style={"color":"MediumSeaGreen"}
class Sphere(m.Particle):
radius=3
frozen = True
style={"color":"orange"}
class Test(m.Particle):
radius=0
frozen = True
style={"color":"orange"}
p = m.Potential.morse(d=100, a=1, max=5)
m.bind(p, A, Sphere)
m.bind(p, A, Test)
m.bind(p, A, m.Cuboid)
m.bind(p, A, m.Universe.boundary_conditions.bottom)
m.bind(p, A, m.Universe.boundary_conditions.top)
m.bind(p, A, m.Universe.boundary_conditions.left)
m.bind(p, A, m.Universe.boundary_conditions.right)
m.bind(p, A, m.Universe.boundary_conditions.front)
m.bind(p, A, m.Universe.boundary_conditions.back)
# above the sphere
Sphere(m.Universe.center + [5, 0, 0])
A(m.Universe.center + [5, 0, Sphere.radius + dist])
class A(m.Particle):
radius = 0.5
dynamics = m.Overdamped
mass = 10
style = {"color": "MediumSeaGreen"}
class B(m.Particle):
radius = 0.5
dynamics = m.Overdamped
mass = 10
style = {"color": "skyblue"}
c1 = C(position=center - (3, 0, 0))
c2 = C(position=center + (7, 0, 0))
c1.A(2000)
c2.B(2000)
p1 = m.Potential.glj(e=7, m=1, max=1)
p2 = m.Potential.glj(e=7, m=1, max=2)
m.bind(p1, C.A, C.A, bound=True)
m.bind(p2, C.B, C.B, bound=True)
rforce = m.forces.random(0, 10)
m.bind(rforce, C.A)
m.bind(rforce, C.B)
m.run()
cutoff=cutoff)
# Create a 12-6 inter-atom potential
# The smallest radius for which the potential will be constructed.
# The largest radius for which the potential will be constructed.
# The first parameter of the Lennard-Jones potential.
# The second parameter of the Lennard-Jones potential.
# The tolerance to which the interpolation should match the exact
# potential.
pot_ArAr = m.Potential.LJ126(range=(0.275, 1.0),
A=9.5075e-06,
B=6.1545e-03,
tol=1.0e-3)
# bind the potential with Argon type
m.bind(pot_ArAr, Argon)
# create a lattice of particles
# these are number of particles in each dimension.
nx = ceil(pow(nr_parts, 1.0 / 3))
hx = dim[0] / nx
ny = ceil(sqrt(nr_parts / nx))
hy = dim[1] / ny
nz = ceil(nr_parts / nx / ny)
hz = dim[2] / nz
# iterate over the how many particles we want, set thier
# initial positions and velocities, and add them to the
# universe.
for i in range(0, nx):
x[0] = 0.05 + i * hx
#pot_yc = m.Potential.glj(e=500, r0=10, m=5, k=100, min=0.1, max=50*Cell.radius, tol=0.1)
pot_yc = m.Potential.glj(e=100,
r0=5,
m=3,
k=500,
min=0.1,
max=50 * Cell.radius,
tol=0.1)
pot_cc = m.Potential.glj(e=1, r0=2, m=2, min=0.05, max=2.2 * Cell.radius)
# bind the potential with the *TYPES* of the particles
m.Universe.bind(pot_yc, Yolk, Cell)
m.Universe.bind(pot_cc, Cell, Cell)
# create a random force. In overdamped dynamcis, we neeed a random force to
# enable the objects to move around, otherwise they tend to get trapped
# in a potential
rforce = m.forces.random(0, 100, durration=0.5)
# bind it just like any other force
m.bind(rforce, Cell)
yolk = Yolk(position=center - [0., 0., yshift])
for i, p in enumerate(m.random_points(m.SolidSphere, count)):
pos = p * clump_radius + center + [0., 0., cshift]
Cell(position=pos)
# run the simulator interactive
m.Simulator.run()
import mechanica as m
m.init(dt=0.1, dim=[15, 5, 5], cutoff = 3,
bc={'x':('periodic','reset')})
class A(m.Particle):
species = ['S1', 'S2', 'S3']
style = {"colormap" : {"species" : "S1",
"map" : "rainbow",
"range" : "auto"}}
a1 = A(m.universe.center - [0, 1, 0])
a2 = A(m.universe.center + [-5, 1, 0], velocity=[0.5, 0, 0])
pressure = m.forces.ConstantForce([0.1, 0, 0])
m.bind(pressure, A, "S1")
a1.species.S1 = 0
a2.species.S1 = 0.1
m.run()
epsilon=0.1,
r0=0.6,
eta=4,
tol=0.05,
min=0.01,
max=3)
pot_vb = m.Potential.soft_sphere(kappa=5,
epsilon=0,
r0=4.8,
eta=4,
tol=0.05,
min=3,
max=5.5)
# bind the potential with the *TYPES* of the particles
m.bind(pot_rr, Receptor, Receptor)
m.bind(pot_vr, Receptor, Virus)
m.bind(pot_vb, Big, Virus)
# create a random force (Brownian motion), zero mean of given amplitide
tstat = m.forces.random(0, 0.1)
vtstat = m.forces.random(0, 0.1)
# bind it just like any other force
m.bind(tstat, Receptor)
m.bind(vtstat, Virus)
b = Big(position=center, velocity=[0., 0., 0.])
Virus(position=center + [0, 0, Big.radius + 0.75])
import mechanica as m
import numpy as np
cutoff = 8
count = 3
# dimensions of universe
dim = np.array([20., 20., 20.])
center = dim / 2
m.init(dim=dim, cutoff=cutoff)
class B(m.Particle):
mass = 1
dynamics = m.Overdamped
# make a glj potential, this automatically reads the
# particle radius to determine rest distance.
pot = m.Potential.glj(e=1)
m.bind(pot, B, B)
p1 = B(center + (-2, 0, 0))
p2 = B(center + (2, 0, 0))
p1.radius = 1
p2.radius = 2
m.Simulator.run()
class C(m.Particle):
radius = 10
frozen = True
style = {"color": "orange"}
pc = m.Potential.glj(e=10, m=3, max=5)
pa = m.Potential.glj(e=2, m=4, max=3.0)
pb = m.Potential.glj(e=1, m=4, max=1)
pab = m.Potential.harmonic(k=10, r0=0, min=0.01, max=0.55)
# simple harmonic potential to pull particles
h = m.Potential.harmonic(k=40, r0=0.001, max=5)
m.bind(pc, A, C)
m.bind(pc, B, C)
m.bind(pa, A, A)
#m.bind(pb, B, B)
#m.bind(pab, A, B)
r = m.forces.random(0, 5)
m.bind(r, A)
#m.bind(r, B)
c = C(m.Universe.center)
pos_a = m.random_points(m.SolidSphere, 3000, dr=0.25, phi=(0, 0.60 * np.pi)) \
* ((1 + 0.25/2) * C.radius) + m.Universe.center
# locations of initial receptor positions
receptor_pts = m.random_points(m.SolidSphere, receptor_count) * 5 + center
pot_nr = m.Potential.well(k=15, n=3, r0=7)
pot_rr = m.Potential.soft_sphere(kappa=15,
epsilon=0,
r0=0.3,
eta=2,
tol=0.05,
min=0.01,
max=1)
# bind the potential with the *TYPES* of the particles
m.bind(pot_rr, Receptor, Receptor)
m.bind(pot_nr, Nucleus, Receptor)
# create a random force (Brownian motion), zero mean of given amplitide
tstat = m.forces.random(0, 3)
vtstat = m.forces.random(0, 5)
# bind it just like any other force
m.bind(tstat, Receptor)
n = Nucleus(position=center, velocity=[0., 0., 0.])
for p in receptor_pts:
Receptor(p)
# run the simulator interactive
style = {"color": "skyblue"}
class Yolk(m.Particle):
"""
The yolk type, only have a single instance of this
"""
radius = 10
frozen = True
style = {"color": "orange"}
# Make some potentials (forces) to connect the different cell types together.
m.bind(p_yolk, Cell, Yolk)
m.bind(p_yolk, Actin, Yolk)
m.bind(p_cell, Cell, Cell)
m.bind(p_cellactin, Cell, Actin)
r = m.forces.random(0, 5)
m.bind(r, Cell)
#m.bind(r, Actin)
# make a yolk at the center of the simulation domain
yolk = Yolk(m.Universe.center)
# create the initial cell positions
cell_positions = m.random_points(m.SolidSphere, 6000, dr=dr, phi=(0, epiboly_percent * np.pi)) \
* ((1 + dr/2) * Yolk.radius) + yolk.position
pot_yc = m.Potential.glj(e=100, r0=5, m=3, k=500, min=0.1, max=1.5 * Big.radius, tol=0.1)
#pot_cc = m.Potential.glj(e=0, r0=2, m=2, k=10, min=0.05, max=1 * Big.radius)
pot_cc = m.Potential.harmonic(r0=0, k=0.1, max=10)
#pot_yc = m.Potential.glj(e=10, r0=1, m=3, min=0.1, max=50*Small.radius, tol=0.1)
#pot_cc = m.Potential.glj(e=100, r0=5, m=2, min=0.05, max=0.5*Big.radius)
# bind the potential with the *TYPES* of the particles
m.Universe.bind(pot_yc, Big, Small)
m.Universe.bind(pot_cc, Small, Small)
# create a random force. In overdamped dynamcis, we neeed a random force to
# enable the objects to move around, otherwise they tend to get trapped
# in a potential
rforce = m.forces.random(0, 100, durration=0.5)
# bind it just like any other force
m.bind(rforce, Small)
yolk = Big(position=center)
for p in m.random_points(m.Sphere, count):
pos = p * (Big.radius + Small.radius) + center
Small(position=pos)
# run the simulator interactive
m.Simulator.run()
'x': 'periodic',
'z': 'no_slip',
'y': 'periodic'
},
perfcounter_period=100)
# lattice spacing
a = 0.7
class A(m.Particle):
radius = 0.3
style = {"color": "seagreen"}
dynamics = m.Newtonian
mass = 10
dpd = m.Potential.dpd(sigma=1.5)
m.bind(dpd, A, A)
f = m.forces.ConstantForce([0.01, 0, 0])
m.bind(f, A)
uc = m.lattice.sc(a, A)
parts = m.lattice.create_lattice(uc, [15, 15, 15])
m.run()
# simple harmonic potential to pull particles
h = m.Potential.harmonic(k=200, r0=0.001, max = 5)
#h = m.Potential.linear(k=0.5, max = 5)
#pb= m.Potential.glj(e=0.00001, r0=0.1, m=3, min=0.01, max=Blue.radius*3)
pb = m.Potential.coulomb(q=0.01, min=0.01, max=3)
# potential between the small and big particles
pot = m.Potential.glj(e=1, m=2, max=5)
Big(m.Universe.center)
Big.style.visible = False
m.bind(pot, Big, Blue)
m.bind(pb, Blue, Blue)
parts, bonds = m.bind_sphere(h, type=Blue, n=4, phi=(0.55 * np.pi, 1 * np.pi), radius = Big.radius + Blue.radius)
#for b in bonds:
# print("energy(", b.id, "): ", b.energy())
#print("parts: ", parts)
#parts[0].destroy()
'top':{'velocity':[-0.4, 0, 0]}},
perfcounter_period=100)
# lattice spacing
a = 0.3
#m.universe.boundary_conditions.left.restore = 0.5
class A (m.Particle):
radius = 0.2
style={"color":"seagreen"}
dynamics = m.Newtonian
mass=10
dpd = m.Potential.dpd(alpha=0.3, gamma=1, sigma=1, cutoff=0.6)
dpd_wall = m.Potential.dpd(alpha=0.5, gamma=10, sigma=1, cutoff=0.1)
dpd_left = m.Potential.dpd(alpha=1, gamma=100, sigma=0, cutoff=0.5)
m.bind(dpd, A, A)
m.bind(dpd_wall, A, m.Universe.boundary_conditions.top)
m.bind(dpd_left, A, m.Universe.boundary_conditions.left)
uc = m.lattice.sc(a, A)
parts = m.lattice.create_lattice(uc, [25, 25, 25])
print(m.universe.boundary_conditions)
m.show()
class B(m.Particle):
radius = 0.3
style = {"color": "red"}
dynamics = m.Overdamped
class Fixed(m.Particle):
radius = 0.3
style = {"color": "blue"}
frozen = True
repulse = m.Potential.coulomb(q=0.08, min=0.01, max=2 * a)
m.bind(repulse, A, A)
m.bind(repulse, A, B)
f = m.forces.ConstantForce(lambda: [0.3, 1 * np.sin(0.4 * m.Universe.time), 0],
0.01)
m.bind(f, B)
pot = m.Potential.power(r0=0.5 * a, alpha=2)
uc = m.lattice.sc(a, A,
lambda i, j: m.Bond(pot, i, j, dissociation_energy=1.3))
parts = m.lattice.create_lattice(uc, [15, 15, 15])
for p in parts[14, :].flatten():
class Sphere(m.Particle):
radius = 3
frozen = True
style = {"color": "orange"}
class Test(m.Particle):
radius = 0
frozen = True
style = {"color": "orange"}
p = m.Potential.glj(e=1, m=2, max=10)
m.bind(p, A, Sphere)
m.bind(p, A, Test)
m.bind(p, A, m.Cuboid)
m.bind(p, A, A)
# above the sphere
#Sphere(m.Universe.center + [5, 0, 0])
#A(m.Universe.center + [5, 0, 5.8])
# above the test
Test(m.Universe.center + [0, -10, 3])
#A(m.Universe.center + [0, -10, 5.8])
# above the scube
c = m.Cuboid(m.Universe.center + [0, 0, 0],
radius = 0.1
dynamics = m.Overdamped
mass = 5
style = {"color": "MediumSeaGreen"}
class B(m.Particle):
radius = 0.1
dynamics = m.Overdamped
mass = 10
style = {"color": "skyblue"}
p = m.Potential.coulomb(q=2, min=0.01, max=3)
m.bind(p, A, A)
m.bind(p, B, B)
m.bind(p, A, B)
r = m.forces.random(0, 1)
m.bind(r, A)
pos = m.random_points(m.SolidCube, 50000) * 10 + m.Universe.center
[A(p) for p in pos]
a = A.items()[0]
[p.become(B) for p in a.neighbors(3)]
pot_bb = m.Potential.soft_sphere(kappa=5, epsilon=0.25, r0=1, \
eta=2, tol = 0.05, min=0.01, max=3)
pot_ab = m.Potential.soft_sphere(kappa=5, epsilon=0.0025, r0=1, \
eta=2, tol = 0.05, min=0.01, max=3)
# bind the potential with the *TYPES* of the particles
m.Universe.bind(pot_aa, A, A)
m.Universe.bind(pot_bb, B, B)
m.Universe.bind(pot_ab, A, B)
# create a random force. In overdamped dynamcis, we neeed a random force to
# enable the objects to move around, otherwise they tend to get trapped
# in a potential
rforce = m.forces.random(0, 5)
# bind it just like any other force
m.bind(rforce, A)
m.bind(rforce, B)
# create particle instances, for a total A_count + B_count cells
for p in np.random.random((A_count, 3)) * 15 + 2.5:
A(p)
for p in np.random.random((B_count, 3)) * 15 + 2.5:
B(p)
# run the simulator
m.Simulator.run()
center = dim / 2
# new simulator, don't load any example
m.Simulator(example="", dim=dim, cutoff=cutoff)
class Bead(m.Particle):
mass = 1
radius = 0.5
dynamics = m.Overdamped
pot = m.Potential.glj(e=1)
# bind the potential with the *TYPES* of the particles
m.bind(pot, Bead, Bead)
# create a random force. In overdamped dynamcis, we neeed a random force to
# enable the objects to move around, otherwise they tend to get trapped
# in a potential
rforce = m.forces.random(0, 0.01)
m.bind(rforce, Bead)
r = 0.8 * Bead.radius
positions = [
center + (x, 0, 0) for x in np.arange(-count * r + r, count * r + r, 2 * r)
]
for p in positions:
print("position: ", p)
cutoff=10,
integrator=m.FORWARD_EULER,
cells=[3, 3, 3],
dt=0.001)
class A(m.Particle):
radius=1
dynamics = m.Newtonian
mass=20
style={"color":"MediumSeaGreen"}
p = m.Potential.glj(e=50, m=6, max=3)
cp = m.Potential.coulomb(q=5000, min=0.05, max=10)
m.bind(p, A, m.Cuboid)
m.bind(cp, A, A)
rforce = m.forces.friction(0.01, 0, 100)
# bind it just like any other force
m.bind(rforce, A)
c = m.Cuboid(m.Universe.center + [0, 0, 0], size=[25, 31, 5])
c.spin = [0.0, 8.5, 0.0]
# uniform random cube
positions = np.random.uniform(low=0, high=30, size=(2500, 3))
for p in positions:
pts = m.random_points(m.Sphere,
10000) * (Green.radius + Big.radius) + m.Universe.center
# make the big particle at the middle
Big(m.Universe.center)
# constuct a particle for each position, make
# a list of particles
beads = [Green(p) for p in pts]
# create an explicit bond for each pair in the
# list of particles. The bind_pairwise method
# searches for all possible pairs within a cutoff
# distance and connects them with a bond.
#m.bind_pairwise(pot, beads, 0.7)
rforce = m.forces.random(0, 0.01, durration=0.1)
# hook up the potentials
#m.bind(rforce, Green)
m.bind(pot_yc, Big, Green)
m.bind(pot_cc, Green, Green)
m.bind_pairwise(
pot,
[p
for p in m.Universe.particles if p.position[1] < m.Universe.center[1]], 1)
# run the model
m.show()
class Bead(m.Particle):
mass = 0.4
radius = 0.2
dynamics = m.Overdamped
pot_bb = m.Potential.soft_sphere(kappa=0.2, epsilon=0.05, \
r0=0.2, eta=4, tol=0.01, min=0.01, max=0.5)
# hamonic bond between particles
pot_bond = m.Potential.harmonic(k=0.4, r0=0.2, max=2)
# angle bond potential
pot_ang = m.Potential.harmonic_angle(k=0.2, theta0=0.85 * np.pi, tol=0.1)
# bind the potential with the *TYPES* of the particles
m.bind(pot_bb, Bead, Bead)
# create a random force. In overdamped dynamcis, we neeed a random force to
# enable the objects to move around, otherwise they tend to get trapped
# in a potential
rforce = m.forces.random(0, 0.1)
# bind it just like any other force
m.bind(rforce, Bead)
# make a array of positions
xx = np.arange(4., 16, 0.15)
p = None # previous bead
bead = Bead([xx[0], 10., 10.0]) # current bead
total_height = 2 * Yolk.radius + 2 * C.radius
yshift = total_height/2 - Yolk.radius
cshift = total_height/2 - C.radius - 1
yolk = Yolk(position=center-[0., 0., yshift])
c = C(position=center+[0., 0., cshift])
C.yolk_pos = yolk.position
c.B(4000)
pb = m.Potential.soft_sphere(kappa=300, epsilon=6, r0=0.5, \
eta=2, tol = 0.05, min=0.01, max=3)
pub = m.Potential.soft_sphere(kappa=400, epsilon=0, r0=0.5, \
eta=2, tol = 0.05, min=0.01, max=1.5)
py = m.Potential.soft_sphere(kappa=300, epsilon=25, r0=1, \
eta=2, tol = 0.04, min=0.01, \
max=10, shift=True)
rforce = m.forces.random(0, 1)
m.bind(rforce, C.B)
m.bind(pb, C.B, C.B, bound=True)
m.bind(pub, C.B, C.B, bound=False)
m.bind(py, Yolk, C.B)
m.Simulator.irun()
m.init(dim=dim,
cutoff=5,
integrator=m.FORWARD_EULER,
dt=0.001)
class A(m.Particle):
radius=0.1
dynamics = m.Overdamped
mass=5
style={"color":"MediumSeaGreen"}
class C(m.Particle):
radius=10
frozen = True
style={"color":"orange"}
C(m.Universe.center)
pos = m.random_points(m.Sphere, 5000) * (C.radius+A.radius) + m.Universe.center
[A(p) for p in pos]
pc = m.Potential.glj(e=30, m=2, max=5)
pa = m.Potential.coulomb(q=100, min=0.01, max=5)
m.bind(pc, A, C)
m.bind(pa, A, A)
m.show()
'bottom': {
'velocity': [0, 0, 0]
}
})
# lattice spacing
a = 0.15
class A(m.Particle):
radius = 0.05
style = {"color": "seagreen"}
dynamics = m.Newtonian
mass = 10
dpd = m.Potential.dpd(alpha=10, sigma=1)
m.bind(dpd, A, A)
# driving pressure
pressure = m.forces.ConstantForce([0.1, 0, 0])
m.bind(pressure, A)
uc = m.lattice.sc(a, A)
parts = m.lattice.create_lattice(uc, [40, 40, 40])
m.run()
# make a ring of of 50 particles pts = m.points(m.Ring, 100) * (C.radius+B.radius) + m.Universe.center - [0, 0, 1] #positions = m.random_points(m.SolidSphere, 5000) * 9 + m.Universe.center #[A(p) for p in pos_a if p[2] > m.Universe.center[2]] [B(p) for p in pts] pc = m.Potential.glj(e=30, m=2, max=5) pa = m.Potential.glj(e=3, m=2.5, max=3) pb = m.Potential.glj(e=1, m=4, max=1) pab = m.Potential.glj(e=1, m=2, max=1) ph = m.Potential.harmonic(r0=0.001, k=200) m.bind(pc, A, C) m.bind(pc, B, C) m.bind(pa, A, A) #m.bind(pb, B, B) m.bind(pab, A, B) r = m.forces.random(0, 5) m.bind(r, A) m.bind(r, B) #m.bind_pairwise(ph, [p for p in m.Universe.particles if p.position[2] < m.Universe.center[2] + 1], 2) m.bind_pairwise(ph, B.items(), 1) #m.bind_pairwise(ph, B.items(), 2) def update(e):
