I’m currently doing my master in physics. I need this for my thesis.

This is my very first post, I wouldn’t ask for help if I wasn’t hopeless (I’m not native in English). I apologize beborehand if I commit mistakes presenting this issue. The folowing is my prompt:

(paper DOI: 10.1049/iet-smt.2017.0221)

```
`I have twelve equations related to the ion mobility spectrum.`
`I need assistance in reading and interpreting these equations. Once the equations are identified, I would like to use the "Wolfram" plugin to analyze these equations and translate them into executable code. The end goal is to generate a graph that depicts the ion mobility spectrum. Could you provide a detailed, step-by-step walk-through of this process, including the developed code?`
`{Equations:`
`1-. $ I =`
```

`\begin{cases}`

```
`\frac{2\pi e n_0 \mu L U}{\ln(r_2/r_1)}, & U < U_0 \\`
`e n_0 \pi(r^2_2 - r^2_1)u_0, & U \geq U_0`
```

`\end{cases} $`

```
`2-. $ \mu = \frac{u_0( r^2_2 - r^2_1 )\ln(r_2/r_1)}{2LU} $`
`3-. $ I =`
```

`\begin{cases}`

```
`\sum_{i=1}^N \frac{2 \pi e n_i \mu_i L U}{\ln \left( r_2/r_1 \right)}, & m=0 \\`
`\sum_{i=1}^m e n_i \pi\left( r_2^2 - r_1^2 \right) u_0 + \sum_{i=m+1}^N \frac{2 \pi e n_i \mu_i L U}{\ln \left( r_2/r_1 \right)}, & m=1,2,3, \ldots, N`
```

`\end{cases} $`

```
`4-. $ n_m = \frac{\sum_{i=m}^N n_i \mu_i - \sum_{i=m+1}^N n_i \mu_i}{\mu_m} $`
`5-. $ \mu_m = \frac{u_0( r^2_2 - r^2_1 )\ln(r_2/r_1)}{2LU_m} $`
`6-. $ n_m =`
```

`\begin{cases}`

```
`\frac{\ln{r_2/r_1}}{2\pi e L}\frac{\Delta I /\Delta U \left|_{U_{m-1} \leq U \leq U_m} \right. - \Delta I /\Delta U \left|_{U_m \leq U \leq U_{m+1}} \right.}{\mu_m}, & m=1,2,3, \ldots, N-1 \\`
`\frac{\ln{r_2/r_1}}{2\pi e L}\frac{\Delta I /\Delta U \left|_{U_{m-1} \leq U \leq U_m} \right.}{\mu_m}, & m=N`
```

`\end{cases} $`

```
`7-. $ n_m =`
```

`\begin{cases}`

```
`\frac{U_m}{e u_0 \pi\left(r_2^2-r_1^2\right)}\left(\left.\frac{\Delta I}{\Delta U}\right|_{U_{m-1} \leq U \leq U_m}-\left.\frac{\Delta I}{\Delta U}\right|_{U_m \leq U \leq U_{m+1}}\right)\!\!, & m=1,2,3, \ldots, N-1 \\`
`\left.\frac{U_m}{e u_0 \pi\left(r_2^2-r_1^2\right)} \frac{\Delta I}{\Delta U}\right|_{U_{m-1} \leq U \leq U_m}, & m=N`
```

`\end{cases} $`

```
`8-. $ \mu_{\text {ave}} = \frac{\sum_{i=1}^N n_i \mu_i}{\sum_{i=1}^N n_i} $`
`9-. $ \mu_\mathrm{ave} = \frac{u_0\left( r_2^2 - r_1^2 \right) \ln(r_2/r_1)}{2L} \frac{\Delta I /\left.\!\! \Delta U\right|_{U_0 \leq U \leq U_1}}{I_N} $`
`10-. $ U_\mathrm{sat} = \frac{I_N}{\Delta I /\left.\!\! \Delta U\right|_{U_0 \leq U \leq U_1}} $`
`11-. $ U_\mathrm{sat} = \frac{\sum_{i=1}^N I_i}{\sum_{i=1}^N I_i/U_{0i}} $`
`12-. $ \mu_\mathrm{ave} = \frac{u_0\left( r_2^2 - r_1^2 \right) \ln(r_2/r_1)}{2LU_\mathrm{sat}} $`
`}`
`This equations are precisely for that, finding number densities $n_i$ and mobilities $μ_i$ given data of Voltaje vs Current curves measured with a Gerdien condenser. I have my own data and I need the code to compute it.`
`Please obtain the context you need from this PDF doc_id: "9e8c573e-3a21-49e6-8276-7b6d5ffd30df"`
```

It simple gets nowhere no matter how I present the issue. Thank you so much for your help!