is three-dimensional.

[TheReasonWhyGuy]

Hey, I have a larger number of not so pretty stars interacting.

But besides that, I'm glad to see another person working on similar simulations

[Persekarva]

Nice, what is the scale of the distances and what are the masses of the objects?

[particlefun]

The scale was somewhat irrelevant to me. The simulation just demonstrates the effect of gravitation on particles with a mass of one in a simple 3d cartesian matrix by applying the inverse-square law to each partical's velocity. The particals all begin with a velocity of zero.

[Corwynn]

Pretty sweet :)

[hboy007]

nice one :)