User Tools

Site Tools


spin:esc201_hs2021

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
Next revision
Previous revision
spin:esc201_hs2021 [2021/10/04 13:59]
stadel [Lectures]
spin:esc201_hs2021 [2021/12/13 14:18] (current)
sebastian [List of assignments]
Line 34: Line 34:
  
 4. Oct. 2021: {{ :​spin:​hs2021_week3.pdf |Population Growth, Chaos and Fractals}} 4. Oct. 2021: {{ :​spin:​hs2021_week3.pdf |Population Growth, Chaos and Fractals}}
 +
 +11. Oct. 2021: {{ :​spin:​hs2021_week4.pdf |Complex Fractals, Start of ODEs}}
 +
 +18. Oct. 2021: {{ :​spin:​hs2021_week5.pdf |Ordinary Differential Equations: Predator-Prey}}
 +
 +25. Oct. 2021: {{ :​spin:​hs2021_week6.pdf |Symplectic Integrators:​ Leap-frog and the Simple Pendulum}}
 +
 +1. Nov. 2021: {{ :​spin:​hs2021_week7.pdf |Many Bodies: a digital Orrery}}
 +
 +8. Nov. 2021: {{ :​spin:​hs2021_week8.pdf |Partial Differential Equations: Jacobi & SOR}}
 +
 +15. Nov. 2021: {{ :​spin:​hs2021_week9.pdf |Bi-linear and Bi-cubic interpolation and Electron Beams}}
 +
 +22. Nov. 2021: {{ :​spin:​hs2021_week10.pdf |Diffusion Equation and Numerical Stability}}
 +
 +29. Nov. 2021: {{ :​spin:​hs2021_week11.pdf |Hyperbolic PDEs}}
 +
 +6. Dec. 2021: {{ :​spin:​hs2021_week12.pdf |Finite Volume Method, Modified Equation, 2-D Advection}}
 +
 +13. Dec. 2021: {{ :​spin:​hs2021_week13.pdf |1-D Hydrodynamics and Riemann Solvers}}
 +
 +
 +
 +
 ====== Assignments ====== ====== Assignments ======
  
Line 85: Line 109:
   - Plot (and/or animate) the elliptical orbit of a planet around the sun by repeatedly solving Kepler'​s equation with Newton'​s method (or the bisection method), as explained in the lecture! (**to submit by 10 October 2021, 9pm**) ​   - Plot (and/or animate) the elliptical orbit of a planet around the sun by repeatedly solving Kepler'​s equation with Newton'​s method (or the bisection method), as explained in the lecture! (**to submit by 10 October 2021, 9pm**) ​
   - Draw a Feigenbaum diagram that results from solving the logistic equation (**to submit by 17 October, 2021, 9pm**). (Optional: Implement a function that allows you to zoom into the Feigenbaum diagram)   - Draw a Feigenbaum diagram that results from solving the logistic equation (**to submit by 17 October, 2021, 9pm**). (Optional: Implement a function that allows you to zoom into the Feigenbaum diagram)
 +  - Fractals: Draw some Julia sets with various constants c (you can start with the Mandelbrot set as it was explained in the lecture and the exercise class)! (**to submit by 24 October, 2021, 9pm**)
 +  - Ordinary Differential Equations: Solve the Lotka-Volterra equation using the Euler method and the midpoint Runge-Kutta method (optional: 4th order Runge Kutta method) and compare the results. Make two plots: the time dependence of both populations (mice and foxes), and the phase diagram using different initial conditions (**to submit by 31 October, 2021, 9pm**).
 +  - Symplectic Integrators:​ Use the Leap-Frog method to make a phase plot (p vs q) of the harmonic oscillator for different total energies. Compare the results with what you get using the Forward Euler method and the midpoint Runge-Kutta method. Make the same plot for a simple pendulum (**to submit by 7 November, 2021, 9pm**).
 +  - Make a solar system orrery following the steps outlined in the lecture (**to submit by 14 November, 2021, 9pm**)!
 +  - Elliptical partial differential equations: Solve the Poisson equation for the electromagnetic potential using the SOR method described in the lecture, with boundary conditions given by a 1000 Volt stick in the center of a 0 Volt box (as depicted in the lecture notes). Plot the contours of the resulting potential (**to submit by 21 November, 2021, 9pm**).
 +  - Interpolation,​ Part 1: Trace the movement of electrons in an electromagnetic potential (e.g. the one from the last exercise) with Leapfrog or Runge-Kutta. Use bilinear or bicubic interpolation for the potential. (**not graded, to submit by 28 November, 2021, 9pm**).
 +  - Interpolation,​ Part 2 (**WIN A PRIZE**): Design an optimal electron detector (specifics in lecture materials) (**to submit by 5 December, 2021, 9pm**).
 +  - Hyperbolic PDEs: Solve the linear advection equation by evolving an initial waveform in a periodic grid. See how the waveform behaves after passing through the grid multiple times and compare the results you get when using various methods introduced in the lecture (e.g. the LAX method, upwind scheme, LAX-Wendroff method...) (you can get 0.5 bonus points if you implement all three variants provided in Stefan'​s Hyperbolic Hints.txt) (**to submit by 12 December, 2021, 9pm**).
 +  - 2D advection: Solve the 2D advection problem using two methods introduced in the lecture (CIR and CTU) and compare if and how your solution diffuses numerically (**to submit by 19 December, 2021, 9pm**).
 +  - **Optional (grade for this exercise can replace your worst grade so far):** 1D Hydrodynamics:​ Solve the “shock tube” problem and the Sedov-Taylor blast wave using the three methods provided in the lecture (detailed assignment can be found in the lecture notes) (**to submit by 19 December, 2021, 9pm **).
spin/esc201_hs2021.1633348760.txt.gz · Last modified: 2021/10/04 13:59 by stadel