This is a tough one for me to even try to communicate much less formulate, so please be patient with me.
I have a substance that has an interesting property. The substance spontaneously aggregates its density until the integral sum of the second derivative of every 3D angle of the instantaneous density slope at every point is zero. I am looking for an equation that yields an instantaneous density per xyz coordinate after the specification has been met.
For example, if given a large volume of the substance wherein a single small region in the center of the volume has become a little more dense than the rest, the density throughout the entire volume will spontaneously shift so as to meet the specification. The result would be that the very center of the volume would have an exceedingly high density (infinite) and exponentially be less dense toward the outer regions of the volume.
But an extended concern is that if two such small regions happen to become more dense, the specification still applies and I will still need a density per xyz equation representing the whole volume that would end up with two (or more) highly dense "centers". That concern might involve the initial conditions, timing, and distance between the centers so as to discern if one gets absorbed by the other while conforming to spec.
I can tell that the equation involves at least a double integral so as to sum the angles of the slopes at each point, but the rest gets more than just a little confusing. And I imagine that I might need to explain a bit more, but I don't know what else might need to be specified.
Any clarification or advance concerning this issue would be appreciated, thks.
I have a substance that has an interesting property. The substance spontaneously aggregates its density until the integral sum of the second derivative of every 3D angle of the instantaneous density slope at every point is zero. I am looking for an equation that yields an instantaneous density per xyz coordinate after the specification has been met.
For example, if given a large volume of the substance wherein a single small region in the center of the volume has become a little more dense than the rest, the density throughout the entire volume will spontaneously shift so as to meet the specification. The result would be that the very center of the volume would have an exceedingly high density (infinite) and exponentially be less dense toward the outer regions of the volume.
But an extended concern is that if two such small regions happen to become more dense, the specification still applies and I will still need a density per xyz equation representing the whole volume that would end up with two (or more) highly dense "centers". That concern might involve the initial conditions, timing, and distance between the centers so as to discern if one gets absorbed by the other while conforming to spec.
I can tell that the equation involves at least a double integral so as to sum the angles of the slopes at each point, but the rest gets more than just a little confusing. And I imagine that I might need to explain a bit more, but I don't know what else might need to be specified.
Any clarification or advance concerning this issue would be appreciated, thks.