47 lines
1.6 KiB
Markdown
47 lines
1.6 KiB
Markdown
---
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title: "Math"
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description: "Math typesetting examples."
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lead: "Math typesetting examples."
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date: 2021-03-16T10:46:05+01:00
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lastmod: 2021-03-16T10:46:05+01:00
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draft: false
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images: []
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menu:
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docs:
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parent: "examples"
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weight: 210
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toc: true
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---
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[KaTeX](https://katex.org/) is switched off by default. Enable it by setting `kaTex = true` in the `[options]` section of `./config/_default/params.toml`.
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## Example 1
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_Excerpt taken from [Supernova Neutrinos](https://neutrino.leima.is/book/introduction/supernova-neutrinos/)_
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### Markdown
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```md
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The average energy of the neutrinos $\langle E \rangle$ emitted during a supernova explosion is of the order of 10MeV, and the neutrino luminosity at the early epoch of the explosion is approximately $10^{52}\mathrm{ergs\cdot s^{-1}}$.
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Therefore, the number density of the neutrinos at the radius $R$ is
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$$
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\begin{equation*}
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n \sim 10^{18} \mathrm{cm^{-3}} \left(\frac{100\mathrm{km}}{R}\right)^2 \left(\frac{10\mathrm{MeV}}{\langle E \rangle}\right).
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\end{equation*}
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$$
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```
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### HTML
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The average energy of the neutrinos $\langle E \rangle$ emitted during a supernova explosion is of the order of 10MeV, and the neutrino luminosity at the early epoch of the explosion is approximately $10^{52}\mathrm{ergs\cdot s^{-1}}$.
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Therefore, the number density of the neutrinos at the radius $R$ is
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$$
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\begin{equation*}
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n \sim 10^{18} \mathrm{cm^{-3}} \left(\frac{100\mathrm{km}}{R}\right)^2 \left(\frac{10\mathrm{MeV}}{\langle E \rangle}\right).
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\end{equation*}
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$$
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It turns out that the ambient dense neutrino medium has a significant impact on neutrino oscillations, which has been intensely investigated in the last decade.
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