Uncertainty estimates for Fermi estimates

In a final year course that I co-teach, I teach Fermi estimation* (my notes are here). Fermi estimates are simple back-of-the-envelope calculations. Let’s say you want a Fermi estimate of how many people in the UK take a train journey on a normal week day. You start by saying “Well the population of the UK is about 60 million people”, then you say “I guess about 10% take a train journey on a given day, as 1% of people taking a train looks too low, while it is clearly not 100%”. The Fermi estimate is then that about 6 million people take the train in one day. To check this estimate, I did a little Googling, and there are about 6 million journeys per day in the UK, so assuming that people who travel in a day take two trips (eg to and from work), it looks like I am about a factor of two, too large. Not bad for a simple estimate.

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Droplets surfing waves of creation and of destruction

I am continuing to play around with transient phase separation, as you can see in the movie above. Droplets of a green phase appear then disappear. In the experiments that I am trying to understand, the experimentalists mix salt, which diffuses fast and promotes protein phase separation, with protein, which diffuses slower. So I have developed the model so that the ‘protein’ in my model diffuses slowly and downwards, and there is also a faster diffusing component, the ‘salt’ in the model, that diffuses upwards. Then the green ‘protein’ droplets start to form when the ‘salt’ has diffused into the top half of the system, but then as the ‘protein’ diffuses downward and out of the top half, this causes dissolution of the droplets.

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Moving to where the energy is

ATPanionChemDrawThe human body is a colony of about 30 trillion cooperating cells, each of which needs to burn energy to survive. Within the cells, a lot of the energy is carried around in the form of a molecule called ATP. A single one of our cells may have ten billion or more molecules of ATP, and these molecules are very dynamic. A single ATP molecule may be used to release its energy, then regenerated only a second later. So, there are huge ATP currents and gradients inside cells. And ATP is a big molecule, its structure is above. From left to right, there are three charged phosphate groups (each with a P = phosphorous), a sugar in the middle, and at the part at the top right is also found in one of the bases in DNA. Continue reading

Excellence framework scored: must do better

The government has introduced the Teaching Excellence Framework (TEF) which purports to assess the excellence or otherwise of teaching in English universities. Surrey was awarded the highest score, a gold, in 2017*. But measuring teaching is hard, it is subjective, and so mostly what the TEF measures is statistics about a university, plus a text summary. There is no actual observation, let alone direct assessment of, teaching, in the TEF. The august body, the Royal Statistics Society (RSS), has just issued a critique of the TEF. The critique reads like the feedback on a piece of statistics coursework submitted by an unusually weak student.

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Dissolving together

I am continuing to play around with systems that start to separate into two phases (the green and the red phase in the movie above) but don’t get very far before one phase (the green one) dissolves. I have tweaked some parameters above, so that green droplets form, and the system is a bit bigger (I also changed the orientation, sorry if that is confusing). if you follow the movie carefully, it seems clear that the dissolution of the green droplets is via fronts that are pretty straight (horizontal), one front that moves upwards, dissolving droplets as it goes, while another moves downwards. When they meet in the middle, the green droplets are all gone.

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Liquids that briefly come apart

Oils and water often spontaneously separate to form two coexisting liquids, one mainly oil, and one mainly water. For example, if you add olive oil to vinegar the two liquids separate out into droplets of oil in the vinegar. But at least for some oils, they mix in at least some proportions with water at higher temperatures, so you can have a single hot mixed liquid, that on cooling separates out into oil droplets in water. This is a well studied and common phenomenon. But what if you simultaneously cool, and mix in more water? For example, what if you start with with hot oil in water, with for example, 20% oil, that is sufficiently hot that water will dissolved all the oil? Then you cool to a lower temperature, where water can only dissolve say 15% oil, but at the same time you mix in an equal volume of pure water?

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A story of a Frenchman, a Baron and a paint guy

Just before Christmas I wrote a blog post about Baron Rayleigh’s work on convection, he showed how a layer of colder fluid (eg air or water) on top of warmer fluid, would lead to convection — flow of the colder fluid downwards to be replaced by warmer fluid from the bottom. Rayleigh’s work is a classic, and has been built on to help us understand, amongst many other things, Earth’s weather/climate. Rayleigh assumed that the flow was driven by gravity. The colder fluid on top falls because it is denser. Convection is everywhere in Earth’s atmosphere and oceans. It is sometimes called Rayleigh-Bénard convection, to honour Baron Rayleigh who developed the theory, and Henri Bénard, who did the experiments that inspired the theory.

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Video

Salt fingers

Above is a computer simulation of a phenomenon often called salt fingers. They occur in world’s seas and oceans, for example they are common in the Caribbean. Salt fingers form when there is a layer of warm salty water above a layer of colder but less salty water. The point is that salty water is denser than less salty water, so typically a layer of salt water on top of a layer of fresher water is unstable, the denser layer on top falls down through the less dense layer below due to gravity — this is convection. However, here the water on top is not just saltier it is also warmer. This temperature difference works in the opposite direction to the difference in the amount of salt. Warmer water is less dense that cold water and so a layer of warm water floats on a layer of colder water.

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What do an American Ivy League university and a Wetherspoons in Wrexham (Wales) have in common?

I currently have 50 reports, and two dissertations to mark, and on Thursday next week I’ll have not one but two exam papers to mark. So I am taking a break from the endless marking to share with you something surprising that I have learnt, not about science but about history. My sister bought me The Silk Roads by Peter Frankopan, for Christmas, and I am enjoying reading it. The book mentions the Ivy League (i.e., posh, presitigious and expensive) Yale university in the north east of the United State, although it omits the Elihu Yale Wetherspoons pub (i.e., pub that is not posh, lacks prestige but has cheap beer) in Wrexham in north east Wales.

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