docs: added report and nanotube simulation results

submission/worksheet5/report.md

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+---
+Group: D
+Members: Julius Kramer, Tim Scholl, Johannes Hupe
+PR: https://github.com/JoHaHu/MolSim/pull/71
+---
+
+# Report Group-D
+
+## Tasks - Worksheet 5
+
+### Task 1 - Simulation of a membrane
+
+- Extend Molecule Class: Modified to store neighboring molecules and initialized on a rectangular grid, setting direct and diagonal neighbors.
+- Harmonic Potential: Implemented interactions for direct and diagonal neighbors using harmonic potential formulas.
+- Self-Penetration Prevention: Applied truncated Lennard-Jones potential to ensure only repulsive forces are active.
+- Ran the simulation with specified parameters.
+
+### Task 2 - Parallelization
+
+- Parallelized the most time-consuming parts of the algorithm using OpenMP.
+- Implemented two parallelization strategies selectable via the input file.
+- Ensured compatibility without OpenMP using precompiler statements (#ifdef OPENMP).
+- Measured speedup with varying amount of threads.
+
+### Task 3 - Rayleigh-Taylor instability in 3D
+
+- Extended the 2D Rayleigh-Taylor instability simulation to a 3D scenario.
+- Applied periodic boundaries on the additional third dimension.
+- Conducted the experiment with specified parameters.
+
+### Contest 2
+
+- 
+
+### Task 4 - Nano-scale flow simulation
+
+- Fixed Wall Particles: Enabled fixing positions of particles in the outer cuboids, ensuring they do not move but still exert forces on fluid particles.
+- Thermostat Extension: Extended the thermostat to ignore total fluid velocity, calculating temperature using velocity deviations from the mean.
+- Velocity Adjustment: For each particle, subtracted the average velocity, scaled the deviation, and then added back the average velocity to obtain new velocities.
+- Profile Computation: Implemented a component to compute density and velocity profiles along the x-axis by subdividing it into bins and calculating averages per bin.
+
+We studied various influences on simulation profiles:
+=====================================================
+
+Gravity factor:
+- The higher the gravity factor, the denser the stable formation (with reflecting boundaries).
+
+Mass:
+- Higher mass of wall molecules leads to the fluid sticking better to it.
+- Vice-versa, lower mass of wall molecules or higher mass of fluid molecules leads to less interaction effects with the wall molecules.
+
+σ or ϵ of the molecules:
+- Higher σ expands the effective diameter of the particles.
+- Higher ϵ leads to higher inter-particle attraction which increases the density of the liquid.
+
+Removing walls:
+- Particles flowing out in various directions
+
+Adding walls:
+- All reflecting boundaries neatly shows the "sagging" of the particles.
+- Settling into stable formation.
+
+Old thermostat:
+- Maintains uniform temperature by scaling velocities directly, allowing potential fluid drift.
+
+New thermostat:
+- Accurately controls temperature by removing average fluid velocity before scaling, proventing net drift.
+
+No thermostat:
+- Temperature fluctuates significantly without control, and velocity distribution deviates over time. Potential for energy build-up and instability.
+
+Task 4 extra thermostat:
+- Maintains temperature by scaling only the x- and z-components of velocities and adjusts the y-component for mean flow,
+resulting in realistic flow dynamics without affecting the temperature.
+This approach differs by focusing on directional components and excluding flow speed from temperature calculations.