bubble ascension and falling droplet rate are dependent on gravity, so no good

the period between sloshes is dependent on the initial water flow rate

though, you might be able to detect how fast they slow down, and use the viscosity of the water

@NathanMerrill I think we essentially have to assume standard gravity.

I think that it can be calculated with pure viscosity

but maybe not

So I tried to do some timing of falling water droplets (ignoring air resistance) and I got some very rough estimates of about 4x4x4 meters for the box.

That makes the clinging clump of water at the right quite large. In wonder how consistent the simulation is - maybe we'll get different answers by different methods

Approach #2: going off of the equation on this page: hyperphysics.phy-astr.gsu.edu/hbase/watwav.html for wave motion

If I time the large back-and-forth sloshes to estimate how fast the wave is moving, then I can set up some equation with X being box size and some unknowns that need to be measured.

Solve[x/time == Sqrt[9.81*(2*x)/(2*Pi)*Tanh[2*Pi*(x*fraction)/(2*x)]], x]

Where 2*x is the wavelength and x*fraction is how full the box is, giving the depth.

x -> 3.12262 time^2 Tanh[Pi * fraction]

And some rough timings range from 1.5 to 1.8 seconds and fraction being somewhere between 1/5 and 1/3 (I think the box is still filling up).

And looking that some of those resulting values, gives results between 4-7 meters.

There's a lot of fudge in that too since it involves waves that aren't ideal and reflecting in odd ways.

But both methods agree that we're probably looking at something in the range of meters.

I wonder if the reason this simulation doesn't seem realistic, is that it's not really in real time.

v'[x] == 0.04*v[x]^2 + 5*v[x] + 140 - u[x] + i
u'[x] == a*(b*v[x] - u[x])

Where a, b, i are constants.

Does this system of differential equations have a solution?

I recognize those equations! :P

Because when I ask Mathematica to solve them symbolically, it can't do it.

IIRC coupled differential equations are rarely solvable.

@El'endiaStarman That's unfortunate. The problem I'm having is that, as I make the time steps smaller and smaller, that the result does not converge nicely.

As in, the behavior depends too much on the time step size.

Wasn't there a comment about numerical stability somewhere in the original paper?

Yeah there was.

Data for time step = 1 ms, 1/2 ms, 1/4, 1/8, and 1/16

Huh, that is rather significant.

The good news is that... this probably isn't too big a deal, as long as the time-step of the simulation is determined beforehand (at the same time I determine the other parameters of the model neurons).

The problem is that I can't simply change the timestep without changing the parameters. Ultimately, it doesn't matter what the timestep and parameters are, as long as they give the desired behavior.

ever heard a sound-rainbow?

this guy has amazing videos

^ I took that picture right before I moved my car from the roof of the parking garage to a lower level.

woah!

I bet /r/stormfront/ would like that=)

@flawr what an unfortunate name, goes right with /r/marijuanaenthusiasts/

are there primes p, q, r, s such that p^p = qrs + 2(qr + qs + rs)?