Improve Langevin tutorial (#4329)

Part of #4052 

Description of changes:
- Add Green-Kubo calculation of the diffusivity. To get at least somewhat acceptably smooth VACFs, the number of simulation steps was increased from 400000 to 1000000, the simulation time is still quite acceptable, I think.
- General improvements, including changes requested by @RudolfWeeber and @christophlohrmann 
- Proper additon of hidden solutions

doc/tutorials/CMakeLists.txt

@@ -101,7 +101,9 @@ add_custom_target(tutorials_python)
 # Here: add new directory
 add_subdirectory(lennard_jones)
 add_subdirectory(error_analysis)
+add_subdirectory(langevin_dynamics)
 add_subdirectory(charged_system)
+add_subdirectory(polymers)
 add_subdirectory(lattice_boltzmann)
 add_subdirectory(raspberry_electrophoresis)
 add_subdirectory(active_matter)

doc/tutorials/Readme.md

@@ -12,8 +12,8 @@ physical systems.
 * **Simulate a simple Lennard-Jones liquid**  
   Modelling of a single-component and a two-component Lennard-Jones liquid.  
   [Guide](lennard_jones/lennard_jones.ipynb)
-* **Error_analysis**  
-  Statistical analysis of simulation results
+* **Error analysis**  
+  Statistical analysis of simulation results  
   Guide
   [Part 1](error_analysis/error_analysis_part1.ipynb) |
   [Part 2](error_analysis/error_analysis_part2.ipynb)
@@ -26,6 +26,9 @@ physical systems.
 * **Charged systems**  
   Modelling of ion condensation around a charged rod.  
   [Guide](charged_system/charged_system.ipynb)
+* **Langevin dynamics**  
+  Modelling of Brownian motion and measurement of diffusion coefficients.  
+  [Guide](langevin_dynamics/langevin_dynamics.ipynb)
 * **Ferrofluid**  
   Modelling of a monolayer ferrofluid system.  
   Guide
@@ -35,10 +38,11 @@ physical systems.
 * **Lattice-Boltzmann**  
   Simulations including hydrodynamic interactions using the Lattice-Boltzmann method.  
   Guide
-  [Part 1](lattice_boltzmann/lattice_boltzmann_part1.ipynb) |
-  [Part 2](lattice_boltzmann/lattice_boltzmann_part2.ipynb) |
-  [Part 3](lattice_boltzmann/lattice_boltzmann_part3.ipynb) |
-  [Part 4](lattice_boltzmann/lattice_boltzmann_part4.ipynb)
+  [Part 1](lattice_boltzmann/lattice_boltzmann_theory.ipynb) |
+  [Part 2](lattice_boltzmann/lattice_boltzmann_poiseuille_flow.ipynb)
+* **Polymers**  
+  Modelling polymers with hydrodynamic interactions.  
+  [Guide](polymers/polymers.ipynb)
 * **Raspberry electrophoresis**  
   Extended objects in a Lattice-Boltzmann fluid, raspberry particles.  
   [Guide](raspberry_electrophoresis/raspberry_electrophoresis.ipynb)

doc/tutorials/langevin_dynamics/CMakeLists.txt

@@ -0,0 +1,3 @@
+configure_tutorial_target(TARGET tutorial_ld DEPENDS langevin_dynamics.ipynb)
+
+nb_export(TARGET tutorial_ld SUFFIX "" FILE "langevin_dynamics.ipynb" HTML_RUN)

doc/tutorials/langevin_dynamics/NotesForTutor.md

@@ -0,0 +1,21 @@
+# Langevin dynamics
+
+## Learning objectives (physics)
+
+* Learning the basics of Brownian motion
+* Modeling the Brownian motion of a spherical object
+* Calculating the diffusion coefficient of a spherical object using the
+  mean square displacement and Green-Kubo relation
+
+After the tutorial, students should be able to:
+
+* Explain the microscopic origin of diffusion and how it is captured in the Langevin equation
+* Describe a typical mean-square-displacement plot and identify the different regimes
+* Estimate the diffusion coefficient from time series of a particle's position or velocity
+* Name the limitations of the Langevin equation, particularly with regards to hydrodynamic interactions
+
+## Learning objectives (ESPResSo)
+
+* Setting up a system in which particles move according to the Langevin equation
+* Calculating the diffusion coefficient using observables and accumulators based
+  on the mean square displacement and the velocity autocorrelation function