Loops Near the surface. Lumped Together in Space.

There was a time, when most articles here looked like lab reports or chapters of a thesis. Occasionally, there was a weird poem thrown in.

Now is the time for art only, and the thesis-like postings provide for raw material. Temperature waves beneath the ground, driven by the oscillation of the temperature on the surface … reloaded, after 6 years. I am combining …

… now in a single three-dimensional plot.

loops near the surface
lumped together in space
a bit of a misnomer

the violent past of the primordial earth
celestial objects colliding with each other
replenished by radioactive decay

a lump of heat
will slowly evolve with time
the boundary of the interesting part of space

temperature moves from the surface to
every textbook of geothermal energy
when the wave has ‘run out’

flow just adds a small distortion
Now varying time instead of space
but also in undisturbed ground

The lag derived from the figure is
some ‘motivation’
space slowly peters out

energy would be created from ‘nothing’
Without sources or sinks

I hinted at this
a vast area of ground
describes the real world

flow just adds a small distortion
Now varying time instead of space
but also in undisturbed ground

a legitimate choice
thanks to linearity
we guess at the solution

Would it be a real
square root of the complex number

temperature increasing to infinity
The thing in the exponent
does not depend on
The wave (any wave)

Note one thing though
time is also a trivial solution
thus no flow from beneath

an amendment to the boundary
would be exactly the same
in my favorite German physics book

Images created with SageMath and custom code; as usual I am stacking parametric curves onto each other: Sets of the sinusoidal waves, repeating themselves year after year, and sets of the exponential spatial change of temperature at a certain point of time. Moving deeper into the earth, the amplitudes become smaller, and there is a time lag until maxima appear.

The boundary conditions are the oscillation imprinted on the surface by solar energy on the one hand, and a constant temperature at ‘infinite’ distance beneath ground level on the other hand (the constant flow of true geothermal energy – the remnants of the ‘violent past of the primordial earth’ –  is not considered here; see the thesis post for more details.). Colors selected for aesthetics, not for educational purpose. No captions, axes, legends etc. for the same reason.


I am again adding my silly version of a donate button. If this was a book, and I would donate all profits. If you have ever found my articles useful, interesting, entertaining, if they have helped you with solving a technical issue, building your CAN bus logger or even your solar/air/ice heat pump system, hacking Public Key Infrastructure, learning about Statistical Mechanics or simulations, or if you enjoyed looking at my visual art in times of panic, or getting into panic because of my strange poetry … please consider donating to your favorite project or charity that supports Ukraine and Ukrainian refugees now. I trust in you and I hope you do – so I will keep blogging and creating!

Edit: I am recommending the Austrian project Cards-for-Ukraine.


4 Comments Add yours

  1. Beautiful. You have subverted the common notion that math is purely objective with the beauty of this post and the political call to action.

    1. elkement says:

      Thanks, Michelle – maybe is has been an act of despair. I have been thinking what I could do (in addition to just donating in silence).

      1. There will be a lot to do over a long period of time, including rebuilding the region and the people after dangers are over. We will find ways.

        1. elkement says:

          Absolutely! I’ve also been thinking about how prepper-y engineering skills might be helpful there, in the future :-)

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