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Applied Fusion Systems

Nuclear Fusion Research

Solar price collapse

Bloomberg have published their annual Energy Outlook. There’s plenty of interesting stuff in there for example:

  • Onshore wind prices to fall by 41% by 2040.
  • Solar PV to fall by 60% by 2040
  • Home installed “behind the meter” battery packs to grow from a total capacity of 400MWh to 760GWh by 2040.

Looks like Musk was right to build that factory. Let’s hope there’s enough Lithium to go around. I know a few other people have plans for that element.

 

 

Lithium Pt2

The metal that keeps on giving!

Researcher at PPPL found that injecting grains of Lithium into turbulent plasma resulted in increased temperature and pressure:

The scientists used a device developed at PPPL to inject grains of  measuring some 45 millionths of a meter in diameter into a plasma in the DIII-D National Fusion Facility – or tokamak – that General Atomics operates for DOE in San Diego. When the lithium was injected while the plasma was relatively calm, the plasma remained basically unaltered. Yet as reported this month in a paper in Nuclear Fusion, when the plasma was undergoing a kind of turbulence known as a “bursty chirping mode,” the injection of lithium doubled the  at the outer edge of the plasma. In addition, the length of time that the plasma remained at high pressure rose by more than a factor of 10.

 

[The above image is a Lithium mine in Argentina. Lithium is recovered by evaporating brine and then electrolysing the Lithium chloride. Lithium mine, Salar del Hombre Muerto, Argentina The Advanced Land Image on NASA’s EO-1 satellite captured this image on May 16, 2009]

Salar del Hombre Muerto means “everything’s fine” I think.

State of the Art

There’s something enchanting about technology sometimes. For example an otherwise gaudy 200  year old fire-arm

But when the trigger is pulled a clockwork bird emerges and sings a life-like song.

The level of care and attention that went into mimicking something as simple and beautiful as birdsong is humbling. It reminded me of Nick Lane’s quote from a few months ago.

How on earth does the music box mechanism produce those sounds? Anyone?

 

SMRs

Late last year the government got ever so slightly interested in small scale nuclear reactors. Small modular reactors, SMRs, are plants which produce a few hundred megawatts as opposed to the gigawatts produced by typical plants.

From the economist:

Such reactors are often billed as one solution for a nuclear industry bedevilled by massive cost overruns and technical snafus.

The hope is to combine the no-carbon, always-on, base-load hyphenated goodness of nuclear power without the appalling cost.

Case in point: Hinkley Point C, £18B 3.2GW.

Check out NuScale’s website. They hope to deliver their reactors on a barge or truck.

Fascinating stuff, they seem to have taken great effort to simplify the design, for example the reactor core is convection cooled, no pumps to go wrong.

Fun stuff. I just with the government could manage more that £250M over 5 years.

 

[Image is from http://nuclearstreet.com/images/img/heu7.jpg showing an experimental reactor at Sandia National Laboratories. Not an SMR]

Adaptive Design Pt.3

No matter how much I play with these growth models I can’t shake the feeling that I’m just scratching the surface.

Here’s what happens when we change our plant’s growing preferences.

So far the algorithm has been

  1. Identify a potential new square to occupy
  2. calculate how this would change your fitness value
  3. decide if you should occupy the new square.

recall that a plant’s fitness is defined as latex-image-1

and that we have been using an expit curve as our transition probability function:

 

plot

 

See the previous post for the python code.

For this curve new growth that doesn’t improve the plant’s fitness is accepted 50% of the time. Growth that lowers or raises the fitness by a given amount is favoured/avoided equally strongly.

But we could have all kinds of different shapes. Let’s see what happens if the plant is really laid back and is more accepting of small decreases in fitness. i.e the curve is shifted left:

plot.png

Now our growth looks like this

What’s the word? It looks more clumpy? That’s what you get when the plant casually accepts new growth even if it doesn’t increase fitness. Now let’s do the other direction with the expit function shifted right by 5:

Now we have a plant which is far more stingy. It only adds new growth that is particularly beneficial to its fitness, hence the preference for diagonals!

 

 

Adaptive design pt2

Following on from the last post I’ve been digging a little deeper to see how these tree-like branchy things behave.

The variable I chose to look at was the fertility of the occupied squares, either:

  • All occupied squares can start new growth regardless of their age.

or

  • Only squares that have been occupied for fewer than N time steps can start new growth.

Call the cut-off age the fertility.

I set the fertility to 30 time steps and ran the simulation for 1000 time steps 1000 times. Here’s the results:

 

to30-1000steps.png

How does this compare to cells that are fertile forever?

 

Histogram.png

So ‘fertile forever’ is not what we want. Here’s a video of a branch that’s fertile forever:

And now look at one with the fertility is set to 30:

Branches where every cell can spawn new growth seem to spend too much time adding cells to their centre which doesn’t increase their fitness much because they open up fewer neighbouring squares.

We see more branching in the plant whose cells are only fertile up to 30 time steps which is really interesting. It branches more because new growth tends to be at its edges.

I repeated the histogram plots for fitnesses of 10 and 20, too. Here they are on the same  graph:multiHistogram.png

 

It’s striking how inconsistently 10 behaves!

There’s so much to play with in these models, next time I’d like to look at changing the probability function the branches use to decide whether to grow or not. Recall at the moment I’m using an expit function:

 

plot

Next time I’ll see what happens if I mess around with this. Perhaps a step function? Or one of these?

expits.png

We’ll see.

Adaptive design

Time to catch you up on a project of mine.

A short while ago I got interested in adaptive design. The broad idea is to apply an evolutionary or fitness maximising algorithm to the design of some object.

Whenever I want to learn about something I like to build a small project of my own. For this I decided to model how roots grow through soil.

I start with a 100 x 100 grid. The squares are either empty soil or occupied by a root cell. The plant wants to maximise its surface area (number of adjacent soil cells) to volume (number of plant cells) ratio. From here on let’s have

latex-image-1.jpeg

The algorithm does this:

  1. Identify all unoccupied squares next to the plant.
  2. Choose a square from step 1.
  3. Calculate how much the plant’s fitness would change by adding the new square.
  4. Decide whether to add the square or not.

Step 1 is done using a convolution which I may detail in another post. Step 2 is just a random selection. Step 4 uses this code:


def shouldTransition(self, changeInFitness):

        #threshold value
        #changeInFitness += 5.0

        #steepness
        #changeInFitness *= 10

        activation = expit(changeInFitness)

        dice = random.uniform(0.0, 1.0)

        return dice <= activation

The expit function looks like this:

plot.png

The idea is that the plant should favour new growth that would increase its fitness so the probability gets closer to 1 to the right. conversely if a change lowers the fitness it gets a probability closer to zero. We can have lots of fun by tweaking the shape of this graph: we can

  1. Make the plant more ambitious; it only accepts big increases to its fitness.
  2. Make the plant more adventurous; it will more happily add growth that harms its fitness. this can be useful to prevent the plant getting stuck in a rut.

Let have a look at some results. Animated for your viewing pleasure. Here 1 second corresponds to 100 time steps.

And another

 

Th eagle eyed among you may notice a few interesting things about these animations: Do all the root cells spawn new growth? No but more on that in another post. What happens if we modify the expit function? Coming soon…

Thanks for reading I’ll follow up with more detail soon.

JL

The Sabre Engine

Speaking of doing hard things. Last week I went to a lecture on the Sabre engine.

The Sabre is a  cross between a traditional engine and a rocket. Reaction engines, the company behind it hopes the sabre will allow them to develop an affordable spaceplane. Unlike conventional rockets, Space planes would afford reusable and cost-effective access to space.

One of the surprising statistics Dr Robert Bond mentioned in the talk was the sheer inefficiency of rockets as a means for getting into space. Take a typical Ariane five rocket pictured below

a5_launch_14august2008_lr.jpg

This rocket carries about 160 tons of fuel: 132 tons of liquid oxygen and 26 tons of liquid hydrogen. The fuel burns to produce water vapour. The huge inefficiency comes in the fact that most of this fuel is merely present to lift the rest of the fuel.

Reaction engines have decided to approach this problem by building an engine that operates in two stages:

  1. An air breathing first stage in which the engine operates as a jet. In this stage the engine burns liquid hydrogen and oxygen from the atmosphere.
  2. A conventional rocket engine stage in which the engine burns liquid hydrogen and liquid oxygen from its on-board tanks.

The fact that a sizeable fraction of the rocket’s ascent takes place in stage 1 means that it can carry far less liquid oxygen allowing for a substantial weight saving.

The talk touched on many fascinating details about the Sabre engine but I’ll just share one here. Take a look at the engine:

 

sabre_nacelle_open_610.jpg

Why is it shaped like a banana?

Well the space plane’s wings are very small so the plane must have a very high angle of attack in order to generate enough lift. But a jet engine works best when air is entering it head on so the front of the engine needs to be tilted downward. Amazing diagram below:

Screen Shot 2016-03-21 at 13.21.35.png

Quote of the Day

Firms build value by doing hard things

 

Elon Musk

In an Economist article on Tesla.

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