![]() ![]() The particles therefore experience two kinds of displacements: first, their ordinary motion due to collisions and interactions with neighboring particles and, second, a corrective displacement to maintain their relative position inside the box when its volume is varied by the barostat and particle positions are rescaled accordingly. In the NpT ensemble, barostats dynamically adjust the volume of the simulation box to maintain a constant pressure. In this Communication, we demonstrate that this widely used heuristic trajectory unwrapping scheme is not suitable for simulations at constant pressure p. 2 t i ( i = 0, 1, …) are the discrete time steps of the saved trajectory, with Δ t = t i+1 − t i being the time-step size if every structure is considered in the unwrapping procedure. MSDs are routinely used for diffusion coefficient estimation via ad hoc fitting to the Einstein relation, although recent developments show that more accurate results can be retrieved either from a rigorous analysis of the particle displacements 1 or by properly accounting for MSD correlations. Calculations of observables, such as the mean squared displacement (MSD), require that the saved, wrapped trajectories r → w ( t i ) are unwrapped back into full space, r → w ( t i ) ↦ r → u ( t i ), in a post-processing step. The particle positions in full space, r → u ∈ R 3, are then wrapped into a reference simulation box, e.g., centered at the origin with r → w ∈ − L / 2, L / 2 3 for a cubic box with edge length L. Molecular dynamics (MD) simulations are routinely performed under periodic boundary conditions (PBCs). We provide practitioners with a formula to assess if and by how much earlier results might have been affected by the widely used heuristic unwrapping scheme. Here and in another paper, we apply the new unwrapping scheme to extensive molecular dynamics and Brownian dynamics simulation data. At each time step, we add the minimal displacement vector according to periodic boundary conditions for the instantaneous box geometry. We propose an alternative unwrapping scheme that resolves this issue. Improper accounting for box-volume fluctuations creates, at long times, unphysical trajectories and, in turn, grossly exaggerated diffusion coefficients. Here, we show that a widely used heuristic unwrapping scheme is not suitable for long simulations at constant pressure. For diffusion coefficient calculations using the Einstein relation, the particle positions need to be unwrapped. We do that for all step size : 1 to the whole length.In molecular dynamics simulations under periodic boundary conditions, particle positions are typically wrapped into a reference box. Then we square the obtained list and take the mean. We reproduce this operation, starting from 0 to the end of the list. We go from start to start + step to get the difference between two positions that are step steps apart. Considering the path for a single walker : not_msd = for start in range(steps-sep)])**2).mean() for sep in range(1, steps)] I don't know how it's called but it can also be calculated in a list comprehension. I hope I understood what you truly wanted. The proposed solution will give you something like this : Your function was not adapted to plot several walkers. You can do it inside a list comprehension in Python (and getting rid of your calcMSD function): msd = **2).mean() for i in range(1, steps)] To get all the MSD at every steps, we vary t from 1 to the number of steps. walkers = 50 # Example for 50 walkersĪs a sidenote, you could also use random.choice to randomly pick -1 or 1 directly, like so: for i in range(1, steps):įrom now, path is a 2D array : a row per walker path. We must edit your code a bit to have several independant paths. Path means here : the positions of each walker at step t. That means : MSD at step t = (path**2).mean() (the element-wise squaring makes it useless to take the absolute values) To get the MSD at step t, we must take all the squared positions at step t, then take the mean of the resulting array. Since we are in 1D, the distance is simply the absolute position : distance at time t = | path | To make sure we are agreeing on the definition, the mean squared displacement (MSD) is the mean of the squared distance from origin of a collection of particles (in our case, walkers) at a specific step. Mean Squared Displacement Definition of mean squared displacement ![]()
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