There's absolutely nothing about the "laws of physics" that guarantees that this particular reactor design is going to be able to contain a full meltdown, because it's never happened before. Nobody knows.
Physics isn't biology/medicine. The laws of physics are not discovered by running experiments to enumerate every possible combination or permutation of configurations.
You're assuming an intact core. Criticality is a function of density, shape and temperature, in addition to mass. Melt the fuel rods, and the guarantees of that nice, well-moderated behavior are off.
The optimal shape for criticality is a sphere - surface/volume is the key factor here. A wide, shallow puddle at the bottom of the containment chamber is the least dangerous shape.
Temperature affects things because higher density makes achieving criticality easier. I.e., the colder things get, the more likely criticality is to be achieved.
"Physics isn't biology/medicine. The laws of physics are not discovered by running experiments to enumerate every possible combination or permutation of configurations."
Wanna bet? Guess how we know most of what we know about criticality and neutron cross-sections? People like Louis Slotkin, who spent hundreds of hours poking at piles of radioactive material in the lab, to derive those mathematical models that you're leaning upon. Critical mass calculations, in particular, are so fiendishly complicated that the entire field of stochastic simulation (i.e. monte carlo methods) were invented to address them. So tell me again about the "laws of physics", and how they're not tested through pemutation.
"The optimal shape for criticality is a sphere....a wide, shallow puddle at the bottom of the containment chamber is the least dangerous shape."
Prove it. 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.
A sphere is definitely a shape where we have good calculations to model critical mass. Otherwise, we don't really know much that wasn't determined empirically. We know that criticality depends strongly on density. We've assumed that the structure of this reactor will prevent that density change from occurring. We don't actually know what will happen.
I can almost understand why a community of nerds is so strongly interested in maintaining the self-delusion that the world is a fully knowable, controllable place, but I don't understand how so many people can ignore so much real-world evidence for so long. If you're seriously telling yourself that a meltdown isn't a big deal, you need to go back and re-examine what you know about the situation, and why you think you know it.
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?
The physical principles behind criticality calculations are not fiendishly complicated. The computations are computationally intensive, yes (Slotin was around in a time where experiments were cheaper and easier than simulations), and (maybe -- I don't know) the exact nature of physical materials involved was not well known, and needed to be measured.
Prove it.
Why don't you prove it? It's not other people's job to do all the work for you. It is provable that a sphere is the optimal shape. If somebody on the internet suggests that you're wrong, you don't win the argument by saying it's their responsibility to do all the hard work of convincing you you're right. You're still the one who is wrong.
Physics isn't biology/medicine. The laws of physics are not discovered by running experiments to enumerate every possible combination or permutation of configurations.
You're assuming an intact core. Criticality is a function of density, shape and temperature, in addition to mass. Melt the fuel rods, and the guarantees of that nice, well-moderated behavior are off.
The optimal shape for criticality is a sphere - surface/volume is the key factor here. A wide, shallow puddle at the bottom of the containment chamber is the least dangerous shape.
Temperature affects things because higher density makes achieving criticality easier. I.e., the colder things get, the more likely criticality is to be achieved.