Monte Carlo polymer random walk simulations in space/time with entanglement dynamics. Used to explore time evolution of entangled/unentangled chains (see 'Context').
Key assumptions are hardcoded as below.
- Noise is drawn from the random uniform distribution.
- Polymer chains are formed by random walks in space of one mer, initialised at random spatial coordinates.
- The time evolution of chains are random walks in time (subject to the constraints of adjacent bonds) of each mer with intrinsic random probability of movement.
- Over many iterations, tends towards equal mer selection probability.
- 1 iteration is the computational time of attempting moves = total number of mers in system (arbitrarily be referred to as the 'time unit').
- At termination of each time unit, system (x,t) stored in array - Dimensions: [Snapshot number, Chain number, Bead number, XYZ coordinates].
- Toroidal Boundary Conditions implemented for pseudo-lattice structure.
Factors such as inter-chain interactions are ignored, only entanglement is considered and investigated. Can potentially be reused for further/alternative dynamics investigations.
Statistical analyses are done using a mean squared displacement routine. 2 are provided.
- Routine 1 uses the maximum number of averages while Routine 2 uses a less computationally expensive number of averages.
- Either way passed through plotting routine providing diffusion graphs.
- Gradients are calculated as per the theoretically expected mean squared displacement regimes.
Later data points have inherently more uncertainty so averaging required for meaningful analysis.
Time scales exponentially relative to input. Parallel computation recommended for longer simulations, using Routine 1 or averaged runs. Time evolution recommended to be translated to C++ for better computational runtime, though the 'Numba' JIT compiler is employed for this work.
The motivation for this work is based on the papers below. Specifically, verifying the emergence of a unique regime under an entanglement constraint.