One big advantage over FreeFem is that it uses plain old Python to describe the problems instead of a domain-specific language. Matplotlib is used for plotting by default, so we get full Python power out of the box!
Also uses variational formulation of a partial differential equation like FreeFem which is a pain.
One downside is that its documentation is a Springer published PDF link.springer.com/content/pdf/10.1007%2F978-3-319-52462-7.pdf which is several years out-of-date (tested with FEnics 2016.2. Newbs. This causes problems e.g.: stackoverflow.com/questions/53730427/fenics-did-not-show-figure-nameerror-name-interactive-is-not-defined/57390687#57390687
system of partial differential equations are mentioned at: link.springer.com/content/pdf/10.1007%2F978-3-319-52462-7.pdf 3.5 "A system of advection–diffusion–reaction equations". You don't need to manually iterate between the equations.
On Ubuntu 20.04 as per fenicsproject.org/download/Before 2020-06, it was failing with:but they seem to have created the Ubuntu 20.04 package as of 2020-06, so it now worked! askubuntu.com/questions/866901/what-can-i-do-if-a-repository-ppa-does-not-have-a-release-file
sudo apt-get install software-properties-common
sudo add-apt-repository ppa:fenics-packages/fenics
sudo apt-get update
sudo apt-get install --no-install-recommends fenics
sudo apt install fenics
python3 -m pip install -u matplotlibE: The repository 'http://ppa.launchpad.net/fenics-packages/fenics/ubuntu focal Release' does not have a Release file.TODO heat equation hello world.
These are the rules which specify what different concurrent read/write memory accesses from different threads/processes can or cannot see.
Notable such set of rules include:
- C++ memory model. These are also reflected on the semantics of memory of the corresponding instruction set architecture
- SQL transaction isolation level
Piezoelectric, and notably used in quartz clock.
In this section we will gather some more advanced ideas besides the basic features described at how the website works.
This is a good project. Limited scope to 2D card-like games, but very good within that scope.
Ciro Santilli used it for the 2D version of his Ciro's 2D reinforcement learning games.
Most promising approaches as of 2020:
Why Private Billions Are Flowing Into Fusion by Bloomberg (2022)
Source. - Joint European Torus
- General Fusion: compress with liquid metal. Intends to demo in JET site.
- Helion Energy: direct fusion to electricity conversion without steam, direct from magnetic field movements
- First Light: shoot microscopic objct at a target to crush it so much that fusion happens
A weapons-grade ring of electrorefined plutonium, typical of the rings refined at Los Alamos and sent to Rocky Flats for fabrication
. Source. The ring has a purity of 99.96%, weighs 5.3 kg, and is approx 11 cm in diameter. It is enough plutonium for one bomb core. Which city shall we blow up today?
Ciro Santilli is mildly obsessed by nuclear reactions, because they are so quirky. How can a little ball destroy a city? How can putting too much of it together produce criticality and kill people like in the Slotin accident or the Tokaimura criticality accident. It is mind blowing really.
More fun nuclear stuff to watch:
- Dr. Strangelove (1964)
- en.wikipedia.org/wiki/Chernobyl_(miniseries)
- The World Of Enrico Fermi by Harvard Project Physics (1970)
- Fat Man and Little Boy (1987) shows a possibly reasonably realistic of the history of the development of the Trinity
The Ultimate Guide to Nuclear Weapons by hypohystericalhistory (2022)
Source. Good overall summary. Some interesting points:- youtu.be/8uIPQBOCJ64?t=2946 talks about the difference between tactical and strategic nuclear weapons
- youtu.be/8uIPQBOCJ64?t=3291 mentions variable yield devices, this is the main new thing Ciro Santilli learned from this video
- youtu.be/8uIPQBOCJ64?t=3416 discusses if a strategic nuclear weapon usage would inevitably lead to tactical nuclear weapon escalation. It then mentions one case in which a possibly comparable escalation didn't happen: the abstinence of using chemical weapon during World War II.
Project to explain each Nobel Prize better by 
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01
Ciro Santilli 35 Updated 2025-01-10 +Created 1970-01-01Understand and explain amazingly every single Nobel Prize in physics, chemistry and biology. Since in particular the Nobel Foundation is unable to do that for any at all, especially of the key old ones, e.g. www.nobelprize.org/prizes/physics/1965/summary/. Hopeless.
To be fair, those in theoretical physics at least basically come down to reading a bunch of books. But perhaps anything slightly more experimental could have
In the context of wave-like equations, an open-boundary condition is one that "lets the wave go through without reflection".
This condition is very useful when we want to simulate infinite domains with a numerical method. Ciro Santilli wants to do this all the time when trying to come up with demos for his physics writings.
Here are some resources that cover such boundary conditions:
- www.asc.tuwien.ac.at/~arnold/pdf/graz/graz.pdf lots of slides
- hplgit.github.io/wavebc/doc/pub/._wavebc_cyborg002.html mentions them and gives a 1D formula. It mentions that things get complicated in 2D and 3D TODO why.The other page: hplgit.github.io/wavebc/doc/pub/._wavebc_cyborg003.html shows solution demos.
Members of the orthogonal group.
Linear map of two variables.
More formally, given 3 vector spaces X, Y, Z over a single field, a bilinear map is a function from:that is linear on the first two arguments from X and Y, i.e.:Note that the definition only makes sense if all three vector spaces are over the same field, because linearity can mix up each of them.
The most important example by far is the dot product from , which is more specifically also a symmetric bilinear form.
For an example with context, have a look at E. Coli K-12 MG1655 and the second protein of the genome, e. Coli K-12 MG1655 gene thrA.
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