# Hello, welcome to Science Docs!

À force de croire en ses rêves, l’homme en fait une réalité.

Hergé

**Science Docs** is a collection of projects, tutorials, reports and study notes that are the product of most of my passion that I have for life, Universe and everything else. They are aimed for explorers and experimenters who are willing to study scientific or engineering subjects with what Richard Feynman called *the pleasure of finding things out*. Many of the materials here are related to my PhD work and I have hope that by sharing them you might find pursuing science fascinating! I have a dream that the PDFs will now enrich your journey through learning and discovery.

I ought to make one more note here: this site is always alive. The PDFs and the associated repositories get updated from time to time. Even though a PDF is completed, it does not mean that its content will not change in the future. Any corrections or update proposals are welcome.

# The linear algebra of Principal Component Analysis (with Python examples)

These are notes on linear algebra aspects of **Principal Component Analysis** with a little bit more insight then you would typically get when reading about PCA from online tutorials. The notes are accompanied by several Python computational examples.

^{This work has been produced during my PhD at Université libre de Bruxelles.}

# Objectif Morse

Did you ever wonder what if there were two computers talking to each other using Morse code? One would send a message with light signals and the other would collect the light and understand the message? No cable connecting the computers. The information simply carried by light that travels through the air.

Well, here it is! In the **Objectif Morse** project you will make an interesting use of Arduino, electronic circuits and C++ while transmitting messages in Morse alphabet between computers.

^{This work has been produced as part of the Arduino Study Group meetings at the Jagiellonian University.}

# POD and DMD decomposition of numerical and experimental data

Using two data decomposition methods: **Proper Orthogonal Decomposition** and **Dynamic Mode Decomposition**, as well as concepts from linear algebra and dynamical systems within Matlab scripts, I searched for low-rank structures in the pulsating Poiseuille flow and in the velocity field of the flow behind a cylinder.

^{This work has been produced as part of the Short Training Programme at the von Karman Institute for Fluid Dynamics.}

# Proof of associative law for matrices

I was reviewing the amazing MIT course on linear algebra. When the associative law appeared on the blackboard, Professor Gilbert Strang said: *It’s not that easy to prove that this is correct. You have to go into the gory details of matrix multiplication, do it both ways and see that you come out the same.*

So I said: *let’s do it!*

# Notes on Gaussian Process Regression

Following a great lecture by Professor Anna Scaife I decided to reproduce her figures and write a small note on Gaussian Process Regression (GPR).

^{This work has been produced during my PhD at Université libre de Bruxelles.}

## Under construction

# Notes on Dynamic Mode Decomposition

These are notes on **Dynamic Mode Decomposition** (DMD), a data-driven method for finding low-rank structures in high-dimensional data sets. These notes come mainly from two lectures by Prof. Nathan Kutz from the University of Washington but also from other sources and my own previous study of DMD.

^{This work has been produced during my PhD at Université libre de Bruxelles.}
^{This PDF is still under construction…}

# Fluid Toolbox

**Fluid Toolbox** is a collection of human-readable, pseudo-random study notes. It contains descriptions and explanations of fluid mechanics concepts, presented in a way that resembles the record of my understanding of them. It is meant to be used complimentary to the regular textbook since it may provide additional insight but it will not substitute thoroughness of a standard course in the subject. I believe that working side by side with a course it can become indeed a useful toolbox of concepts that are ready-to-use and ready-to-understand.

^{This PDF is still under construction…}

# Computational examples in transport phenomena with Python

I collected few interesting computational examples in transport phenomena in a form of a tutorial and created a set of Python codes to accompany a better understanding of the results.

This tutorial has been produced after taking two wonderful courses offered by Delft University: *The Basics of Transport Phenomena* and *Advanced Transport Phenomena*.

^{This PDF is still under construction…}

## A (bit) less scientific section

# Making-of: watercolour Christmas gifts

Let’s paint watercolour Christmas gifts!

# Thought process in watercolours

In this document I show how I apply the thought process to improve my watercolour paintings.

# Cooking water

This small home experiment is for deriving the temperature vs. time curve for cooking water on three types of stoves: electrical, induction and gas.

# About me

Hi, I’m Kamila and I’m currently working as a PhD researcher at Université libre de Bruxelles and The University of Utah in the field that connects combustion, fluid dynamics and data science.

Since childhood, I loved science and enjoyed inventing my own ways of explaining and understanding things. **Science Docs** is pretty much an aftermath of that, a site that I always wanted to create.

When it comes to learning, I believe in the quote of Einstein: *you do not really understand something unless you can explain it to your grandmother*. My aim is to implement that level of understanding into the documents I write (although many times I will assume certain prerequisites that your grandmother should have). But of course, if you wish to profit from the materials presented here, you will need to incorporate them in your journey, make it *your way*. Experiment, sniff around and make many mistakes as you go - or as Richard Feynman said: *study hard what interests you the most in the most undisciplined, irreverent and original manner possible*. I have hopes that you will find doing science fascinating, rewarding and inspiring!

If you wish to contact me via mail, feel free to drop me a line at: `kamilazdybal@gmail.com`

(personal mail) or `kamila.zdybal@ulb.be`

(university mail).