Exercises

-> FS2026_tasks

Vorlesung

#timestamp 2026-02-19

ideal gas: model of gases that consist of small (relative to volume) molecules with low density (low pressure, low density, high temperature -> above condensation) -> few collisions, collisions only randomize velocity
$pV=nRT,R=N_A{k}_B=8.134\frac{J}{mol\cdot K}$

In a molecular system at equilibrium and the classical limit, the average kinetic energy "stored" in each degree of freedom amounts to $\frac{1}{2}{k}_{B}T$

#timestamp 2026-04-01

You don't want complexity in the model where it doesn't matters

try to find the trade-off between accuracy and complexity

#timestamp 2026-04-23

if only interested in thermodynamic properties -> stochastic methods

monte carlo: typically rel. error $\sim N^{-1/2}$

metropolis sampling: average over trajectory -> (directly) canonical average

#todo what is a boltzmann-weighted ensemble of configurations?

#timestamp 2026-04-30

$⟨a⟩\widehat{=}\text{boltzmann-weighted ensemble average}$
to calculate structureal properties, one has to do

• gathering
• roto-translational fitting

#todo bootstrapping

#timestamp 2026-05-28

random walk -> $n^2$

key points for presentation, task 10.2:

• two hypothetical variants of argon with different interaction parameters (\epsilon), but same size (\sigma)
• different combination rules
• calculate local fraction functions

modifications to mdatom:

• added 6 more parameters to input file
• hardcoded the first half of atoms to be variant 1, second half variant 2
  • disadvantage: not equally distributed at start, but easier to implement; the system just needs to be equilibrated for a longer tiem