So tell me again about the "laws of physics", and how they're not tested through pemutation.
Ok. You generally perform a sequence of experiments, construct a low entropy theory, and then apply that theory in the future. Kind of like what Louis Slotkin did.
He doesn't need to redo them on a train, a plane, in a car, at the bar. The fundamental principles discovered tend to be pretty solid.
Prove it.
Not that hard. Take a fixed volume, convolve it with the 1/r kernel of the neutron diffusion equation. If the volume of uranium is a sphere, you get the spot neutron density at the center is [(3V)^{2/3}]/2. If the volume is a disk of height dz, radius R, you find the the local density is 2(pi V dz)^{1/2}. The smaller dz gets, the smaller the local density of neutrons is, and the further from criticality you are.
(Computing the volume at someplace other than the center is left as an exercise for the reader. However, the maximum principle shows that it always goes down.)
Now plug this into the standard soliton machinery (i.e., use Duhamel's principle, L^p-L^q estimates, etc) and you'll always need a bigger source for a flat soliton than a spherical one.
Yes, I'm skipping a few steps. You can find them in Cazenave's book on solitons (that's where I learned it) and most likely any book on nuclear engineering (but with much less of a mathematical bent). No, it's not the "undergrad physics textbook" you seem to think I'm referring to.
It's pretty amazing how everyone wants to cite "physics" to prove that there's no problem with a meltdown (in the face of overwhelming empirical evidence to the contrary), but nobody is doing much more than hand-waving allusions toward their undergrad physics textbook in defense of their assertions.
What is the "overwhelming empirical evidence" that criticality will be achieved?
Ok. You generally perform a sequence of experiments, construct a low entropy theory, and then apply that theory in the future. Kind of like what Louis Slotkin did.
He doesn't need to redo them on a train, a plane, in a car, at the bar. The fundamental principles discovered tend to be pretty solid.
Prove it.
Not that hard. Take a fixed volume, convolve it with the 1/r kernel of the neutron diffusion equation. If the volume of uranium is a sphere, you get the spot neutron density at the center is [(3V)^{2/3}]/2. If the volume is a disk of height dz, radius R, you find the the local density is 2(pi V dz)^{1/2}. The smaller dz gets, the smaller the local density of neutrons is, and the further from criticality you are.
(Computing the volume at someplace other than the center is left as an exercise for the reader. However, the maximum principle shows that it always goes down.)
Now plug this into the standard soliton machinery (i.e., use Duhamel's principle, L^p-L^q estimates, etc) and you'll always need a bigger source for a flat soliton than a spherical one.
Yes, I'm skipping a few steps. You can find them in Cazenave's book on solitons (that's where I learned it) and most likely any book on nuclear engineering (but with much less of a mathematical bent). No, it's not the "undergrad physics textbook" you seem to think I'm referring to.
It's pretty amazing how everyone wants to cite "physics" to prove that there's no problem with a meltdown (in the face of overwhelming empirical evidence to the contrary), but nobody is doing much more than hand-waving allusions toward their undergrad physics textbook in defense of their assertions.
What is the "overwhelming empirical evidence" that criticality will be achieved?