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====== Simulations in the Natural Sciences II ======                                                                              
{{combined.jpg?800x100|}}                                                                                                                            
                                                                                                                                                           
**ESC202:**Spring 2020: Monday Lecture: 13:00-14:00 Exercises: 14:00-17:00 in **Room 36 J 33**

**TAs**: Stefan Schafroth (**schafrot@physik.uzh.ch**)

===== Corona Virus Measures =====
**
Dear Students,

I would like to keep the class going over the next few weeks. In order to adapt I will provide a video lecture from the 23. March onwards until lectures can take place again. Communication will take place via this web-site regarding all assignments as well. As the announcement about the closure of lectures was made on 13. March, it was not possible to provide a video lecture for the 16. March. I will however upload lecture notes for 16. March (today) and I ask you to complete the tree-code based simulation of the planetesimals orbiting the Sun. I hope that we can resume class meetings during the final 1/3 of the semester during the "project phase" of the course. Many thanks for your understanding!
**

Joachim Stadel
----
===== Video Lectures =====

Videos for the lectures can be found here (they are too large for my Wiki):

[[http://www.ics.uzh.ch/~stadel/krone/public_downloads/esc202|ESC202 Video downloads]]


====== Lectures ======

17. Feb. 2020: {{ :spin:sins2-01.pdf |Tree Structures and Dimensional Searching}}

2. Mar. 2020: {{ :spin:sins2-03.pdf |Gravity Tree Walk}}

16./23. Mar. 2020: {{ :spin:sins2-04.pdf |Introduction to SPH}} (Videos sph1.mp4 and sph2.mp4 **see above link**)

30. Mar. 2020: {{ :spin:sins2-05.pdf |SPH Continued}} (Videos sph3.mp4 and sph4.mp4 **see above link**)

6. Apr. 2020: {{ :spin:sins2-06.pdf |SPH Continued}} (Video sph5.mp4  **see above link**)

20. Apr. 2020: {{ :spin:sins2-07.pdf |2-d Ising Model}} (Video ising.mp4  **see above link**)

27. Apr. 2020: {{ :spin:sins2-08.pdf |2-d Traveling salesman problem}} (Video tsp.mp4  **see above link**)

3. May 2020: **Start of group projects!**
====== Assignments ======

Should be handed in every **Sunday night by 21:00** following the Monday lecture.
Assignments should be **individual** and should be in python and **provide a 
correct virtual environment!**

For help getting started with virtual environments, please read carefully [[https://towardsdatascience.com/all-you-need-to-know-about-python-virtual-environments-9b4aae690f97|Python Virtual Environments for Pip]] and [[https://uoa-eresearch.github.io/eresearch-cookbook/recipe/2014/11/20/conda/|Python Virtual Environments for Conda]].

You should email 3 things to Stefan (**schafrot@physik.uzh.ch**):

  - The working **python source code**
  - The **requirements.txt** file for your virtual environment
  - A **.pdf** or **.png** image or animation of the output of your program

Template: {{template.zip}}

** Instructions: **

Please add the names of the people you work together (if you do) to the comment section of your python scripts.

Create a virtual environment using
    
Pip
    
- run **virtualenv yourenv_name** to create a virtual environment

- run **source yourenv_name/bin/activate** to activate yourenv_name

- install necessary libraries that you want using **pip install package_name**

- work in that directory, get your outputs (*.pdf, *.png, *jpeg, *.mp4, etc...)

- run **pip freeze > requirements.txt** to get your list of libraries
      
Conda

- run **conda create -n yourenvname python=x.x anaconda** to create a virtual environment

- run **source activate yourenvname** to activate yourenv_name

- install necessary libraries that you want using **conda install -n yourenv_name package_name**

- work in that directory, get your outputs (*.pdf, *.png, *jpeg, *.mp4, etc...)

- run **conda list --export > requirements.txt** to get your list of libraries

====== List of assignments ======

1.k-Nearest Neighbors algorithm (you can set k=8 or other values to test). You should check the code via direct computation (O(N^2)). Solution is expected to include a priority queue over the 8 NN particles, but could also explore the use of a further prioq over the nearest cells during the treewalk as discussed in the lecture.

2.  **Extended to Sunday 22.03.2020**: Gravity simulation using 2-D trees. Implement a 2-D gravity tree-code to solve the forces between the 12'095 planetesimals in the early solar system. While the data structure is 2-D, the forces and motions are actually 3-D. The data file below contains the planetesimals in the following format (one per line):
<x y z vx vy vz m r> in unit of AU, AU/day, solar mass and AU. Recall these are the same units used in the ESC201 course for the solar system simulations. You will have to use the Gaussian gravitational constant k^2 instead of G.

{{ :spin:esc202-planetesimals.zip | esc202-planetesimals data file}}

3. **SPH Density calculation using Kernel**: You can use the data set from your planetesimals simulations to calculate the densities and make nice color density plots of the planetesimal disk. **As discussed in the Zoom meeting:** you should try to put uniform randomly distributed particles in a box from [0,1)x[0,1) (2-D) and calculate the density. You should see a bias that the density is too low at the edges. If you do this with a correctly working working periodic boundary condition density code you should no longer see this bias. Please think about how to efficiently calculate the density using nearest neighbors with periodic boundary conditions. Even better, implement it in your code and test it!

4. **Sedov Taylor Explosion in SPH**: Set up a uniform grid of SPH particles in a 2-D unit cell. Make it so that there are an odd number of particle on a side, such that you have a particle centered exactly in the center of the unit cell. All particle should have v = 0 and mass = 1/N, where N is the total number of particles such that the mass of the fluid in the unit cell is 1. If we use gamma=2, then for e=1 we have c=sqrt(2) for all particles and the SPH code should maintain the uniform density as everything should be in pressure equilibrium. Test this. Now set the specific internal energy of the central particle to e = 100! Now the gas should react by producing the Sedov-Taylor blast wave. You will have to think about the appropriate timestep for the simulation. Think back to the Courant Condition from the first semester, or simply experiment with different values (hint: you know the sound speed, but what is the grid speed? What defines a resolution length scale here? h? So could we regard h/delta_t as a "grid speed"?

5. **2-d Ising Model**

6. **2-d Travelling Salesman Problem**
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