def velo_verlet(R, V, F, box_width, dt):
""" Take a velo verlet step
"""
# Step 1: Calculate new positions
R = R + V * dt + 0.5 * dt * dt * F
# Step 2: Calculate new forces
F_old = copy.deepcopy(F)
e_pot, F, k_vir = lennard_jones(R, box_width)
# Step 3: Calculate new velocities
V = V + 0.5 * dt * (F + F_old)
return R, V, F
def simulation(n_atoms, n_steps, rho, T_want, eps, dt):
dist = []
t_together = 0.0
t_apart = 0.0
N_a = 2 * n_atoms
R, V, F, box_width = md.initialize_particles(n_atoms, T_want, rho, eps)
KinE = []
PotE = []
TotE = []
Temp = []
for i in range(n_steps):
Rnew = R + V*dt + 0.5*dt**2*F
if i%1000 ==0:
video.add_frame(R[0],R[1], i)
if i%100000 == 0:
print i
energy_potential, Fnew = md.lennard_jones(Rnew, box_width, eps)
V = scale_temp(V, T_want, N_a)
ke = (1.0/2.0) * np.sum(V*V)
d = dister(0,1,R, box_width)
dist.append(d)
if d < 1.52:
t_together += 1.0
if d > 1.52:
t_apart += 1.0
KinE.append(ke)
PotE.append(energy_potential)
TotE.append(ke + energy_potential)
Temp.append(2 * ke / (N_a))
Vnew = V + 0.5*dt*(F + Fnew)
V = Vnew.copy()
R = Rnew.copy()
video.save("colorparticle", periodic_boundary=True)
return PotE, KinE, TotE, Temp, dist, t_together/t_apart
te_list = []
pr_list = []
p_tail = 16.0/3.0 * np.pi * rho *( 2.0/3.0 * (2.5**-9) - (2.5**-3))
print "p_tail", p_tail
for n in range(n_steps+1):
# Step 1: Calculate new positions
R = R + V * dt + 0.5 * dt * dt * F
# Step 2: Calculate new forces
F_old = copy.deepcopy(F)
e_pot, F, k_vir = lennard_jones(R, box_width)
# Step 3: Calculate new velocities
V = V + 0.5 * dt * (F + F_old)
e_kin = calc_ekin(V)
T = calc_temperature(V)
e_kin = calc_ekin(V)
e_tot = e_kin + e_pot
p = rho * T + 1.0/(3.0 * box_width**3) * k_vir + p_tail
# Print output
if (n % save_freq == 0 ):
print n, e_pot, e_kin, e_tot, T
R_frames.append(R)
ek_list = [] # Kinetic energy
ep_list = [] # Potential energy
et_list = [] # Total energy
pr_list = [] # Pressure
te_list = [] # Temperature
# Run simulation for n_steps
for n in range(n_steps+1):
# Step 1: Calculate new positions
R += V*dt + 0.5*F*dt*dt
# Step 2: Calculate new forces
F0 = copy.copy(F)
potential_energy, F, vir = md.lennard_jones(R, box_size)
# Step 3: Calculate new velocities
V += 0.5*(F + F0)*dt
if n % save_freq == 0:
# Calculate properties
kinetic_energy = calc_kinetic(V)
total_energy = kinetic_energy + potential_energy
temperature = calc_temperature(V)
pressure = rho*temperature + 1.0/(3.0*box_size**3)*vir + p_tail
ek_list.append(kinetic_energy)
ep_list.append(potential_energy)
et_list.append(total_energy)
t_list = []
te_list = []
pr_list = []
p_tail = 16.0 / 3.0 * np.pi * rho * (2.0 / 3.0 * (2.5**-9) - (2.5**-3))
print "p_tail", p_tail
for n in range(n_steps + 1):
# Step 1: Calculate new positions
R = R + V * dt + 0.5 * dt * dt * F
# Step 2: Calculate new forces
F_old = copy.deepcopy(F)
e_pot, F, k_vir = lennard_jones(R, box_width)
# Step 3: Calculate new velocities
V = V + 0.5 * dt * (F + F_old)
e_kin = calc_ekin(V)
T = calc_temperature(V)
e_kin = calc_ekin(V)
e_tot = e_kin + e_pot
p = rho * T + 1.0 / (3.0 * box_width**3) * k_vir + p_tail
# Print output
if (n % save_freq == 0):
print n, e_pot, e_kin, e_tot, T
R_frames.append(R)
def simulation(n_atoms, n_steps, rho, temperature, dt,
eps = [],
save_freq=60,
video_filename='',
constant_temperature=False):
n_eq = 200*save_freq
if video_filename != '':
save_video = True
if len(eps) == 0:
eps = np.ones((n_atoms, n_atoms))
else:
# set particle 1 and 2 to other color
colors = ['#4daf4a' for _ in range(n_atoms)]
colors[0] = "#377eb8"
colors[1] = "#377eb8"
video.add_color(colors)
# Initialize simulation
R, V, F, box_width = md.initialize_particles(n_atoms, temperature, rho, eps)
print 'Initialized'
# # Calculate the tail correction
# p_tail = 16.0/3.0 * np.pi * rho * (2.0/3.0 * (2.5**-9) - (2.5**-3))
# Storage arrays
ek_list = [] # Kinetic energy
ep_list = [] # Potential energy
et_list = [] # Total energy
# pr_list = [] # Pressure
te_list = [] # Temperature
r_list = [] # distance list
# Run simulation for n_steps
for n in range(n_steps + 1):
# Step 1: Calculate new positions
R += V*dt + 0.5*F*dt*dt
# Step 2: Calculate new forces
F0 = copy.copy(F)
potential_energy, F = md.lennard_jones(R, box_width, eps)
# Step 3: Calculate new velocities
V += 0.5*(F + F0)*dt
# if temperture is set to constant, then scale the velocities
if constant_temperature:
V = md.scale_temp(V, temperature)
# for every save_freq steps
if n % save_freq == 0 and n > n_eq:
print "step:", n
# Calculate properties
kinetic_energy = calc_kinetic(V)
total_energy = kinetic_energy + potential_energy
temperature = calc_temperature(V)
# pressure = rho*temperature + 1.0/(3.0*box_width**3)*vir + p_tail
ek_list.append(kinetic_energy)
ep_list.append(potential_energy)
et_list.append(total_energy)
# pr_list.append(pressure)
te_list.append(temperature)
# calculate the distance between 0 and 1
X = R[0, 0] - R[0, 1]
Y = R[1, 0] - R[1, 1]
# Periodic boundary condition
X -= box_width * np.rint(X/box_width)
Y -= box_width * np.rint(Y/box_width)
d = np.sqrt(X**2 + Y**2)
r_list.append(d)
# Add frame to video
if save_video:
video.add_frame(R[0], R[1])
# Remember not to save a video for large n_steps
if save_video:
video.save(video_filename, box_width, periodic_boundary=True)
return ek_list, ep_list, et_list, te_list, r_list
# Storage arrays
ek_list = [] # Kinetic energy
ep_list = [] # Potential energy
et_list = [] # Total energy
pr_list = [] # Pressure
te_list = [] # Temperature
# Run simulation for n_steps
for n in range(n_steps + 1):
# Step 1: Calculate new positions
R += V * dt + 0.5 * F * dt * dt
# Step 2: Calculate new forces
F0 = copy.copy(F)
potential_energy, F, vir = md.lennard_jones(R, box_size)
# Step 3: Calculate new velocities
V += 0.5 * (F + F0) * dt
if n % save_freq == 0:
# Calculate properties
kinetic_energy = calc_kinetic(V)
total_energy = kinetic_energy + potential_energy
temperature = calc_temperature(V)
pressure = rho * temperature + 1.0 / (3.0 * box_size**3) * vir + p_tail
ek_list.append(kinetic_energy)
ep_list.append(potential_energy)
et_list.append(total_energy)
def simulation(n_atoms, n_steps, rho, temperature, dt,
eps = [],
save_freq=60,
video_filename='',
constant_temperature=False):
n_eq = 200*save_freq
if video_filename != '':
save_video = True
if len(eps) == 0:
eps = np.ones((n_atoms, n_atoms))
else:
# set particle 1 and 2 to other color
colors = ['#4daf4a' for _ in range(n_atoms)]
colors[0] = "#377eb8"
colors[1] = "#377eb8"
video.add_color(colors)
# Initialize simulation
R, V, F, box_width = md.initialize_particles(n_atoms, temperature, rho, eps)
print 'Initialized'
# # Calculate the tail correction
# p_tail = 16.0/3.0 * np.pi * rho * (2.0/3.0 * (2.5**-9) - (2.5**-3))
# Storage arrays
ek_list = [] # Kinetic energy
ep_list = [] # Potential energy
et_list = [] # Total energy
# pr_list = [] # Pressure
te_list = [] # Temperature
r_list = [] # distance list
# Run simulation for n_steps
for n in range(n_steps + 1):
# Step 1: Calculate new positions
R += V*dt + 0.5*F*dt*dt
# Step 2: Calculate new forces
F0 = copy.copy(F)
potential_energy, F = md.lennard_jones(R, box_width, eps)
# Step 3: Calculate new velocities
V += 0.5*(F + F0)*dt
# if temperture is set to constant, then scale the velocities
if constant_temperature:
V = md.scaletemp(V, temperature)
# for every save_freq steps
if n % save_freq == 0 and n > n_eq:
print "step:", n
# Calculate properties
kinetic_energy = calc_kinetic(V)
total_energy = kinetic_energy + potential_energy
temperature = calc_temperature(V)
# pressure = rho*temperature + 1.0/(3.0*box_width**3)*vir + p_tail
ek_list.append(kinetic_energy)
ep_list.append(potential_energy)
et_list.append(total_energy)
# pr_list.append(pressure)
te_list.append(temperature)
# calculate the distance between 0 and 1
X = R[0, 0] - R[0, 1]
Y = R[1, 0] - R[1, 1]
# Periodic boundary condition
X -= box_width * np.rint(X/box_width)
Y -= box_width * np.rint(Y/box_width)
d = np.sqrt(X**2 + Y**2)
r_list.append(d)
# Add frame to video
if save_video:
video.add_frame(R[0], R[1])
# Remember not to save a video for large n_steps
if save_video:
video.save(video_filename, box_width, periodic_boundary=True)
return ek_list, ep_list, et_list, te_list, r_list