Event disks box.py
From Werner KRAUTH
This page presents a Python3 implementation of the program event_disks_box.py, a naive event-driven molecular dynamics algorithm for four disks in a square box of sides 1 without periodic boundary conditions. This algorithm was first presented in the SMAC book, and discussed in the present form (in Python2) in my MOOC.
Contents |
[edit]
Description
[edit]
Program
import math def wall_time(pos_a, vel_a, sigma): if vel_a > 0.0: del_t = (1.0 - sigma - pos_a) / vel_a elif vel_a < 0.0: del_t = (pos_a - sigma) / abs(vel_a) else: del_t = float('inf') return del_t def pair_time(pos_a, vel_a, pos_b, vel_b, sigma): del_x = [pos_b[0] - pos_a[0], pos_b[1] - pos_a[1]] del_x_sq = del_x[0] ** 2 + del_x[1] ** 2 del_v = [vel_b[0] - vel_a[0], vel_b[1] - vel_a[1]] del_v_sq = del_v[0] ** 2 + del_v[1] ** 2 scal = del_v[0] * del_x[0] + del_v[1] * del_x[1] Upsilon = scal ** 2 - del_v_sq * ( del_x_sq - 4.0 * sigma **2) if Upsilon > 0.0 and scal < 0.0: del_t = - (scal + math.sqrt(Upsilon)) / del_v_sq else: del_t = float('inf') return del_t pos = [[0.25, 0.25], [0.75, 0.25], [0.25, 0.75], [0.75, 0.75]] vel = [[0.21, 0.12], [0.71, 0.18], [-0.23, -0.79], [0.78, 0.1177]] singles = [(0, 0), (0, 1), (1, 0), (1, 1), (2, 0), (2, 1), (3, 0), (3, 1)] pairs = [(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (2, 3)] sigma = 0.15 t = 0.0 n_events = 100 for event in range(n_events): wall_times = [wall_time(pos[k][l], vel[k][l], sigma) for k, l in singles] pair_times = [pair_time(pos[k], vel[k], pos[l], vel[l], sigma) for k, l in pairs] next_event = min(wall_times + pair_times) t += next_event for k, l in singles: pos[k][l] += vel[k][l] * next_event if min(wall_times) < min(pair_times): collision_disk, direction = singles[wall_times.index(next_event)] vel[collision_disk][direction] *= -1.0 else: a, b = pairs[pair_times.index(next_event)] del_x = [pos[b][0] - pos[a][0], pos[b][1] - pos[a][1]] abs_x = math.sqrt(del_x[0] ** 2 + del_x[1] ** 2) e_perp = [c / abs_x for c in del_x] del_v = [vel[b][0] - vel[a][0], vel[b][1] - vel[a][1]] scal = del_v[0] * e_perp[0] + del_v[1] * e_perp[1] for k in range(2): vel[a][k] += e_perp[k] * scal vel[b][k] -= e_perp[k] * scal print(event', event) print('time', t) print('pos', pos) print('vel', vel)
[edit]
Version
See history for version information. For a more elaborate version of this program, see the HistoricDisks repository connected to our paper Li et al.: Hard-disk computer simulations -- a historic perspective (2022)