def experiment(num_particles):
L = 0.25
D = 1
timesteps = 100000;
max_t = 4.0/(2.0*num_particles**0.5);
mol_dt = max_t/timesteps;
k2 = num_particles
k1 = 0.01
print 'hcrit = ',k1/(2.0*D)
binding = 0.01
unbinding = 0.01
A = tyche.new_species(D)
bd = tyche.new_diffusion()
bd.add_species(A)
xlow = tyche.new_xplane(0,1)
xhigh = tyche.new_xplane(L,-1)
ylow = tyche.new_yplane(0,1)
yhigh = tyche.new_yplane(L,-1)
zlow = tyche.new_zplane(0,1)
zhigh = tyche.new_zplane(L,-1)
xminboundary = tyche.new_jump_boundary(xlow,[L,0,0])
xmaxboundary = tyche.new_jump_boundary(xhigh,[-L,0,0])
yminboundary = tyche.new_jump_boundary(ylow,[0,L,0])
ymaxboundary = tyche.new_jump_boundary(yhigh,[0,-L,0])
zminboundary = tyche.new_jump_boundary(zlow,[0,0,L])
zmaxboundary = tyche.new_jump_boundary(zhigh,[0,0,-L])
boundaries = tyche.group([xminboundary, xmaxboundary, yminboundary, ymaxboundary, zminboundary, zmaxboundary])
boundaries.add_species(A)
dr2 = tyche.new_bi_reaction(k1, A, A, [A], binding,unbinding, mol_dt,
[0,0,0], [L,L,L], [True, True, True],True)
dr3 = tyche.new_bi_reaction(k1, A, A, [A], mol_dt,
[0,0,0], [L,L,L], [True, True, True],True)
dr = tyche.new_uni_reaction(k2,A,[A,A],unbinding)
algorithm = tyche.group([bd,boundaries,dr2,dr,boundaries])
A.fill_uniform([0,0,0],[L,L,L],int(num_particles*L**3/k1))
output_dt = max_t/100.0
time = 0;
print algorithm
for i in range(100):
print A
print 'time = ',time,' ',i,' percent done'
time = algorithm.integrate_for_time(output_dt,mol_dt)
# grid = tvtk.to_tvtk(A.get_vtk())
# g = init_vis(grid)
print algorithm
def experiment_ab(num_particles):
L = 0.5
#L = 50e-9
D = 1
#D = 1e-10
timesteps = 100000
#timesteps = 10000
max_t = 4.0/(2.0*num_particles**0.5);
mol_dt = max_t/timesteps
#mol_dt = 0.025*1e-8
#max_t = mol_dt * timesteps
k2 = num_particles
#k2 = 6.67e6
k1 = 1.0
#k1 = (k2*L**3)/num_particles
binding = 0.00303416
#binding = 3.76432e-10
unbinding = 0.15*0.00303416
#unbinding = 0.01*3.76432e-10
A = tyche.new_species(D)
B = tyche.new_species(D)
C = tyche.new_species(D)
bd = tyche.new_diffusion()
bd.add_species(A)
bd.add_species(B)
bd.add_species(C)
xlow = tyche.new_xplane(0,1)
xhigh = tyche.new_xplane(L,-1)
ylow = tyche.new_yplane(0,1)
yhigh = tyche.new_yplane(L,-1)
zlow = tyche.new_zplane(0,1)
zhigh = tyche.new_zplane(L,-1)
xminboundary = tyche.new_jump_boundary(xlow,[L,0,0])
xmaxboundary = tyche.new_jump_boundary(xhigh,[-L,0,0])
yminboundary = tyche.new_jump_boundary(ylow,[0,L,0])
ymaxboundary = tyche.new_jump_boundary(yhigh,[0,-L,0])
zminboundary = tyche.new_jump_boundary(zlow,[0,0,L])
zmaxboundary = tyche.new_jump_boundary(zhigh,[0,0,-L])
boundaries = tyche.group([xminboundary, xmaxboundary, yminboundary, ymaxboundary, zminboundary, zmaxboundary])
boundaries.add_species(A)
boundaries.add_species(B)
boundaries.add_species(C)
dr2 = tyche.new_bi_reaction(k1, A, B, [C], binding,unbinding, mol_dt,
[0,0,0], [L,L,L], [True, True, True],True)
dr3 = tyche.new_bi_reaction(k1, A, B, [C], mol_dt,
[0,0,0], [L,L,L], [True, True, True],True)
dr = tyche.new_uni_reaction(k2,C,[A,B],unbinding)
algorithm = tyche.group([bd,boundaries,dr2,dr,boundaries])
A.fill_uniform([0,0,0],[L,L,L],int(num_particles*L**3))
B.fill_uniform([0,0,0],[L,L,L],int(num_particles*L**3))
C.fill_uniform([0,0,0],[L,L,L],int(num_particles*L**3))
output_dt = max_t/100.0
time = 0;
print algorithm
for i in range(100):
print A,B,C
print 'time = ',time,' ',i,' percent done'
time = algorithm.integrate_for_time(output_dt,mol_dt)
# grid = tvtk.to_tvtk(A.get_vtk())
# g = init_vis(grid)
print algorithm
def experiment(num_particles):
L = 1
#L = 50e-9
D = 1
#D = 1e-10
timesteps = 100000
#timesteps = 10000
max_t = 4.0/(2.0*num_particles**0.5);
mol_dt = max_t/timesteps
#mol_dt = 0.025*1e-8
#max_t = mol_dt * timesteps
A = tyche.new_species(D)
B = tyche.new_species(D)
C = tyche.new_species(D)
bd = tyche.new_diffusion()
bd.add_species(A)
bd.add_species(B)
bd.add_species(C)
xlow = tyche.new_xplane(0,1)
xhigh = tyche.new_xplane(L,-1)
ylow = tyche.new_yplane(0,1)
yhigh = tyche.new_yplane(L,-1)
zlow = tyche.new_zplane(0,1)
zhigh = tyche.new_zplane(L,-1)
xminboundary = tyche.new_jump_boundary(xlow,[L,0,0])
xmaxboundary = tyche.new_jump_boundary(xhigh,[-L,0,0])
yminboundary = tyche.new_jump_boundary(ylow,[0,L,0])
ymaxboundary = tyche.new_jump_boundary(yhigh,[0,-L,0])
zminboundary = tyche.new_jump_boundary(zlow,[0,0,L])
zmaxboundary = tyche.new_jump_boundary(zhigh,[0,0,-L])
boundaries = tyche.group([xminboundary, xmaxboundary, yminboundary, ymaxboundary, zminboundary, zmaxboundary])
boundaries.add_species(A)
boundaries.add_species(B)
boundaries.add_species(C)
algorithm = tyche.group([bd,boundaries])
A.fill_uniform([0,0,0],[L,L,L],int(num_particles*L**3))
B.fill_uniform([0,0,0],[L,L,L],int(num_particles*L**3))
C.fill_uniform([0,0,0],[L,L,L],int(num_particles*L**3))
output_dt = max_t/100.0
time = 0;
print algorithm
for i in range(100):
print A,B,C
print 'time = ',time,' ',i,' percent done'
time = algorithm.integrate_for_time(output_dt,mol_dt)
grid = tvtk.to_tvtk(A.get_vtk())
g = init_vis(grid)
print algorithm
def experiment():
# Domain size
L = 1.0
# Number of compartments in x direction
num_comps = 20
# Diffusion constant
D = 1.0
# Assumed average number of particles to the left of domain (fixed
# concentration boundary conditions
A0 = 10
# Time step
mol_dt = 0.000001
# Create species
A = tyche.new_species(D)
# Create domain bounds
xlow = tyche.new_xplane(1e-5,1)
xghost = tyche.new_xplane(L/2.,1);
xhigh = tyche.new_xplane(L,-1)
ylow = tyche.new_yplane(0,1)
yhigh = tyche.new_yplane(L,-1)
zlow = tyche.new_zplane(0,1)
zhigh = tyche.new_zplane(L,-1)
# Create interface box
interface = tyche.new_box([0,0,0],[L/2.,L,L],True)
# Boundary conditions on the domain bounds and the interface
# Need a reflective boundary at the ghost cell interface
xghostboundary = tyche.new_reflective_boundary(xghost)
xminboundary = tyche.new_reflective_boundary(xlow)
xmaxboundary = tyche.new_reflective_boundary(xhigh)
yminboundary = tyche.new_reflective_boundary(ylow)
ymaxboundary = tyche.new_reflective_boundary(yhigh)
zminboundary = tyche.new_reflective_boundary(zlow)
zmaxboundary = tyche.new_reflective_boundary(zhigh)
# Add all boundaries to a single operator
boundaries = tyche.group([xghostboundary,xmaxboundary,yminboundary, ymaxboundary, zminboundary, zmaxboundary])
boundaries.add_species(A)
# Create compartments throughout the domain
compartments = tyche.new_compartments([0,0,0],[L,L,L],[L*1./num_comps,L,L])
compartments.add_diffusion(A);
# Boundary reaction on leftmost boundary (particle creation)
compartments.add_reaction_on(A0/(L/num_comps)**3, [[],[A]], xlow)
compartments.add_reaction_on(1./(L/num_comps)**2, [[A],[]], xlow)
# Removal reaction
compartments.add_reaction(1., [[A],[]])
# Introduce ghost cell interface at L/2
compartments.set_ghost_cell_interface(interface)
# Diffusion operator with tracking (tracks number of particles in ghost
# compartment at the interface
bd = tyche.new_diffusion_with_tracking(interface,compartments)
bd.add_species(A)
# Removal reaction in molecular domain
remove = tyche.new_uni_reaction(1., [[A],[]])
# Create algorithm
algorithm = tyche.group([bd,boundaries,compartments, remove])
# Get data every Dt
output_dt = 1e-2
# Set up plotting
ion()
figure()
ax = subplot(211)
ax2 = subplot(212)
# List to hold number of particles in compartments
nums = []
# Run until steady state is reached
time = algorithm.integrate_for_time(5.,mol_dt)
while True:
# Collect data
for i in range(10):
# Run for Dt
time = algorithm.integrate_for_time(output_dt,mol_dt)
# Put molecules in bins similar to compartment spacing
h,b = histogram(A.get_particles()[0], range=(0,L), bins=num_comps)
# Get compartment data
c = A.get_compartments()[:,0,0]
# Fix ghost compartment so that we do not count it twice
c[num_comps/2] = 0
# Add compartments to molecule histogram
h += c
nums.append(h)
#P Plotting
ax.clear()
ax2.clear()
x = (arange(0,num_comps)+0.5)*L*1./num_comps
# Plot mean number of particles
ax.plot(x,mean(nums,axis=0))
# Solution for steady state of reaction-diffusion PDE (has an error
# whereby the first compartment should be shifted by h/2)
ax.plot((1-x), A0*1./cosh(1.)*cosh(x))
# Plot standard deviation
ax2.plot(x,std(nums,axis=0))
ax.set_xlabel("x")
ax.set_ylabel("Mean Frequency")
ax2.set_xlabel("x")
ax2.set_ylabel("Standard deviation")
draw()
A.set_grid(grid)
dummy.set_grid(grid)
not_dummy.set_grid(grid)
xlow = tyche.new_xplane(0,1)
xhigh = tyche.new_xplane(L,-1)
xminboundary = tyche.new_reflective_boundary(xlow)
xmaxboundary = tyche.new_reflective_boundary(xhigh)
sink = tyche.new_uni_reaction(conversion_rate,[[A,dummy.pde()],[A.pde()]])
source = tyche.new_zero_reaction_lattice(conversion_rate,[[A.pde(),not_dummy.pde()],[A]])
uni = tyche.new_uni_reaction(k,[[A],[]])
flux = tyche.new_zero_reaction(lam/dx,[0,0,0],[dx,1,1])
diffusion = tyche.new_diffusion()
algorithm = tyche.group([diffusion,xminboundary,flux,uni,sink,source])
algorithm.add_species(A)
############
# Plotting #
############
def concentration_gradient(x,t):
exact = (lam/(D*beta)) * (
np.exp(-beta*(x))
- 0.5*np.exp(-beta*(x))*erfc((2.0*beta*D*t-(x))/np.sqrt(4.0*D*t))
- 0.5*np.exp(beta*(x))*erfc((2.0*beta*D*t+(x))/np.sqrt(4.0*D*t))
)
return exact
def experiment():
L = 1.0
num_comps = 20
D = 1.0
num_particles = 100
mol_dt = 0.000001
A = tyche.new_species(D)
xlow = tyche.new_xplane(0,1)
xghost = tyche.new_xplane(L/2.,1);
xhigh = tyche.new_xplane(L,-1)
ylow = tyche.new_yplane(0,1)
yhigh = tyche.new_yplane(L,-1)
zlow = tyche.new_zplane(0,1)
zhigh = tyche.new_zplane(L,-1)
interface = tyche.new_box([0,0,0],[L/2.,L,L],True)
xghostboundary = tyche.new_reflective_boundary(xghost)
xminboundary = tyche.new_reflective_boundary(xlow)
xmaxboundary = tyche.new_reflective_boundary(xhigh)
yminboundary = tyche.new_reflective_boundary(ylow)
ymaxboundary = tyche.new_reflective_boundary(yhigh)
zminboundary = tyche.new_reflective_boundary(zlow)
zmaxboundary = tyche.new_reflective_boundary(zhigh)
boundaries = tyche.group([xghostboundary,xmaxboundary,yminboundary, ymaxboundary, zminboundary, zmaxboundary])
boundaries.add_species(A)
compartments = tyche.new_compartments([0,0,0],[L,L,L],[L*1./num_comps,L,L])
compartments.fill_uniform(A, [0,0,0],[L/2.,L,L],num_particles/2)
compartments.add_diffusion(A);
A.fill_uniform([L/2.,0,0], [L,L,L], num_particles/2)
compartments.set_ghost_cell_interface(interface)
ghostcoupling = tyche.new_ghost_cell_boundary(interface,compartments)
ghostcoupling.add_species(A)
bd = tyche.new_diffusion_with_tracking(interface,compartments)
bd.add_species(A)
algorithm = tyche.group([bd,boundaries,compartments])
compartments.list_reactions()
output_dt = 1e-2
time = 0;
print algorithm
ion()
figure()
ax = subplot(211)
ax2 = subplot(212)
nums = []
while True:
for i in range(10):
time = algorithm.integrate_for_time(output_dt,mol_dt)
h,b = histogram(A.get_particles()[0], range=(0,L), bins=num_comps)
c = A.get_compartments()[:,0,0]
c[num_comps/2] = 0
h += c
if h.sum()!=num_particles:
raise ValueError("Inconsistent Ghost Cell! Number of particles is %d and not %d as it should be!" % (h.sum(), num_particles))
nums.append(h)
ax.clear()
ax2.clear()
x = (arange(0,num_comps)+0.5)*L*1./num_comps
ax.plot(x,mean(nums,axis=0))
ax2.plot(x,std(nums,axis=0))
ax2.set_xlabel(str(time))
ax.set_xlabel("x")
ax.set_ylabel("Mean Frequency")
ax2.set_xlabel("x")
ax2.set_ylabel("Standard deviation")
draw()
xlow = tyche.new_xplane(0,1) xhigh = tyche.new_xplane(L,-1) xminboundary = tyche.new_reflective_boundary(xlow) xmaxboundary = tyche.new_reflective_boundary(xhigh) #set off-lattice sink and source sink = tyche.new_uni_reaction(conversion_rate,[[A],[A.pde()]]) pde_region = tyche.new_xplane(interface,1) sink.set_geometry(0,pde_region) source = tyche.new_zero_reaction_lattice(conversion_rate,[[A.pde()],[A]]) offlattice_region = tyche.new_xplane(interface,1) source.set_geometry(offlattice_region) diffusion = tyche.new_diffusion() algorithm = tyche.group([diffusion,sink,source,xminboundary, xmaxboundary]) algorithm.add_species(A) mesh = Grid1D(nx=nx, dx=dx) phi = CellVariable(name="solution variable", mesh=mesh, value=1000.) # setup plotting plt.figure() x = np.arange(0,L,dx) plot_pde, = plt.plot(x,phi.value,linewidth=2,label='PDE') off_lattice_concentration = A.get_concentration([0,0,0],[L,1,1],[nx,1,1]) plot_off_lattice = plt.bar(x,off_lattice_concentration[:,0,0],width=dx) plt.legend() plt.ylim(0,1200) for step in range(steps):
def experiment(num_particles,timesteps):
L = 1
D = 1
k2 = 1000.0
k1 = k2/num_particles**3
max_t = 1.0
DAB = D+D;
DABC = D + D*D/DAB;
Rsq = ( k1 / (4*3.14**3*(DAB*DABC)**(3.0/2.0) ) )**0.5;
mol_dt = Rsq/10000;
A = tyche.new_species(D)
B = tyche.new_species(D)
C = tyche.new_species(D)
bd = tyche.new_diffusion()
bd.add_species(A)
bd.add_species(B)
bd.add_species(C)
xlow = tyche.new_xplane(0,1)
xhigh = tyche.new_xplane(L,-1)
ylow = tyche.new_yplane(0,1)
yhigh = tyche.new_yplane(L,-1)
zlow = tyche.new_zplane(0,1)
zhigh = tyche.new_zplane(L,-1)
xminboundary = tyche.new_jump_boundary(xlow,[L,0,0])
xmaxboundary = tyche.new_jump_boundary(xhigh,[-L,0,0])
yminboundary = tyche.new_jump_boundary(ylow,[0,L,0])
ymaxboundary = tyche.new_jump_boundary(yhigh,[0,-L,0])
zminboundary = tyche.new_jump_boundary(zlow,[0,0,L])
zmaxboundary = tyche.new_jump_boundary(zhigh,[0,0,-L])
boundaries = tyche.group([xminboundary, xmaxboundary, yminboundary, ymaxboundary, zminboundary, zmaxboundary])
boundaries.add_species(A)
boundaries.add_species(B)
boundaries.add_species(C)
dr3 = tyche.new_tri_reaction(k1, A, B, C, [B,C], mol_dt,
[0,0,0], [L,L,L], [True, True, True])
dr = tyche.new_zero_reaction(k2,[0,0,0],[L,L,L])
dr.add_species(A)
algorithm = tyche.group([bd,boundaries,dr,dr3])
A.fill_uniform([0,0,0],[L,L,L],int(num_particles))
B.fill_uniform([0,0,0],[L,L,L],int(num_particles))
C.fill_uniform([0,0,0],[L,L,L],int(num_particles))
N = 1000
output_dt = max_t/N
time = 0;
print algorithm
grid = tvtk.to_tvtk(A.get_vtk())
numA = np.zeros(N)
for i in range(N):
print A,B,C
numA[i] = A.get_concentration([0,0,0],[L,L,L],[1,1,1])[0]
print 'time = ',time,' ',i*100.0/N,' percent done'
time = algorithm.integrate_for_time(output_dt,mol_dt)
# grid = tvtk.to_tvtk(A.get_vtk())
# g = init_vis(grid)
print algorithm
return numA
def experiment():
L = 1.0
D = 1.0
num_particles = 10000.0
max_t = 10.0;
factor = 2.0;
mol_dt = 0.001
A = tyche.new_species(D)
bd = tyche.new_diffusion()
bd.add_species(A)
xlow = tyche.new_xplane(0,1)
xhigh = tyche.new_xplane(L,-1)
ylow = tyche.new_yplane(0,1)
yhigh = tyche.new_yplane(L,-1)
zlow = tyche.new_zplane(0,1)
zhigh = tyche.new_zplane(L,-1)
interface = tyche.new_box([0,0,0],[L/2.0,L,L],True)
xminboundary = tyche.new_reflective_boundary(xlow)
yminboundary = tyche.new_reflective_boundary(ylow)
ymaxboundary = tyche.new_reflective_boundary(yhigh)
zminboundary = tyche.new_reflective_boundary(zlow)
zmaxboundary = tyche.new_reflective_boundary(zhigh)
boundaries = tyche.group([xminboundary, yminboundary, ymaxboundary, zminboundary, zmaxboundary])
boundaries.add_species(A)
dr = tyche.new_uni_reaction(1.0,[[A],[]])
compartments = tyche.new_compartments([0,0,0],[L,L,L],[L/20.0,L,L])
compartments.add_diffusion(A);
compartments.add_reaction(1.0,[[A],[]])
compartments.add_reaction_on(num_particles*20.0/L,[[],[A]],xlow)
corrected_interface = True
compartments.set_interface(interface, mol_dt, corrected_interface)
coupling = tyche.new_coupling_boundary(interface,compartments,corrected_interface)
coupling.add_species(A)
algorithm = tyche.group([bd,compartments,dr,boundaries,coupling])
output_dt = max_t/100.0
time = 0;
print algorithm
# plt.figure()
# plt.ion()
# concentration = A.get_concentration([0,0,0],[2.0*L,L,L],[40,1,1])
# x = np.arange(0,2.0*L,L/20.0)
# l, = plt.plot(x,concentration[:,0,0])
# plt.ylim([0,num_particles])
for i in range(100):
print A
print 'time = ',time,' ',i,' percent done'
time = algorithm.integrate_for_time(output_dt,mol_dt)
# concentration = A.get_concentration([0,0,0],[2.0*L,L,L],[40,1,1])
# l.set_ydata(concentration[:,0,0])
# plt.draw()
# x,y,z = A.get_particles()
# mlab.points3d(np.array(x),np.array(y),np.array(z),scale_factor = 0.05,color=(1,1,1))
# [0,0,0],[L,L,L],[L/20.0,L,L]
# x, y, z = np.mgrid[0:L:L/20.0, 0:L:L, 0:L:L]
# comps = A.get_compartments()
# values = tools.pipeline.scalar_field(x,y,z,comps)
# mlab.pipeline.volume(values)
print algorithm
