Coli bretheren let's discuss power laws

[Hawaiian Punch]

First forgive my ignorance on the subject. From what little I have learned about it has blown me away. The formulas of power law, as I am learning, describe our world and to greater effect the universe. What do these pictures have in common?

A city and a neuron

A tree branch

The universe and a neuron

The growth of all of these are determined by power law. Metabolism, heart rate, body mass, size of cities, the stock market and fractals are a few more examples. Others stated in wiki are 'the sizes of earthquakes, craters on the moon and of solar flares,[1] the foraging pattern of various species,[2] the sizes of activity patterns of neuronal populations,[3] the frequencies of words in most languages, frequencies of family names, the species richness in clades of organisms,[4] the sizes of power outages, wars" So what it's it?

Power law - Wikipedia, the free encyclopedia

a power law is a functional relationship between two quantities, where one quantity varies as a power of another. For instance, the number of cities having a certain population size is found to vary as a power of the size of the population.

Why is this important bretheren? Because if you can predict the growth of systems you can use existing information to predict the future. I won't post the articles here, but from what I have read researchers have already started to use power laws to succe$$fully predict certain future events.


Study up y'all.

 

[Domingo Halliburton]

Because if you can predict the growth of systems you can use existing information to predict the future. I won't post the articles here, but from what I have read researchers have already started to use power laws to succe$$fully predict certain future events.

so the most interesting part of your thread you're not going to link to or talk about?

 

[tmonster]

Though the pictures are fascinating (I have seen them before) I don't subscribe to the idea that there are analogous form/function relationships across these structures, mainly because of the available data on the cause of their particular forms and functions and the significance of their particular functions. Maybe there is an inherent electromagnetically derived fractal relationship in the forms of natural micro/macroscopic structures (neuron/universal web) but clearly that is not ascribable to function and clearly that is even less inferable to the unnatural causal derivation of unnatural forms like a modern city's electric grid patterns. The phenomenon may easier be found attributable to the human predilection of pattern finding and universal entropy's predilection for pattern creation.

 

[tmonster]

Sun's fractal surprise could help fusion on Earth

• 01 May 2014 by Nicola Jenner
• Magazine issue 2967. Subscribe and save
• For similar stories, visit the Solar System , Energy and Fuels and The Nuclear Age Topic Guides

THE sun has thrown us a fractal surprise. An unexpected pattern has been glimpsed in the solar wind, the turbulent plasma of charged particles that streams from the sun. It offers clues for handling plasmas that roil inside nuclear fusion reactors on Earth.

Composed of charged particles such as protons and electrons, the solar wind streams from the sun and pervades the solar system. Its flow is turbulent, containing eddies and moving at different speeds in different directions. It was thought that this turbulence was similar to that in a fluid, behaving like mixing ocean currents or the air flows that make aeroplane flights bumpy.

Now, Sandra Chapman of the University of Warwick, UK, and her colleagues have examined the solar wind's behaviour using NASA's twin STEREO spacecraft

. One flies just within Earth's orbit around the sun, the other just outside it, allowing the pair to obtain unique measurements of solar wind behaviour.

STEREO revealed that when the movement of the wind's particles is perpendicular to the sun's magnetic field, they resemble a fluid, with sections that are smooth, interrupted by bursts of violence. "If you look out of a plane window you see mountain ranges and then long rolling plains. This is what the perpendicular fluid turbulence is like," says Chapman.

But when the particles move in parallel with the field lines, they behave very differently, with the turbulence evenly spread, like crinkly mountains that extend as far as the eye can see (see diagram). "It's a different kind of physics," says Chapman.

What's more, that crinkliness is constant, no matter how much you zoom in or out on a patch of wind, making its behaviour fractal (The Astrophysical Journal Letters, doi.org/skf). Snowflakes, shorelines and most recently black holes (see "Turbulent black holes grow fractal skins as they feed") also exhibit such fractal behaviour.

The result may help to control nuclear fusion reactors. These create energy in the same way as the sun, by fusing a superheated plasma of hydrogen nuclei to form helium.

One problem with optimising their energy output is deducing what is going on inside them – inserting a probe isn't an option as it would melt. Enter the solar wind. Though less dense and cooler than the hydrogen of a fusion reactor, the wind is a plasma – and can be probed thanks to STEREO. "The great thing about solar wind turbulence is that the satellites sit right inside, so it can be observed in exquisite detail," says Steve Cowley of the Culham Centre for Fusion Energy, UK.

By adding the fractal behaviour to their plasma models, fusion scientists may be able to control turbulence, which can cause plasma to escape the magnetic field containing it in the reactor. They may also be able to use turbulence to disrupt high energy plasma blobs that can rip holes in the reactor. "These results look very promising," says Todd Evans of nuclear energy firm General Atomics in San Diego, California.

This article appeared in print under the headline "Sunny surprise for fusion reactors"

 

[Hawaiian Punch]

Sun's fractal surprise could help fusion on Earth

• 01 May 2014 by Nicola Jenner
• Magazine issue 2967. Subscribe and save
• For similar stories, visit the Solar System , Energy and Fuels and The Nuclear Age Topic Guides

THE sun has thrown us a fractal surprise. An unexpected pattern has been glimpsed in the solar wind, the turbulent plasma of charged particles that streams from the sun. It offers clues for handling plasmas that roil inside nuclear fusion reactors on Earth.

Composed of charged particles such as protons and electrons, the solar wind streams from the sun and pervades the solar system. Its flow is turbulent, containing eddies and moving at different speeds in different directions. It was thought that this turbulence was similar to that in a fluid, behaving like mixing ocean currents or the air flows that make aeroplane flights bumpy.

Now, Sandra Chapman of the University of Warwick, UK, and her colleagues have examined the solar wind's behaviour using NASA's twin STEREO spacecraft

. One flies just within Earth's orbit around the sun, the other just outside it, allowing the pair to obtain unique measurements of solar wind behaviour.

STEREO revealed that when the movement of the wind's particles is perpendicular to the sun's magnetic field, they resemble a fluid, with sections that are smooth, interrupted by bursts of violence. "If you look out of a plane window you see mountain ranges and then long rolling plains. This is what the perpendicular fluid turbulence is like," says Chapman.

But when the particles move in parallel with the field lines, they behave very differently, with the turbulence evenly spread, like crinkly mountains that extend as far as the eye can see (see diagram). "It's a different kind of physics," says Chapman.

What's more, that crinkliness is constant, no matter how much you zoom in or out on a patch of wind, making its behaviour fractal (The Astrophysical Journal Letters, doi.org/skf). Snowflakes, shorelines and most recently black holes (see "Turbulent black holes grow fractal skins as they feed") also exhibit such fractal behaviour.

The result may help to control nuclear fusion reactors. These create energy in the same way as the sun, by fusing a superheated plasma of hydrogen nuclei to form helium.

One problem with optimising their energy output is deducing what is going on inside them – inserting a probe isn't an option as it would melt. Enter the solar wind. Though less dense and cooler than the hydrogen of a fusion reactor, the wind is a plasma – and can be probed thanks to STEREO. "The great thing about solar wind turbulence is that the satellites sit right inside, so it can be observed in exquisite detail," says Steve Cowley of the Culham Centre for Fusion Energy, UK.

By adding the fractal behaviour to their plasma models, fusion scientists may be able to control turbulence, which can cause plasma to escape the magnetic field containing it in the reactor. They may also be able to use turbulence to disrupt high energy plasma blobs that can rip holes in the reactor. "These results look very promising," says Todd Evans of nuclear energy firm General Atomics in San Diego, California.

This article appeared in print under the headline "Sunny surprise for fusion reactors"

And for those that don't know fractal geometry is based on power law


Now does this begin to change your earlier view of this being nothing more than 'human predilection of pattern finding'?