def test_potential_increasing_right_of_R0():
"""potential increases to the right of R0, and remains negative."""
ri = rprev = R0
vprev = lj.potential(ri**2)
for i in range(10):
ri = 2*ri
vi = lj.potential(ri**2)
print(f'{i} {ri}: {vi}')
assert vprev < vi
assert vi < 0.0
vprev = vi
rprev = ri
def test_potential_minimum():
"""potential has a minimum at r = R0"""
r0 = R0
vr0 = lj.potential(r0**2)
d = 0.1
for i in range(5):
rLeft = r0 - d
rRight = r0 + d
vLeft = lj.potential(rLeft**2)
vRight = lj.potential(rRight**2)
print(f'{d}: {vLeft} < {vr0} < {vRight}')
assert vLeft > vr0
assert vRight > vr0
d *= 0.1
def test_force_is_derivative_of_potential():
n = 1000
# Generate n random numbers in ]0,5*R0]
# np.random.random generate numbers in [
rij = (5*R0)*(1.0 - np.random.random(n))
fij = lj.force_factor(rij**2)*rij
d = 1e-10
rij0 = rij - d
vij0 = lj.potential(rij0**2)
rij1 = rij + d
vij1 = lj.potential(rij1**2)
dvij = (vij1 - vij0)/(2*d)
for i in range(n):
print(f'{i} {fij[i]} == {dvij[i]} {np.abs(fij[i]-dvij[i])}')
assert fij[i] == pytest.approx(dvij[i],1e-4)
def test_potential_decreasing_left_of_R0():
"""potential increases to the right of R0, and remains negative."""
ri = rprev = R0
vprev = lj.potential(ri**2)
for i in range(10):
ri = 0.9*ri
vi = lj.potential(ri**2)
print(f'{i} {ri}: {vi}')
assert vi > vprev
if ri > 1:
assert vi < 0.0
else:
assert vi > 0.0
vprev = vi
rprev = ri
def test_computeEnergy():
""""""
box = md.Box(0., 0., 5. * md.hcp.uc_centered_a, 0.5 * md.hcp.uc_centered_b)
atoms = md.MD(box, cutoff=2.5)
if __plot:
cmn.figure()
cmn.plotBox(box)
cmn.plotAtoms(atoms.x, atoms.y, radius=atoms.radius)
cmn.plt.show()
atoms.buildVerletLists()
print(atoms.vl)
energy = atoms.computeEnergy()
r01sq = md.hcp.uc_centered_a**2
r02sq = (2 * md.hcp.uc_centered_a)**2
expected = 4 * lj.potential(r01sq) + 3 * lj.potential(r02sq)
print(energy)
print(expected)
assert energy == expected
def test_potential_cutoff():
"""not actually a test, just to show the magnitude of the interaction at cut-off."""
for i in range(1,11):
rc = i*R0
vrc = lj.potential(rc**2)
print(f'{i} {rc}: `{vrc} {"cut-off" if i==3 else ""}')
def test_potential_zero():
"""potential has a zero at r = 1.0"""
r = 1.0
vr = lj.potential(r**2)
assert vr == 0.0