47 lines
1.6 KiB
Markdown
47 lines
1.6 KiB
Markdown
|
---
|
||
|
|
title: "Math"
|
||
|
|
description: "Math typesetting examples."
|
||
|
|
lead: "Math typesetting examples."
|
||
|
|
date: 2021-03-16T10:46:05+01:00
|
||
|
|
lastmod: 2021-03-16T10:46:05+01:00
|
||
|
|
draft: false
|
||
|
|
images: []
|
||
|
|
menu:
|
||
|
|
docs:
|
||
|
|
parent: "examples"
|
||
|
|
weight: 210
|
||
|
|
toc: true
|
||
|
|
---
|
||
|
|
|
||
|
|
[KaTeX](https://katex.org/) is switched off by default. Enable it by setting `kaTex = true` in the `[options]` section of `./config/_default/params.toml`.
|
||
|
|
|
||
|
|
## Example 1
|
||
|
|
|
||
|
|
_Excerpt taken from [Supernova Neutrinos](https://neutrino.leima.is/book/introduction/supernova-neutrinos/)_
|
||
|
|
|
||
|
|
### Markdown
|
||
|
|
|
||
|
|
```md
|
||
|
|
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 $10^{52}\mathrm{ergs\cdot s^{-1}}$.
|
||
|
|
Therefore, the number density of the neutrinos at the radius $R$ is
|
||
|
|
|
||
|
|
$$
|
||
|
|
\begin{equation*}
|
||
|
|
n \sim 10^{18} \mathrm{cm^{-3}} \left(\frac{100\mathrm{km}}{R}\right)^2 \left(\frac{10\mathrm{MeV}}{\langle E \rangle}\right).
|
||
|
|
\end{equation*}
|
||
|
|
$$
|
||
|
|
```
|
||
|
|
|
||
|
|
### HTML
|
||
|
|
|
||
|
|
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 $10^{52}\mathrm{ergs\cdot s^{-1}}$.
|
||
|
|
Therefore, the number density of the neutrinos at the radius $R$ is
|
||
|
|
|
||
|
|
$$
|
||
|
|
\begin{equation*}
|
||
|
|
n \sim 10^{18} \mathrm{cm^{-3}} \left(\frac{100\mathrm{km}}{R}\right)^2 \left(\frac{10\mathrm{MeV}}{\langle E \rangle}\right).
|
||
|
|
\end{equation*}
|
||
|
|
$$
|
||
|
|
|
||
|
|
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.
|