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Unified all previous electro-magnetism theories into one equation.
Explains the propagation of light as a wave, and matches the previously known relationship between the speed of light and electromagnetic constants.
The equations are a limit case of the more complete quantum electrodynamics, and unlike that more general theory account for the quantization of photon.
The equations are a system of partial differential equation.
The system consists of 6 unknown functions that map 4 variables: time t and the x, y and z positions in space, to a real number:and two known input functions:
- , , : directions of the electric field
- , , : directions of the magnetic field
- : density of charges in space
- : current vector in space. This represents the strength of moving charges in space.
Due to the conservation of charge however, those input functions have the following restriction:
Equation 1.
Charge conservation
. Also consider the following cases:
- if a spherical charge is moving, then this of course means that is changing with time, and at the same time that a current exists
- in an ideal infinite cylindrical wire however, we can have constant in the wire, but there can still be a current because those charges are movingSuch infinite cylindrical wire is of course an ideal case, but one which is a good approximation to the huge number of electrons that travel in a actual wire.
The goal of finding and is that those fields allow us to determine the force that gets applied to a charge via the Equation "Lorentz force", and then to find the force we just need to integrate over the entire body.
Finally, now that we have defined all terms involved in the Maxwell equations, let's see the equations:
Equation 2.
Gauss' law
. Equation 3.
Gauss's law for magnetism
. Equation 4.
Faraday's law
. Equation 5.
Ampere's circuital law
. You should also review the intuitive interpretation of divergence and curl.
Why is COVID-19 so serious in some people but not in others? by 
Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01
Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01There are a few possibilities:
- genetics
- bibliography:
- www.science.org/doi/10.1126/scitranslmed.abj7521 Identification of driver genes for critical forms of COVID-19 in a deeply phenotyped young patient cohort by Carapito et al. (2021)
- bibliography:
- state of the immune system based on disease history
- age
So, it turns out that Wikipedia does have a (ultra obscure as usual) mechanism for pull requests. You learn a new one every day.
Wilkinson Microwave Anisotropy Probe by Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01
Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01
A collection of closely related and curated C. elegans datasets.
64 bits is still too much address for current RAM sizes, so most architectures will use less bits.
x86_64 uses 48 bits (256 TiB), and legacy mode's PAE already allows 52-bit addresses (4 PiB). 56-bits is a likely future candidate.
12 of those 48 bits are already reserved for the offset, which leaves 36 bits.
If a 2 level approach is taken, the best split would be two 18 bit levels.
But that would mean that the page directory would have
2^18 = 256K entries, which would take too much RAM: close to a single-level paging for 32 bit architectures!Therefore, 64 bit architectures create even further page levels, commonly 3 or 4.
x86_64 uses 4 levels in a
9 | 9 | 9 | 9 scheme, so that the upper level only takes up only 2^9 higher level entries.The 48 bits are split equally into two disjoint parts:
----------------- FFFFFFFF FFFFFFFF
Top half
----------------- FFFF8000 00000000
Not addressable
----------------- 00007FFF FFFFFFFF
Bottom half
----------------- 00000000 00000000A 5-level scheme is emerging in 2016: software.intel.com/sites/default/files/managed/2b/80/5-level_paging_white_paper.pdf which allows 52-bit addresses with 4k pagetables.
Using the TLB makes translation faster, because the initial translation takes one access _per TLB level_, which means 2 on a simple 32 bit scheme, but 3 or 4 on 64 bit architectures.
The TLB is usually implemented as an expensive type of RAM called content-addressable memory (CAM). CAM implements an associative map on hardware, that is, a structure that given a key (linear address), retrieves a value.
Mappings could also be implemented on RAM addresses, but CAM mappings may required much less entries than a RAM mapping.
For example, a map in which:could be stored in a TLB with 4 entries:
- both keys and values have 20 bits (the case of a simple paging schemes)
- at most 4 values need to be stored at each time
linear physical
------ --------
00000 00001
00001 00010
00010 00011
FFFFF 00000However, to implement this with RAM, _it would be necessary to have 2^20 addresses_:which would be even more expensive than using a TLB.
linear physical
------ --------
00000 00001
00001 00010
00010 00011
... (from 00011 to FFFFE)
FFFFF 00000 Multiple addresses translate to a single physical address by Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01
Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01The same linear address can translate to different physical addresses for different processes, depending only on the value inside
cr3.Both linear addresses
00002 000 from process 1 and 00004 000 from process 2 point to the same physical address 00003 000. This is completely allowed by the hardware, and it is up to the operating system to handle such cases.This often in normal operation because of Copy-on-write (COW), which be explained elsewhere.
Such mappings are sometime called "aliases".
Subset of Galilean transformation with speed equals 0.
This is a good company, first they truly helped reduce international transfer fees. They they continued to morph into a decent challenger bank.
Their Wise Interest account was amazing as of late 2023: wise.com/gb/interest/
Instant access with representative national interests and 0.29% fees.
Brick and mortar banks were way way behind in that regard!
E.g. October 2023, Wise was doing 4.87% interest after fees, while Barclay's best option was 1.16% above 5k pounds on the Rainy Day Saver (5% below). Ridiculous!
Update: On November 2023 unfortunately they more than doubled their fees from 0.19% to 0.46%:but it still was a good option to keep cash in.
Structure of Some Crystalline Lysozyme-Inhibitor Complexes Determined by X-Ray Analysis At 6 Å Resolution (1965) by Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01
Ciro Santilli 35 Updated 2024-12-23 +Created 1970-01-01www.nature.com/articles/206761a0 on Nature 206, 761-763. Paywalled as of 2022. Has some nice pictures in it.
Pinned article: ourbigbook/introduction-to-the-ourbigbook-project
Welcome to the OurBigBook Project! Our goal is to create the perfect publishing platform for STEM subjects, and get university-level students to write the best free STEM tutorials ever.
Everyone is welcome to create an account and play with the site: ourbigbook.com/go/register. We belive that students themselves can write amazing tutorials, but teachers are welcome too. You can write about anything you want, it doesn't have to be STEM or even educational. Silly test content is very welcome and you won't be penalized in any way. Just keep it legal!
We have two killer features:
- topics: topics group articles by different users with the same title, e.g. here is the topic for the "Fundamental Theorem of Calculus" ourbigbook.com/go/topic/fundamental-theorem-of-calculusArticles of different users are sorted by upvote within each article page. This feature is a bit like:
- a Wikipedia where each user can have their own version of each article
- a Q&A website like Stack Overflow, where multiple people can give their views on a given topic, and the best ones are sorted by upvote. Except you don't need to wait for someone to ask first, and any topic goes, no matter how narrow or broad
This feature makes it possible for readers to find better explanations of any topic created by other writers. And it allows writers to create an explanation in a place that readers might actually find it.
Figure 1. Screenshot of the "Derivative" topic page. View it live at: ourbigbook.com/go/topic/derivative - local editing: you can store all your personal knowledge base content locally in a plaintext markup format that can be edited locally and published either:This way you can be sure that even if OurBigBook.com were to go down one day (which we have no plans to do as it is quite cheap to host!), your content will still be perfectly readable as a static site.
- to OurBigBook.com to get awesome multi-user features like topics and likes
- as HTML files to a static website, which you can host yourself for free on many external providers like GitHub Pages, and remain in full control
Figure 2. You can publish local OurBigBook lightweight markup files to either OurBigBook.com or as a static website.
Figure 3. Visual Studio Code extension installation.
Figure 4. Visual Studio Code extension tree navigation.
Figure 5. . You can also edit articles on the Web editor without installing anything locally. Video 3. Edit locally and publish demo. Source. This shows editing OurBigBook Markup and publishing it using the Visual Studio Code extension.Video 4. OurBigBook Visual Studio Code extension editing and navigation demo. Source. - Internal cross file references done right:
- Infinitely deep tables of contents:
Figure 6. Dynamic article tree with infinitely deep table of contents.Live URL: ourbigbook.com/cirosantilli/chordateDescendant pages can also show up as toplevel e.g.: ourbigbook.com/cirosantilli/chordate-subclade
All our software is open source and hosted at: github.com/ourbigbook/ourbigbook
Further documentation can be found at: docs.ourbigbook.com
Feel free to reach our to us for any help or suggestions: docs.ourbigbook.com/#contact