def test_random_droplet(dim):
""" tests simple droplet """
pos = np.random.uniform(0, 10, dim)
radius = np.random.uniform(2, 3)
d1 = droplets.SphericalDroplet(pos, radius)
d2 = droplets.SphericalDroplet(np.zeros(dim), radius)
d2.position = pos
assert d1.dim == dim
assert d1.volume > 0
assert d1.surface_area > 0
assert d1 == d2
d3 = d1.copy()
assert d1 == d3
assert d1 is not d3
vol = np.random.uniform(10, 30)
d2.volume = vol
assert d2.volume == pytest.approx(vol)
f = d1.get_phase_field(UnitGrid([10] * dim),
vmin=0.2,
vmax=0.8,
label="test")
assert f.label == "test"
assert np.all(f.data >= 0.2)
assert np.all(f.data <= 0.8)
assert np.any(f.data == 0.2)
assert np.any(f.data == 0.8)
def test_from_data():
""" test the from_data constructor """
for d1 in [
droplets.SphericalDroplet((1, ), 2),
droplets.SphericalDroplet((1, 2), 3),
droplets.PerturbedDroplet2D((1, 2), 3, 0.1, [0.1, 0.2]),
droplets.PerturbedDroplet3D((1, 2, 3), 4, 0.1, [0.1, 0.2]),
]:
d2 = d1.__class__.from_data(d1.data)
assert d1 == d2
assert d1 is not d2
def test_surface_area():
""" test surface area calculation of droplets """
# perturbed 2d droplet
R0 = 3
amplitudes = np.random.uniform(-1e-2, 1e-2, 6)
# unperturbed droplets
d1 = droplets.SphericalDroplet([0, 0], R0)
d2 = droplets.PerturbedDroplet2D([0, 0], R0)
assert d1.surface_area == pytest.approx(d2.surface_area)
assert d2.surface_area == pytest.approx(d2.surface_area_approx)
# perturbed droplet
d1 = droplets.SphericalDroplet([0, 0], R0)
d2 = droplets.PerturbedDroplet2D([0, 0], R0, amplitudes=amplitudes)
assert d1.surface_area != pytest.approx(d2.surface_area)
assert d2.surface_area == pytest.approx(d2.surface_area_approx, rel=1e-4)
def test_simple_droplet():
""" test a given simple droplet """
d = droplets.SphericalDroplet((1, 2), 1)
assert d.surface_area == pytest.approx(2 * np.pi)
np.testing.assert_allclose(d.interface_position(0), [2, 2])
np.testing.assert_allclose(d.interface_position([0]), [[2, 2]])
d.volume = 3
assert d.volume == pytest.approx(3)
def test_triangulation_2d():
""" test the 2d triangulation of droplets """
d1 = droplets.SphericalDroplet([1, 3], 5)
d2 = droplets.PerturbedDroplet2D([2, 4],
5,
amplitudes=[0.1, 0.2, 0.1, 0.2])
for drop in [d1, d2]:
tri = drop.get_triangulation(0.1)
l = sum(
np.linalg.norm(tri["vertices"][i] - tri["vertices"][j])
for i, j in tri["lines"])
assert l == pytest.approx(drop.surface_area, rel=1e-3), drop
def test_triangulation_3d():
""" test the 3d triangulation of droplets """
d1 = droplets.SphericalDroplet([1, 2, 3], 5)
d2 = droplets.PerturbedDroplet3D([2, 3, 4],
5,
amplitudes=[0.1, 0.2, 0.1, 0.2])
for drop in [d1, d2]:
tri = drop.get_triangulation(1)
vertices = tri["vertices"]
vol = 0
for a, b, c in tri["triangles"]:
# calculate the total volume by adding the volumes of the tetrahedra
mat = np.c_[vertices[a], vertices[b], vertices[c], drop.position]
mat = np.vstack([mat, np.ones(4)])
vol += abs(np.linalg.det(mat) / 6)
assert vol == pytest.approx(drop.volume, rel=0.1), drop
def test_timecourse():
"""test some droplet track functions"""
t1 = emulsions.EmulsionTimeCourse()
for i in range(4):
d = droplets.SphericalDroplet([i], i)
t1.append([d], i)
for track, length in [(t1, 4), (t1[:2], 2)]:
assert len(track) == length
assert track.times == list(range(length))
assert [t for t, _ in track.items()] == list(range(length))
assert t1 == t1[:]
assert t1[3:3] == emulsions.EmulsionTimeCourse()
t2 = emulsions.EmulsionTimeCourse(t1)
assert t1 == t2
assert t1 is not t2
t1.clear()
assert len(t1) == 0
def test_curvature():
""" test interface curvature calculation """
# spherical droplet
for dim in range(1, 4):
d = droplets.SphericalDroplet(np.zeros(dim),
radius=np.random.uniform(1, 4))
assert d.interface_curvature == pytest.approx(1 / d.radius)
# perturbed 2d droplet
R0 = 3
epsilon = 0.1
amplitudes = epsilon * np.array([0.1, 0.2, 0.3, 0.4])
def curvature_analytical(φ):
""" analytical expression for curvature """
radius = (
3.0 *
(5.0 * (40.0 + 27.0 * epsilon**2.0) + epsilon *
(40.0 * (4.0 * np.cos(2.0 * φ) + np.sin(φ)) + np.cos(φ) *
(80.0 + 66.0 * epsilon + 240.0 * np.sin(φ)) - epsilon *
(10.0 * np.cos(3.0 * φ) + 21.0 * np.cos(4.0 * φ) - 12.0 *
np.sin(φ) + 20.0 * np.sin(3.0 * φ) + 72.0 * np.sin(4.0 * φ))))
**(3.0 / 2.0) /
(10.0 * np.sqrt(2.0) *
(200.0 + 60.0 * epsilon *
(2.0 * np.cos(φ) + 8.0 * np.cos(2.0 * φ) + np.sin(φ) +
6.0 * np.sin(2.0 * φ)) + epsilon**2.0 *
(345.0 + 165.0 * np.cos(φ) - 5.0 * np.cos(3.0 * φ) -
21.0 * np.cos(4.0 * φ) + 30.0 * np.sin(φ) -
10.0 * np.sin(3.0 * φ) - 72.0 * np.sin(4.0 * φ)))))
return 1 / radius
d = droplets.PerturbedDroplet2D([0, 0], R0, amplitudes=amplitudes)
φs = np.linspace(0, np.pi, 64)
np.testing.assert_allclose(d.interface_curvature(φs),
curvature_analytical(φs),
rtol=1e-1)