For a first exercise, forget Dijkstra and just solve a maze by doing Value Iteration, and plot the cost-to-go at each step.
Then consider that this function doesn't have to take a graph vertex or grid cell, but could instead be some continuous function on R^n.
The next step usually is to learn about the Linear Quadratic Regulator problem, where the cost-to-go is a quadratic, and you get to do an iteration of "Value Iteration" by updating the quadratic coefficients.
To connect to physics, see how you'd write the Action Integral in these terms.
What people normally call "CCS" is mostly a short-term hack to keep the coal mines running. If you're going to burn coal, then, yes, please do CCS, but pretty soon you need to stop burning coal. I also don't trust that CO2 will stay underground forever; that also makes it "short term".
That said, we do need direct air capture (DAC) to repair the damage and to provide an alternative source for CO2 and hydrocarbons.
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To this end, I kind-of like algae as a low-tech solar-powered method:
I feel you could do this in a moderate-sized backyard.
You wouldn't want to bury the biomass directly (say as biochar) because you wouldn't want to lose the NPK nutrients -- but the above article deals with that. It describes a couple methods to extract carbon while recycling the other nutrients. None seem too difficult.
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In a completely different direction, nuclear-powered Sabatier/Bosch/electrolysis is also interesting:
Either way, you have to combine your DAC with... not mining fossil fuels out of the ground. You have to do both.
(Note: Carbon-neutral fuels (bio-, synthesized) are fine, e.g. for air travel. You just can't mine them from the earth. That's the one rule. Then the cost of recapturing CO2 has to be baked into everything else.)
An interesting theoretical calculation is the rate of entropy production due simply to mixing of smokestack gasses (high partial pressure of CO2) with atmosphere (low partial pressure of CO2). In principle this is wasted exergy -- lots of it. One could imagine some combination of semipermeable membranes and turbines to extract power from the mixing process (your mention of membrane separation reminded me of this). To be clear this is sci-fi though at this point.
(I do believe, however, that there exist methods to extract energy from the mixing of salt and fresh water.)
Likewise, this same idea is a strong argument for capturing CO2 from smokestacks instead of from atmosphere: Fundamentally, it takes energy to undo mixing. And if you want to capture the CO2 eventually anyway, then better to just do that than invent a theoretical "heat engine" driven by the difference in CO2 partial pressure, to get energy that you'll just need to spend somewhere else later (and then some) to get the CO2 back out of atmosphere...
...Actually this phrase "heat engine" now makes me think that maybe this isn't even that hard (in theory) using cold temperatures and phase changes to make dry ice. If it's possible to efficiently cycle the gas through these large temperature swings at all, it must require some kind of heat exchangers and regeneration between stages... (Surely if this were realistic people would have figured out how to do it by now, but it's an interesting thought/design experiment in thermodynamics...)
This discussion of heat pumps makes me want to add that we may also ignore cogeneration too much. We just don't think about heat flows and temperature enough.
There is, of course, the communal thing, done in Sweden and Russia and college campuses, with a power plant and steam pipes going to apartments.
But what about an appliance for suburban America? Like, combine a gas turbine generator with an HVAC system and hot water tank (pretty sure you can buy things like this in Germany). No unsolved technical problems here. You generate electricity for your home, heat it with waste heat, and absorb temporary excesses in capacity by usefully heating water. You could imagine integrating other things too: If you need more heat than you use electricity, then you might as well use the electricity to do something high-value (cryptocurrency is a crime against the environment, but you might as well compute some hashes in your resistive heater). All this becomes an elaborate way to burn natural gas to make heat, but you get a bunch of other things out besides. The "smart controller" aspect then becomes interesting -- but even that is "just simple automation", not super-difficult AI.
Maybe logistically, the "everything is electric; electricity comes from renewables/nuclear; and heat comes from heat pumps" solution is easier in the long run?
But this more "decentralized heat engines" solution has the "advantage"(?) that it could run on biomass, which is easy to store (however, I am aware of the problems of wood pellets and deforestation).
I'm curious about this cartridge idea. I'm picturing a pipe with quicklime inside and coffee filters on the ends, with a blower to force air through. How tightly would the contents be packed?
This is a little different from what I'd been thinking before your message, which would be more of a fluidized bed reactor -- like quicklime swirling around in air in a garbage can. I think that's closer to how some powerplants treat exhaust.
I've read that there are microscopic changes to the quicklime particles after a couple absorbtion/heating cycles (their pores fill up or something), after which you need to do something to further refresh it, maybe by dissolving it and precipitating it back out of solution.
This led me to considering whether aqueous chemistry might be better.
The simplest would be to react air with calcium hydroxide (would you use a bubbler? Or a packed counterflow tower? Or a spray tower?) and collect the calcium carbonate that precipitates out.
But, based on my shaky chemistry, I understand solubility of calcium hydroxide is low, so you do better with a two-stage process like the Kraft Process:
1. Absorb CO2 in contactor:
2NaOH + CO2 -> Na2CO3 + H2O
2. Regenerate solution in causticizer:
- CaO + H2O -> Ca(OH)2
- Na2CO3 + Ca(OH)2 -> 2 NaOH + CaCO3
3. Decompose calcium carbonate:
CaCO3 -> CaO + CO2
The concentrated NaOH solution would be very caustic, so you'd have to be careful with that, but apart from that none of this seems too terribly scary?
Some parts of the above are endothermic, others exothermic, so maybe this could even let you shift energy from the summer (solar furnace?) to the winter when you need it, as part of the deal.
Or maybe this is all too complicated and you should just use a canister of soda lime granules, like an anesthesia machine? ( https://en.m.wikipedia.org/wiki/Soda_lime )
I'd be interested to hear more from people whose chemistry is better than mine.
Here I assume that the gas has to dissolve as part of the reaction so use CO2(g) instead of CO2(aq) on the left hand side. I get an enthalpy delta of -111.33 kJ/mol. This differs from some homework answers I find online like [4] because I use NaOH(aq) while they use NaOH(s), etc; I hope I'm right for this application.
The easy thing would be to run at least (2b) (causticization) concurrently with (1) so you're always precipitating out CaCO3 and don't accumulate any Na2CO3 solution. It would also be easiest to combine (2a) with (2b) in a single causticization chamber. And it'd be simplest to skip (3) entirely, just treat CaO as a consumable, and be happy that you've sequestered carbon as CaCO3.
However, in a temperate climate, you can imagine doing the following to shift energy around the year (how realistic this is I don't know):
- Only run (2a) during the winter, to heat your home; you'd accumulate Ca(OH)2 solution to be used during the summer in (2b).
- Only run (2b) during the summer, to cool your home. During the winter you'd accumulate Na2CO3 solution from (1), which you'd need to store.
- If you're doing (3), do it during the summer, when a solar furnace can be operated. This gives you a reagent that you'll use in (2a) during the winter.
- You'd want to run (1) all year round, to scrub the CO2.
The main inefficiency this is trying to make useful is that you need to go down in energy with (2a) and back up in (3). And down in energy with (1) and back up in (2b).
I'll next need to understand the soda lime method to compare.
https://news.ycombinator.com/item?id=24530731