def plotMeanSquaredDisplacement(particles,
t,
N,
eps,
chartName,
plotDiffusionConstant=False,
filename="meanSquaredDisplamcent"):
msd, diffusion_constant = MDFunctions.ComputeMeanSquaredDisplacement(
t, particles)
msd, yLabel = MDFunctions.SigmaToAngstrom(msd)
t, xLabel = MDFunctions.ArgonTimeToSeconds(t)
plt.title(chartName)
plt.plot(t, msd, label=f'Mean squared displacement')
plt.xlabel(xLabel)
plt.ylabel(f"Mean sq. disp {yLabel}")
plt.legend()
plt.savefig(f'./fig/{filename}.jpg')
plt.show()
if plotDiffusionConstant:
plt.title("Diffusion constant")
plt.plot(t, diffusion_constant, label=f'Diffusion constant')
plt.xlabel(xLabel)
plt.ylabel('D')
plt.legend()
plt.savefig(f'{filename}_diffusionConstant.jpg')
plt.show()
def Task4b_iv_avg():
print("TASK : Task4b_iv_avg")
maxTime = 0.7
t, N, T = SetTime(maxTime, increments)
vac = []
sampling = 5
for i in range(0, sampling):
particles = MDGenerators.PopulateCreateCrystalStructure(
4, "Ar", 1.7, N, constants.mass, 190)
MDFunctions.MoveToCentreOfBox(particles)
MDSolver.solveFaster(MDSolver.velocityVerletFast2, particles, maxTime,
N)
vag, diffu_coeff = MDFunctions.ComputeVelocityAutoCorrelation(
t, particles)
vac.append(vag)
avgVag = vac[0]
for i in range(0, sampling):
avgVag += vac[i]
avgVag[0] /= sampling
chartName = f"Avg Vel AUtocorrelation {sampling}"
MDPlot.plot([avgVag], t, N, chartName, ["vac"], "time (s)", "4biv_avg")
MDFileWriter.WriteXYZFile(particles, "4b_ii", N)
MDFileWriter.WriteLastFrame(particles, "4b_iiii_lastFrame", N)
def Task2FasterCompare2():
print("TASK : Task2FasterCompare2")
maxTime = 0.7
t, N, T = SetTime(maxTime, increments)
v0 = np.array([0, 0, 0])
particles = [
MDParticle.Particle('left', 'Ar', np.array([0.0, 0.0, 0.0]), v0, N,
constants.mass),
MDParticle.Particle('right', 'Ar', np.array([1.5, 0.0, 0.0]), v0, N,
constants.mass)
]
#particles = [MDParticle.Particle('left', 'Ar', np.array([0.0,0.0,0.0] ), v0, N, constants.mass)]
MDFunctions.MoveToCentreOfBox(particles)
MDSolver.solve(MDSolver.velocityVerlet, particles, T, N)
#MDSolver.solve(MDSolver.eulerCromer, particles, T, N)
MDPlot.plotAllEnergies(particles, t, "Test slow", "testSlow")
MDFileWriter.WriteXYZFile(particles, "twoparticlesVelVerSlow", N, 50)
particles = [
MDParticle.Particle('left', 'Ar', np.array([0.0, 0.0, 0.0]), v0, N,
constants.mass),
MDParticle.Particle('right', 'Ar', np.array([1.5, 0.0, 0.0]), v0, N,
constants.mass)
]
#particles = [MDParticle.Particle('left', 'Ar', np.array([0.0,0.0,0.0] ), v0, N, constants.mass)]
MDFunctions.MoveToCentreOfBox(particles)
MDSolver.solveFaster(MDSolver.velocityVerletFast2, particles, T, N)
MDPlot.plotAllEnergies(particles, t, "Test fast", "testFast")
MDFileWriter.WriteXYZFile(particles, "twoparticlesVelVerFast", N, 50)
def plotShiftedPotentialDiff(minDist,
maxDist,
chartName,
filename="plotPotentialDiff"):
shift = MDFunctions.LennardJonesPotential(3, constants.eps, constants.sig)
series = np.linspace(2.8, 3.1, 100)
pot = MDFunctions.LennardJonesPotential(series, constants.eps,
constants.sig, 0)
pot2 = MDFunctions.LennardJonesPotential(series, constants.eps,
constants.sig, shift)
diff = pot - pot2
plt.subplot(1, 1, 1)
plt.title(chartName)
plt.plot(series, pot, label=f'Non shifted')
plt.plot(series, pot2, label=f'Shifted')
plt.plot(series, diff, label=f'Difference between shifted and non shifted')
plt.xlabel('distance (sigmas)')
plt.ylabel('force')
plt.legend()
plt.savefig(f'./fig/{filename}.jpg')
plt.show()
def Task3d_ii():
print("TASK : Task3d_i")
maxTime = 5 #should be 3
t, N, T = SetTime(maxTime, increments)
nthFrame = 10
dist = 1.7
v0 = np.array([0, 0, 0])
particles = [
MDParticle.Particle('left', 'Ar', np.array([0., 0., 0.]), v0, N,
constants.mass),
MDParticle.Particle('right', 'Ar', np.array([dist, 0.0, 0.0]), v0, N,
constants.mass)
]
MDSolver.solveFaster(MDSolver.velocityVerletFast2, particles, maxTime, N)
MDFunctions.MoveToCentreOfBox(particles)
MDPlot.plotAllEnergies(particles, t,
"Total Energy (Velocity Verlet) 1.5 sigma",
"3dii_energy_two")
MDFileWriter.WriteXYZFile(particles, "3dii_two", N)
particles = MDGenerators.PopulateCreateCrystalStructure(
1, "AR", dist, N, constants.mass)
MDFunctions.MoveToCentreOfBox(particles)
MDSolver.solveFaster(MDSolver.velocityVerletFast2, particles, maxTime, N)
MDPlot.plotAllEnergies(
particles, t, "Total Energy (Velocity Verlet) 4 particles, random",
"3dii_energy_four")
MDFileWriter.WriteXYZFile(particles, "3dii_four", N, nthFrame)
def plotVelocityAutoCorrelation(particles,
t,
N,
chartName,
includeDiffusionCoefficientSubPlot=False,
filename="velocityAutoCorrelation"):
vac, diffusion_coefficcient = MDFunctions.ComputeVelocityAutoCorrelation(
t, particles)
t, timeUnits = MDFunctions.ArgonTimeToSeconds(t)
plt.subplot(1, 1, 1)
plt.title(f"{chartName} Velocity correlation")
plt.plot(t, vac, label=f'Velocity auto correlation')
plt.xlabel(f"time ({timeUnits})")
plt.ylabel('Vel. Autocorrelation')
plt.legend()
plt.savefig(f'{filename}_velcorr.jpg')
plt.show()
if includeDiffusionCoefficientSubPlot:
plt.subplot(2, 1, 1)
plt.title(f"{chartName} Diffusion Coefficient")
plt.plot(t, diffusion_coefficcient, label=f'Diffusion coefficient')
plt.xlabel('time(s)')
plt.ylabel('Diffusion coefficient')
plt.legend()
plt.savefig(f'{filename}_diffcoeff.jpg')
plt.show()
def plotTemperature(particles, t, N, chartName, filename="plotTemperature"):
tPrime = MDFunctions.ComputeTemperatureReduced(N, particles)
tKelvin = MDFunctions.ArgonTPrimeToKelvin(tPrime)
tToSeconds, xLabel = MDFunctions.ArgonTimeToSeconds(t)
plt.title(chartName)
plt.plot(tToSeconds, tKelvin, label=f'Temperature (K)')
plt.xlabel(xLabel)
plt.ylabel('Kelvin (K)')
plt.legend()
plt.savefig(f'./fig/{filename}.jpg')
plt.show()
def Task3b_ii():
print("TASK : Task3b_ii")
maxTime = 5
t, N, T = SetTime(maxTime, increments)
v0 = np.array([0, 0, 0])
print("Simulating four atom")
## Create particless
particles = [
MDParticle.Particle('one', 'Ar', np.array([1., 0.0, 0.]), v0, N,
constants.mass),
MDParticle.Particle('two', 'Ar', np.array([0., 1., 0.]), v0, N,
constants.mass),
MDParticle.Particle('three', 'Ar', np.array([-1., 0., 0.]), v0, N,
constants.mass),
MDParticle.Particle('four', 'Ar', np.array([0., -1., 0.]), v0, N,
constants.mass)
]
MDFunctions.MoveToCentreOfBox(particles)
MDSolver.solveFaster(MDSolver.velocityVerletFast2, particles, T, N)
MDPlot.plotAllEnergies(particles, t,
"Total Energy (Velocity Verlet)(fast) 1.0 sigma",
"allEnergies15velocityVerlet15fast")
MDFileWriter.WriteXYZFile(particles, "fourparticlesVelVer1Fast", N)
def Task4_di_read(t, filename):
num_bins = 10
bin_edges = np.linspace(0, 5, num_bins + 1)
bin_centres = 0.5 * (bin_edges[1:] + bin_edges[:-1])
V = constants.box**3
#Read the file prepared by the previous
particles, maxTindex = MDFileWriter.ReadEverything(filename, N)
#Convert x-axis units from sigma to Ångstrøm
bin_centres = MDFunctions.SigmaToAngstrom(bin_centres)
if t is None:
t = maxTindex
elif t > maxTindex:
raise Exception(
"Trying to read out rdf from frame {t} which only simulated {maxTindex} frames"
)
tInSeconds = MDFunctions.ArgonTimeToSeconds(t)
count = len(particles)
x = np.array([[0., 0., 0.] for i in range(count)]) # Velocity
j = 0
counter = 0
for j in range(0, count):
x[counter] = particles[j].x[t]
counter += 1
#x = np.where(x > 0)
#Bin the distance counts
data = MDFunctions.rdf(bin_edges, x, V)
chartName = f"Ar N={count} RDF after {tInSeconds[0]:11.6} {tInSeconds[1]}"
# def barchart(data, xlabels, chartName, filename = "barChart"):
MDPlot.barchart(data, bin_centres, "RDF", chartName, f"RDF_{filename}")
strLabels = []
for lb in bin_centres[0]:
strLabels.append(f"{lb:11.1f}")
def plotPotential(minDist, maxDist, chartName, filename="plotPotential"):
series = np.linspace(minDist, maxDist, 100)
pot = MDFunctions.LennardJonesPotential(series, constants.eps,
constants.sig)
shiftedPot = MDFunctions.LennardJonesPotential(series, constants.eps,
constants.sig,
constants.cutOffRange)
#plt.subplot(1,1,1)
plt.title(chartName)
plt.plot(series, pot, label=f'Unmodified')
plt.plot(series, shiftedPot, label=f'Shifted')
plt.xlabel('distance (sigmas)')
plt.ylabel('force')
plt.legend()
plt.savefig(f'./fig/{filename}.jpg')
plt.show()
def Task4b_simAndWrite():
print("TASK : Task4b_ii_write")
maxTime = 1.5
t, N, T = SetTime(maxTime, increments)
particles = MDGenerators.PopulateCreateCrystalStructure(
4, "Ar", 1.7, N, constants.mass, 190)
MDFunctions.MoveToCentreOfBox(particles)
MDSolver.solveFaster(MDSolver.velocityVerletFast2, particles, maxTime, N)
MDFileWriter.WriteEverything(particles, "4b_ii_everything", N)
def Task4d_i_write(nGrid, sigmaDistance, initTemperature, filename):
print("TASK : Task4b_ii_write+ ")
maxTime = 2
t, N, T = SetTime(maxTime, increments)
particles = MDGenerators.PopulateCreateCrystalStructure(
nGrid, "Ar", sigmaDistance, N, constants.mass, initTemperature)
MDFunctions.MoveToCentreOfBox(particles)
MDSolver.solveFaster(MDSolver.velocityVerletFast2, particles, maxTime, N)
MDFileWriter.WriteEverything(particles, filename, N)
def Task3d_i():
print("TASK : Task3d_i")
maxTime = 3 #should be 3
t, N, T = SetTime(maxTime, increments)
nthFrame = 10
particles = MDGenerators.PopulateCreateCrystalStructure(
4, "AR", 1.7, N, constants.mass)
MDFunctions.MoveToCentreOfBox(particles)
MDSolver.solveFaster(MDSolver.velocityVerletFast2, particles, maxTime, N)
MDPlot.plotAllEnergies(
particles, t, "Total Energy (Velocity Verlet) 256 particles, random",
"3d_ii")
MDFileWriter.WriteXYZFile(particles, "256_random", N, nthFrame)
def Task4a_iii_fast():
print("TASK : Task4a_iii")
maxTime = 10
t, N, T = SetTime(maxTime, increments)
t_initial = 190
particles = MDGenerators.PopulateCreateCrystalStructure(
3, "Ar", 1.7, N, constants.mass, t_initial)
MDFunctions.MoveToCentreOfBox(particles)
MDSolver.solveFaster(MDSolver.velocityVerletFast2, particles, maxTime, N)
#temp = MDFunctions.ComputeTemperatureReduced(N-1, particles, constants.eps)
#print(f"AT time {maxTime} temperature is {temp} kelvin")
chartName = f"4a) iii Temp ({t_initial} K) (fast)"
MDPlot.plotTemperature(particles, t, N, chartName, "4a_iii_fast")
def Task3e_ii():
print("TASK : Task3e_ii")
maxTime = 1 #should be 3
nthFrame = 1
t, N, T = SetTime(maxTime, increments)
particles = MDGenerators.PopulateCreateCrystalStructure(
2, "AR", 1.7, N, constants.mass)
MDFunctions.MoveToCentreOfBox(particles)
#MDFileWriter.WriteXYZFile(particles, "108_initial", N, nthFrame)
#MDSolver.solve(MDSolver.velocityVerlet, particles, T, N)
MDSolver.solveFaster(MDSolver.velocityVerletFast2, particles, maxTime, N)
MDFileWriter.WriteXYZFile(particles, "108_initial", N, nthFrame)
def createParticles(count,
atomType,
avgDistanceSigma,
N,
mass,
temperature=None):
particles = []
x0 = [0, 0, 0]
if temperature is not None:
v0 = MDFunctions.CreateRandomVelocityFromTemperature(
count, temperature)
else:
v0 = np.array([[0., 0., 0.] for i in range(N)]) # Velocity
xPositions = MDFunctions.getPositionInBox(count)
# v0speedVector = MDFunctions.getRandomNormalizedDirection()
for i in range(0, count):
particle = MDParticle.Particle(i, atomType, xPositions[i], v0[i], N,
mass)
particles.append(particle)
return particles
def Task4c_ii():
print("TASK : Task4c_ii")
maxTime = 0.7
t, N, T = SetTime(maxTime, increments)
particles = MDGenerators.PopulateCreateCrystalStructure(
6, "Ar", 1.7, N, constants.mass, 190)
MDFunctions.MoveToCentreOfBox(particles)
MDSolver.solveFaster(MDSolver.velocityVerletFast2, particles, maxTime, N)
MDPlot.plotMeanSquaredDisplacement(particles, t, N, constants.eps,
"4c) i - Mean squared displacement",
True, "4c_ii")
MDFileWriter.WriteXYZFile(particles, "4c_ii", N)
MDFileWriter.WriteLastFrame(particles, "4c_ii_lastFrame", N)
def Task4b_v():
print("TASK : Task4b_v")
maxTime = 0.7
t, N, T = SetTime(maxTime, increments)
particles = MDGenerators.PopulateCreateCrystalStructure(
4, "Ar", 1.7, N, constants.mass, 190)
MDFunctions.MoveToCentreOfBox(particles)
MDSolver.solveFaster(MDSolver.velocityVerletFast2, particles, maxTime, N)
MDPlot.plotVelocityAutoCorrelation(particles, t, N,
"4b) ii - Vel.Corr / Diff.coeff ",
"4b_v")
MDFileWriter.WriteXYZFile(particles, "4b_v", N)
MDFileWriter.WriteLastFrame(particles, "4b_v_lastFrame", N)
def plotDistanceBetween(t,
chartName,
p1,
p2,
filename="two-particle-distance"):
N = len(t)
dist = np.zeros(N)
distanceVectors = np.subtract(p1.x, p2.x)
for i in range(N):
dist[i] = MDFunctions.getDistance(p1.x[i], p2.x[i])
#plt.subplot(3,1,1)
plt.title(chartName)
plt.plot(t, dist, label=f'x(t) ')
plt.xlabel('time(s)')
plt.ylabel('distance (sigmas)')
plt.legend()
plt.savefig(f'./fig/{filename}.jpg')
def eulerCromer(p, n, dt, particles, eps, sig):
scaleBy = 24
acc_vec = np.array([0.0, 0.0, 0.0])
pot = 0.
for op in particles:
if op is p:
continue
distvec = np.subtract(p.x[n], op.x[n])
dist = np.sqrt(distvec[0]**2 + distvec[1]**2 + distvec[2]**2)
forcescalar = 2 * (dist**-12) - dist**-6
acc_vec += forcescalar * (distvec / dist**2.0)
pot += MDFunctions.LennardJonesPotential(dist, eps, sig)
p.p[n + 1] = pot
p.a[n + 1] = scaleBy * acc_vec
p.v[n + 1] = p.v[n] + dt * p.a[n + 1]
p.x[n + 1] = p.x[n] + dt * p.v[n + 1]
return p
def plotAllEnergies(particles, t, chartName, filename="allEnergies"):
kinetic = np.zeros(len(t))
potential = np.zeros(len(t))
total = np.zeros(len(t))
for i in range(0, len(t) - 1):
for p in particles:
kinetic[i] += (MDFunctions.getLength(p.v[i])**2) / 2
potential[i] += p.p[i] / 2
total = np.add(kinetic, potential)
plt.title(chartName)
plt.plot(t, total, label=f'Total ')
plt.plot(t, potential, label=f'Potential')
plt.plot(t, kinetic, label=f'Kinetic')
plt.xlabel('time(s)')
plt.ylabel('energy')
plt.legend()
plt.savefig(f'./fig/{filename}.jpg')
plt.show()
def PopulateCreateCrystalStructure(n,
periodicCode,
distance,
N,
mass,
temperature=None):
print(
f"Computes {n}x{n}x{n} tetrahedral crystal lattice with cell size {distance}"
)
faceCenteredCubicLattice = np.array([
np.array([0, 0, 0]), # corner
np.array([0.5, 0.5, 0]), # floor
np.array([0.5, 0, 0.5]), # hither wall,
np.array([0, 0.5, 0.5]) # tither wall
])
particles = []
if temperature is not None:
v0 = MDFunctions.CreateRandomVelocityFromTemperature(
4 * n**3, temperature)
else:
v0 = np.array([[0., 0., 0.] for i in range(4 * n**3)]) # Velocity
index = 0
for i in range(n):
for j in range(n):
for k in range(n):
cellPos = np.array([i, j, k]) * distance
for lstr in faceCenteredCubicLattice:
particles.append(
MDParticle.Particle(f"{i}-{j}-{k}", periodicCode,
distance * lstr + cellPos,
v0[index], N, mass))
index += 1
print(f"Done popluating, created {index} particles")
density = mass * 4 / distance**3
print(f"Density of this structure is {density}")
return particles
def euler(p, n, dt, particles, eps, sig):
scaleBy = 24
acc_vec = np.array([0.0, 0.0, 0.0])
pot = 0.
#for op in particles:
plen = len(particles)
for op in particles:
if op is p:
continue
distvec = np.subtract(p.x[n], op.x[n])
dist = np.sqrt(distvec[0]**2 + distvec[1]**2 + distvec[2]**2)
# pointTo = np.linalg.norm(distvec)
forcescalar = 2 * (dist**-12) - dist**-6
acc_vec = forcescalar * (distvec / dist**2)
pot = MDFunctions.LennardJonesPotential(dist, eps, sig)
#Initial particle
p.p[n + 1] += pot
p.a[n + 1] += scaleBy * acc_vec
p.v[n + 1] += p.v[n] + dt * p.a[n + 1]
p.x[n + 1] += p.x[n] + dt * p.v[n]
p.swap(n + 1)
def Task2c_iv():
print("TASK : Task2c_iv")
maxTime = 5
t, N, T = SetTime(maxTime, increments)
v0 = np.array([0, 0, 0])
particles = [
MDParticle.Particle('left', 'Ar', np.array([0., 0., 0.]), v0, N,
constants.mass),
MDParticle.Particle('right', 'Ar', np.array([1.5, 0.0, 0.0]), v0, N,
constants.mass)
]
MDFunctions.MoveToCentreOfBox(particles)
MDSolver.solve(MDSolver.euler, particles, T, N)
MDPlot.plotAllEnergies(particles, t, "Total Energy (Euler) 1.5 sigma",
"2civ_allEnergiesEuler15")
MDFileWriter.WriteXYZFile(particles, "twoparticlesEuler15", N)
particles = [
MDParticle.Particle('left', 'Ar', np.array([0., 0., 0.]), v0, N,
constants.mass),
MDParticle.Particle('right', 'Ar', np.array([1.5, 0.0, 0.0]), v0, N,
constants.mass)
]
MDFunctions.MoveToCentreOfBox(particles)
MDSolver.solve(MDSolver.eulerCromer, particles, T, N)
MDPlot.plotAllEnergies(particles, t,
"Total Energy (Euler Cromer) 1.5 sigma",
"2civ_allEnergiesEulerCromer15")
MDFileWriter.WriteXYZFile(particles, "twoparticlesEulerCromer15", N)
particles = [
MDParticle.Particle('left', 'Ar', np.array([0., 0., 0.]), v0, N,
constants.mass),
MDParticle.Particle('right', 'Ar', np.array([1.5, 0.0, 0.0]), v0, N,
constants.mass)
]
MDFunctions.MoveToCentreOfBox(particles)
MDSolver.solve(MDSolver.velocityVerlet, particles, T, N)
MDPlot.plotAllEnergies(particles, t,
"Total Energy (Velocity Verlet) 1.5 sigma",
"2civ_allEnergiesVelocityVerlet15")
MDFileWriter.WriteXYZFile(particles, "twoparticlesVelVer15", N)
particles = [
MDParticle.Particle('left', 'Ar', np.array([0.0, 0.0, 0.0]), v0, N,
constants.mass),
MDParticle.Particle('right', 'Ar', np.array([0.95, 0.0, 0.0]), v0, N,
constants.mass)
]
MDFunctions.MoveToCentreOfBox(particles)
MDSolver.solve(MDSolver.eulerCromer, particles, T, N)
MDPlot.plotAllEnergies(particles, t, "Total Energy (Euler) 0.95 sigma",
"2civ_allEnergiesEuler095")
MDFileWriter.WriteXYZFile(particles, "twoparticlesEuler095", N)
particles = [
MDParticle.Particle('left', 'Ar', np.array([0.0, 0.0, 0.0]), v0, N,
constants.mass),
MDParticle.Particle('right', 'Ar', np.array([0.95, 0.0, 0.0]), v0, N,
constants.mass)
]
MDFunctions.MoveToCentreOfBox(particles)
MDFileWriter.WriteXYZFile(particles, "twoparticlesEulerCromer095", N)
MDPlot.plotAllEnergies(particles, t,
"Total Energy (Euler Cromer) 0.95 sigma",
"2civ_allEnergiesEulerCromer095")
MDFileWriter.WriteXYZFile(particles, "twoparticlesEulerCromer095", N)
particles = [
MDParticle.Particle('left', 'Ar', np.array([0.0, 0.0, 0.0]), v0, N,
constants.mass),
MDParticle.Particle('right', 'Ar', np.array([0.95, 0.0, 0.0]), v0, N,
constants.mass)
]
MDFunctions.MoveToCentreOfBox(particles)
MDSolver.solve(MDSolver.velocityVerlet, particles, T, N)
MDPlot.plotAllEnergies(particles, t,
"Total Energy (Velocity Verlet) 0.95 sigma",
"2civ_allEnergiesVelocityVerlet095")
MDFileWriter.WriteXYZFile(particles, "twoparticlesVelVer095", N)