sethoflagos

There seems to have been some progress there too. Quoting from https://www.cambridge.org/core/journals/quarterly-reviews-of-biophysics/article/nucleic-acids-function-and-potential-for-abiogenesis/842529B9BDAD6E86F7919827725C1931

Just how excited ought we be about these recently published results? Craig A. Jerome, Hyo-Joong Kim, Stephen J. Mojzsis, Steven A. Benner, and Elisa Biondi.Astrobiology.ahead of print http://doi.org/10.1089/ast.2022.0027

I'm so sorry, Genady, I missed this last post of yours. So for the maximum we get the Legrangian function L(x1, x2 ... xn, k) = -x1.ln(x1) -x2.ln(x2) ... -xn.ln(xn) - k.(x1 +x2 ... +xn -1) The partial derivatives for all xi = -(ln(xi) +k +1) and therefore are zero at -ln(xi) = k+1 or xi = e^(-k-1) The partial derivative wrt k is zero for the constraint condition x1 +x2 ... +xn = 1 Hence n.e^(-k-1) = 1 which solves to k = ln(n) -1 Hence xi = 1/n and ln(xi) = -ln(n) Hence max value of original function = n.(1/n.ln(n)) = ln(n) And you were not wrong! Thankyou so much for putting a new string on my mathematical bow. I think I'll go away now and quietly try this method out on a few other functions.

Important to point out that this does not exclude there being a significant iridium content in the sample. Merely that the iridescent surface coating has other causes. Much of the world's accessible iridium reserves are in sulphide minerals, including pyrite, associated with some very particular geological structures. But in the absence of any information from the OP as to exactly where the sample came from or what other minerals and rock types it was associated with, the anomalous x-ray fluorescence data will probably remain just that. We have nothing else to go on.

Interesting article! It's easier to see the common threads when a good mix of examples are explained in a single source.

Pyrite is unstable in air, and frequently accumulates a tarnish of goethite - a hydrated Fe III oxide. Goethite is quite well known (in the jewellery trade and elsewhere) for the iridescence that can develop in the right conditions.

Have a look at https://en.wikipedia.org/wiki/Crystal_growth, particularly the section entitled 'Non-uniform lateral growth'. I believe that will help explain the regular stepped edges you can see.

Not really my field of expertise here! Not even sure what the question is. But if the query is the strong zigzag features, my first guess would be crystal twinning. Iron pyrites (if that's what the samples are) does have an interesting form in the iron cross twin (example below). Erode an oblique cross-section through that and you might find a similar surface. The 'pyritohedra' form can also generate some exotic angles.

You are absolutely right that most of the water involved is absorbed during the alteration of forsterite the magnesium component of olivine. And olivine is mostly forsterite. But there is always >~8% fayalite in olivine, so in that sense there is always hydrogen produced during serpentisation. I'm just paraphrasing the commonly held understanding of the process eg (from https://en.wikipedia.org/wiki/Serpentinite) Yes, some intriguing ideas here. Most of the quoted research is dated recently and some seems to be a bit dismissive of the standard sequence of metamorphic grades and facies that I'm familiar with from a different century(!) If they are suggesting that the slab is subducting so quickly that the water content (whatever its form) is unable to rise fast enough to escape being dragged down, then I'd be more than interested to know what form it actually is in. Some exotic new hydrated mineralogy would be fascinating. Free water even more so. Unfortunately the authors do not say. I'm not suggesting these ideas are impossible, and in support, the material returned deeply emplaced at constructive plate margins (typically gabbro) always has a bit of hydrated material in it in the form of 2-3% hornblende. So there must be some water content deep down. It's one of the standard equilibrium shifts for eclogite facies metamorphism which I simply accept as read. I guess it must be 2-3 GPa or so. But your point is well taken. It's the sort of question I ask myself, and I wish I could get my hands on the thermodynamic data for these materials to plot out the relevant phase equilibria for the benefit of both of us. It's got to be out there somewhere,

Me too. I'm no more than a hobby geologist but it has been a somewhat obsessive fascination since I was about 8! (a very long time ago) One observation that strongly colours my view of this topic is that it must square with not only the surface geology we see around us, but also a very long term gradual trend of oxidation from the global reducing conditions of the earliest times due to photosynthesis. The banded iron formations around the world record oxygen fugacity being controlled by the oxidation of oceanic Fe II to Fe III in the Archean. And to this day, there is still an iron oxidation front controlling oxygen fugacity - called the FMQ (fayalite-magnetite-quartz) redox buffer - now deep within the earth's crust. 3Fe2SiO4 + O2 = 2Fe3O4 + 3SiO2 Compare this with @exchemist's serpentisation reaction 1a) 3Fe2SiO4 + 2H2O → 2Fe3O4 + 3SiO2 + 2H2 ... which can proceed when FMQ has exhausted all the free silica in its environment, and water becomes the favoured source of oxygen. I'm all too aware that this picture is simplistic in the extreme, and maybe the second reaction is not favoured at some key limiting temperature, but it does raise a question in my mind about the stability of water in the low silica reducing environments found at depth. Or perhaps I'm completely off-track, and the ocean is busy converting the lower mantle to topaz!

But eventually this reaction reverses as the high pressure form of serpentine (antigorite) breaks down at ~600 C into forsterite, enstatite and water.

But Ca(OH)2 (and the more relevant Mg form, brucite) thermally decompose, releasing their water while still at only modest depth. For water to get beyond say 100 km depth, it has to find its way into a high density mineral that is stable at the elevated temperatures found down there. All the likely candidates I can think of are hydrogen depleted.

One issue I have difficulty in getting my head around here is the apparent assumption that 'hydrous minerals' accounts for all the lost water. These hydrous minerals (such as amphiboles etc) incorporate -OH presumably sourced from a water molecule in which case one can ask, 'What happens to the missing hydrogen?' The paper references serpentinisation quite extensively as a major consumer of oceanic water. Serpentisation is a highly exothermic reaction occuring in strongly reducing conditions where water becomes a primary oxidising agent, releasing large quantities of hydrogen. Again. Same question. I'm not seeing a distinct water cycle as such here. I'm seeing separate oxygen and hydrogen cycles. My guess is that if one ignores the hydrogen cycle (as some seem to), one is likely to miss a good chunk of the returned water.

The total mass of the oceans slightly depresses the equilibrium level of the oceanic plates, thereby slightly increasing the underlying mantle pressure sufficient to raise the less dense continental plates by an (approximately) equivalent degree. The causal factors for the onset of plate tectonics, and its timing are currently major open questions. As @exchemisthas noted, it seems entirely plausible for the oceans to have supplied some chemical and lubricative effects to facilitate the process. As they still do.

A bit after the lord mayor's show,. However ... While thermal expansion must play some part in mantle convection, it seems that the primary driver is phase change (ref: https://authors.library.caltech.edu/25038/145/Chapter 5. The eclogite engine.pdf). This implies that most of the transported energy is locked up in the enthalpies of various sequences of crystal structural readjustments with depth (eg the olivine-wadsleyite-ringwoodite-perovskite sequence) rather than as thermal energy. Hence there is within the mantle a huge reservoir of energy bound up in high pressure mineral polymorphs, that may be released as heat at specific lower pressure locations (mid-ocean ridges. volcanic island arcs etc) moreorless independently of the overall thermal gradient. This localised heat release drives the processes of crustal magmatic fractionation, adding low density granitic material to the continents, and consequently increasing the density of the returning subduction slab. The excess of gravitational potential energy of this continental scale mass of dense material over and above the surrounding asthenosphere represents a second huge reserve of energy that is partially returned as heat back to the base of the mantle, but is mainly consumed in restoring the high pressure polymorphs of its constituent mineralogy. Overall, the process of continent building via magmatic convection and fractionation might be approximated as raising 3 billion km3 of granite (SG ~2.5) through 1,000 km of mantle (SG ~ 4) which looks like 4.5 x 10^28 Joules over a period of 4.5 billion years resulting in a heat output of 0.3 TW purely on isostatic considerations. Contrast this with the estimated total crustal heat flow of 47+/-2 TW (based on 38,000 measurements). If we were to consider the approach toward gravitational equilibrium of all structures within the earth (not just the surface ones), then the process of planetary differentiation (ref: https://en.wikipedia.org/wiki/Planetary_differentiation) would seem to amount to an appreciable percentage of the total. And that's based only on the isostatic aspect. We are as yet nowhere near full planetary chemical equilibrium either, and that must also factor into the balance sheet. I've seen figures of ~20 TW given for the heat produced by radioactive decay, and can only add the comment that it seems credible. More critically some authors have ascribed the balance to 'primordial heat'. I don't quite know what they mean by that. Or rather, I do. It's the heat generated during the initial accretionary growth of the planet, the sum total of initial gravitational potential energy of all its constituent parts and released as heat on impact. But isn't this just the initial phase of planetary differentiation? The phase where space was gravitationally displaced by matter? And has it been sat around doing nothing since? I think not. Rather its being doing what heat does - driving convection currents and fuelling endothermic reactions for the last 4.5 billion years. Seen in this light, I'm tending to lean towards there being an approximate balance between radiogenic heating and the nett release of gravitational and chemical potential energy arising from planetary differentiation.

Of course this is true. However centrifuges can work perfectly well in the absence of gravitational forces so for the purposes of the OP ... etc. Not that it's much of a complication. Gravity simply adds a vertical gradient to the pressure field caused by the fluid rotation, and the particles respond accordingly. Btw For some light reading, try 'Spray Drying of Detergents in Counter Current Towers', Victor Francia Garcia, School of Chem. Eng., University of Birmingham (2014). Link https://etheses.bham.ac.uk/id/eprint/5646/1/Francia-Garcia15EngD.pdf (if permitted) Interesting stuff on particle structures, density, porosity etc in Appendix II (page 260 and on)

Just reproduced the experiment with a capful of Ariel Original in a saucepan of freshly swirled water. The powder takes a significant time to wet thoroughly (about a minute). So while many of the individual components may well have densities equal to or exceeding that of water, under what I understand to be the OP's conditions, it appears that the detergent 'phase' while it exists retains a substantial air content, significantly suppressing its density. Putting numbers to this would be very difficult, but the proof of the pudding is in the eating. Until wetting and dissolution is complete, the detergent sits in the central vortex of the swirling liquid.

Best to consider this in terms of pressure gradients as concepts such as centrifugal force are artefacts of circular frames of reference and lead to misunderstandings. Suppose the fluid comprises x parcels all of equal volume. Each parcel is subject to an acceleration towards the centre of the bowl due to the rotational flow regime that you initially imposed on it. Each responds by generating a reactive inertial force (your 'centrifugal' force) in the opposite direction acting on their immediate outward neighbour. These reaction forces stack up to generate a pressure field that is a minimum at the centre of the bowl and a maximum at the outer wall. And it is this pressure field that gives a nett push toward the centre (ie, your 'centripetal' force) on each parcel causing the acceleration that maintains the rotational flow regime. Now consider a single parcel that is a little denser than its immediate neighbours. Due to its extra mass, the local pressure gradient is insufficient to accelerate it as much and so it tends to better maintain its course and moves outward, using its extra inertia to displace its outward neighbour(s). In turn, lower density (lower mass) parcels subject to the same pressure gradient will tend to accelerate toward the centre more readily, lacking the inertial punch necessary to prevent heavier neighbours from displacing them.

In principle, it should be possible to incorporate a micro Combined Cycle Gas Turbine power plant into the design of a large tractor unit. Modern designs of CCGT are routinely specified at >50% thermal efficiency, so it should represent a major advance on your historic baseline. Putting solid fuel through a GT is a bit problematic so you'd likely be looking at some version of liquid biofuel (biodiesel, ethanol etc) for base fuel as a practical proposition. Following combustion in the GT, the exhaust gas would pass to a HRSG (Heat Recovery Steam Generator) raising superheated mains steam to feed a condensing steam turbine, with condensate recovered from (perhaps) overhead air cooled condensers for return to the steam drum. The water circuit would therefore be closed cycle. The split of power output between the cycles would be of order 2:1 (GT:ST) so I guess it wouldn't quite be pure steam punkery.

Yes, thank you, Genady. Trial and error seems to indicate so. But how does one derive those values mathematically?

My scribblings came up with the following interesting function f(x1,x2,... xn) = -ln(x1^x1*x2^x2*,... xn^xn) Where: x1+x2+... xn = 1 0<xi<1 I suspect that this function ranges 0 to ln(n) but a proof is beyond me. Assistance would be most appreciated.

I'm more familiar with the sprung ball detent type wrench, so notwithstanding ... : As stated in my previous post, deflection angle is proportional to the applied moment for a given wrench length, so providing you dont try to apply load from somewhere other than the end grip, the two should be linearly correlated. I see no need to go any further than the static force balance here. Serious bolt tensioning is best done without significant dynamic loadings.

It's called the 'angle of deflection' and for an ideal weightless cantilever is proportional to the end load times the square of the cantilever length. Since this is a fixed displacement (the beam doesn't continue to move) mechanics in particular will tend to refer to the loading force as a moment rather than a torque. They are sort of the same thing, but torque is used more in the context of rotating bodies like crankshafts, and this can lead to confusion if the terms are applied haphazardly. Useful Wikipedia lpages to browse through may be Deflection (engineering) and Euler-Bernoulli beam theory.

No. At point A, the fluid is high pressure liquid phase at ambient temperature. At closure of valve B, it is low pressure mixed-phase stream at some lower temperature. Getting back to point A requires both recondensation (path B-C) and recompression stages (path C-A), which you have indicated on your P-V diagram, but failed to address in your process description.

On this sunny Lagos afternoon, the first thought that occurs is that liquid carbon dioxide in my ambient conditions would be in the neighbourhood of its critical point (78.3 bara, 31.1 deg C). Perhaps it's a shade cooler in most of Russia today, but even so, we need to be extremely wary of any processes that seek to gain advantage from assumed PV behaviour under gas-liquid phase changes. In the vicinity of the critical point, such leverage vanishes as gas and liquid become indistinguishable. Next thought is that the OP process schematics (Fig. 1-3) do not match the PV cycle shown in Fig. 4. Since no actual numbers are supplied, it's reasonable to take path AB (piston induced vapourisation/vapour expansion) at face value. However Figs 2&3 indicate a subsequent reversal of this process (piston induced compression/condensation). Even if it were possible to remove all thermodynamic inefficiencies from this cycle, the return PV path BA would simply overlie AB. No nett work, no nett cooling, no creation of the 'convenient' heat sink of tank B. By contrast, Fig 4 gives path BC, an isobaric contraction (~ideal condenser stage) followed by path CA, an isochoric compression (~ideal liquid pumping stage), both of which represent parasitic external energy inputs not disclosed by the OP. The implied external refrigeration plant (realising BC) is going to be a thermodynamically expensive item in particular.