Note
Go to the end to download the full example code.
Jamming of bidisperse spheres (or disks).#
In this example, we use a bisection search to find the nearest jammed state for a set of random configurations of bidisperse spheres (or disks). The particles sit in a 3D (or 2D) periodic box.
The particles use a purely repulsive harmonic interaction potential. The potential energy is zero when the particles are not in contact. Otherwise it is proportional to the square of the overlap distance.
The bisection search works as follows. It compresses the box in small steps (equivalently, it grows the radii of the particles) and minimizes the total potential energy after each step. If the potential energy is nonzero after a compression, the state is possibly jammed. The algorithm then goes back to the last unjammed state and runs a bisection search between the jammed and unjammed states. It finds the largest packing fraction in these bounds whose total potential energy is near zero. Compressing beyond this packing fraction increases the potential energy sharply.
bisection_jam() implements the bisection search.
Imports#
import jax
import jax.numpy as jnp
import jaxdem as jdem
# We enable double precision to reach the accuracy that conventional jamming analysis needs.
jax.config.update("jax_enable_x64", True)
Parameters#
We jam 10 systems of 10 particles in parallel. This shows system-level parallelism in JaxDEM. Note that the parallel run is only as fast as the slowest system. Close to jamming, the systems take longer to minimize, so the jamming algorithm can be slow when you parallelize over many systems. We place the particles randomly in the box at an initial packing fraction of 0.4.
N_systems = 10
N = 10
phi = 0.4
dim = 2
e_int = 1.0
dt = 1e-2
# For the one-call equivalent see
# :func:`~jaxdem.utils.particle_creation.build_sphere_system`
# (sphere_construction example).
def build_microstate(i):
# assign bidisperse radii
rad = jnp.ones(N)
rad = rad.at[: N // 2].set(0.5)
rad = rad.at[N // 2 :].set(0.7)
# set the box size for the packing fraction and the radii
volume = (jnp.pi ** (dim / 2) / jax.scipy.special.gamma(dim / 2 + 1)) * rad**dim
L = (jnp.sum(volume) / phi) ** (1 / dim)
box_size = jnp.ones(dim) * L
# create microstate
key = jax.random.PRNGKey(i)
pos = jax.random.uniform(key, (N, dim), minval=0.0, maxval=L)
mass = jnp.ones(N)
mats = [jdem.Material.create("elastic", young=e_int, poisson=0.5, density=1.0)]
matcher = jdem.MaterialMatchmaker.create("harmonic")
mat_table = jdem.MaterialTable.from_materials(mats, matcher=matcher)
# create system and state
state = jdem.State.create(pos=pos, rad=rad, mass=mass, volume=volume)
system = jdem.System.create(
state_shape=state.shape,
dt=dt,
minimizer=jdem.minimizers.fire,
minimizer_kw={"dt": dt},
domain_type="periodic",
force_model_type="spring",
collider_type="naive",
mat_table=mat_table,
domain_kw={
"box_size": box_size,
},
)
return state, system
Run the Jamming Algorithm for Multiple Systems#
We first create the systems and states with JAX’s vmap function. This creates 10 states and systems in parallel. We could also use the State.stack method to join a list of states and systems.
state, system = jax.vmap(build_microstate)(jnp.arange(N_systems))
# We then run the jamming algorithm on the systems with JAX's vmap function.
# This runs the jamming algorithm on each system in parallel.
# It returns a :class:`~jaxdem.utils.jamming.JamResult` named tuple with the last
# unjammed state/system, the jammed state/system, and the jammed state's
# packing fraction and potential energy.
# The final potential energy per particle should be less than the tolerance of 1e-16.
result = jax.vmap(lambda st, sys: jdem.utils.jamming.bisection_jam(st, sys))(
state, system
)
state, system = result.jammed_state, result.jammed_system
print(f"Final potential energy: {result.potential_energy}")
print(f"Final packing fraction: {result.packing_fraction}")
Initial minimization took 68 steps.
Initial minimization took 61 steps.
Initial minimization took 108 steps.
Initial minimization took 67 steps.
Initial minimization took 71 steps.
Initial minimization took 78 steps.
Warning: Initial state is already jammed (PE=0.0 > tol=1e-16). Skipping.
Warning: Initial state is already jammed (PE=0.0 > tol=1e-16). Skipping.
Warning: Initial state is already jammed (PE=0.0 > tol=1e-16). Skipping.
Initial minimization took 115 steps.
Initial minimization took 76 steps.
Initial minimization took 47 steps.
Initial minimization took 89 steps.
Warning: Initial state is already jammed (PE=0.0 > tol=1e-16). Skipping.
Warning: Initial state is already jammed (PE=0.0 > tol=1e-16). Skipping.
Warning: Initial state is already jammed (PE=0.0 > tol=1e-16). Skipping.
Warning: Initial state is already jammed (PE=0.0 > tol=1e-16). Skipping.
Warning: Initial state is already jammed (PE=0.0 > tol=1e-16). Skipping.
Warning: Initial state is already jammed (PE=0.0 > tol=1e-16). Skipping.
Warning: Initial state is already jammed (PE=0.0 > tol=1e-16). Skipping.
Step: 1 - phi=0.4000000000000001, PE=0.0 after 0 steps
Step: 1 - phi=0.4000000000000001, PE=0.0 after 0 steps
Step: 1 - phi=0.4000000000000001, PE=0.0 after 0 steps
Step: 1 - phi=0.4000000000000001, PE=0.0 after 0 steps
Step: 1 - phi=0.4000000000000001, PE=0.0 after 0 steps
Step: 1 - phi=0.4000000000000001, PE=0.0 after 0 steps
Step: 1 - phi=0.4000000000000001, PE=0.0 after 0 steps
Step: 1 - phi=0.4000000000000001, PE=0.0 after 0 steps
Step: 1 - phi=0.4000000000000001, PE=0.0 after 0 steps
Step: 1 - phi=0.4000000000000001, PE=0.0 after 0 steps
Step: 2 - phi=0.4010000000000001, PE=0.0 after 35 steps
Step: 2 - phi=0.4010000000000001, PE=0.0 after 35 steps
Step: 2 - phi=0.4010000000000001, PE=0.0 after 35 steps
Step: 2 - phi=0.4010000000000001, PE=0.0 after 35 steps
Step: 2 - phi=0.4010000000000001, PE=0.0 after 0 steps
Step: 2 - phi=0.4010000000000001, PE=0.0 after 0 steps
Step: 2 - phi=0.4010000000000001, PE=0.0 after 35 steps
Step: 2 - phi=0.4010000000000001, PE=0.0 after 41 steps
Step: 2 - phi=0.4010000000000001, PE=0.0 after 67 steps
Step: 2 - phi=0.4010000000000001, PE=0.0 after 0 steps
Step: 3 - phi=0.4020000000000001, PE=0.0 after 35 steps
Step: 3 - phi=0.4020000000000001, PE=0.0 after 35 steps
Step: 3 - phi=0.4020000000000001, PE=0.0 after 35 steps
Step: 3 - phi=0.4020000000000001, PE=0.0 after 35 steps
Step: 3 - phi=0.4020000000000001, PE=0.0 after 35 steps
Step: 3 - phi=0.4020000000000001, PE=0.0 after 0 steps
Step: 3 - phi=0.4020000000000001, PE=0.0 after 35 steps
Step: 3 - phi=0.4020000000000001, PE=0.0 after 46 steps
Step: 3 - phi=0.4020000000000001, PE=0.0 after 41 steps
Step: 3 - phi=0.4020000000000001, PE=0.0 after 35 steps
Step: 4 - phi=0.4030000000000001, PE=0.0 after 35 steps
Step: 4 - phi=0.4030000000000001, PE=0.0 after 35 steps
Step: 4 - phi=0.4030000000000001, PE=0.0 after 35 steps
Step: 4 - phi=0.4030000000000001, PE=0.0 after 35 steps
Step: 4 - phi=0.4030000000000001, PE=0.0 after 35 steps
Step: 4 - phi=0.4030000000000001, PE=0.0 after 0 steps
Step: 4 - phi=0.4030000000000001, PE=0.0 after 35 steps
Step: 4 - phi=0.4030000000000001, PE=0.0 after 43 steps
Step: 4 - phi=0.4030000000000001, PE=0.0 after 41 steps
Step: 4 - phi=0.4030000000000001, PE=0.0 after 35 steps
Step: 5 - phi=0.4040000000000001, PE=0.0 after 35 steps
Step: 5 - phi=0.4040000000000001, PE=0.0 after 38 steps
Step: 5 - phi=0.4040000000000001, PE=0.0 after 35 steps
Step: 5 - phi=0.4040000000000001, PE=0.0 after 35 steps
Step: 5 - phi=0.4040000000000001, PE=0.0 after 35 steps
Step: 5 - phi=0.4040000000000001, PE=0.0 after 35 steps
Step: 5 - phi=0.4040000000000001, PE=0.0 after 35 steps
Step: 5 - phi=0.4040000000000001, PE=0.0 after 43 steps
Step: 5 - phi=0.4040000000000001, PE=0.0 after 41 steps
Step: 5 - phi=0.4040000000000001, PE=0.0 after 35 steps
Step: 6 - phi=0.4050000000000001, PE=0.0 after 35 steps
Step: 6 - phi=0.4050000000000001, PE=0.0 after 38 steps
Step: 6 - phi=0.4050000000000001, PE=0.0 after 35 steps
Step: 6 - phi=0.4050000000000001, PE=0.0 after 35 steps
Step: 6 - phi=0.4050000000000001, PE=0.0 after 35 steps
Step: 6 - phi=0.4050000000000001, PE=0.0 after 35 steps
Step: 6 - phi=0.4050000000000001, PE=0.0 after 35 steps
Step: 6 - phi=0.4050000000000001, PE=0.0 after 43 steps
Step: 6 - phi=0.4050000000000001, PE=0.0 after 41 steps
Step: 6 - phi=0.4050000000000001, PE=0.0 after 35 steps
Step: 7 - phi=0.4060000000000001, PE=0.0 after 35 steps
Step: 7 - phi=0.4060000000000001, PE=0.0 after 41 steps
Step: 7 - phi=0.4060000000000001, PE=0.0 after 35 steps
Step: 7 - phi=0.4060000000000001, PE=0.0 after 35 steps
Step: 7 - phi=0.4060000000000001, PE=0.0 after 35 steps
Step: 7 - phi=0.4060000000000001, PE=0.0 after 35 steps
Step: 7 - phi=0.4060000000000001, PE=0.0 after 35 steps
Step: 7 - phi=0.4060000000000001, PE=0.0 after 43 steps
Step: 7 - phi=0.4060000000000001, PE=0.0 after 41 steps
Step: 7 - phi=0.4060000000000001, PE=0.0 after 35 steps
Step: 8 - phi=0.4070000000000001, PE=0.0 after 35 steps
Step: 8 - phi=0.4070000000000001, PE=0.0 after 38 steps
Step: 8 - phi=0.4070000000000001, PE=0.0 after 35 steps
Step: 8 - phi=0.4070000000000001, PE=0.0 after 35 steps
Step: 8 - phi=0.4070000000000001, PE=0.0 after 35 steps
Step: 8 - phi=0.4070000000000001, PE=0.0 after 35 steps
Step: 8 - phi=0.4070000000000001, PE=0.0 after 35 steps
Step: 8 - phi=0.4070000000000001, PE=0.0 after 42 steps
Step: 8 - phi=0.4070000000000001, PE=0.0 after 64 steps
Step: 8 - phi=0.4070000000000001, PE=0.0 after 35 steps
Step: 9 - phi=0.4080000000000001, PE=0.0 after 35 steps
Step: 9 - phi=0.4080000000000001, PE=0.0 after 41 steps
Step: 9 - phi=0.4080000000000001, PE=0.0 after 35 steps
Step: 9 - phi=0.4080000000000001, PE=0.0 after 35 steps
Step: 9 - phi=0.4080000000000001, PE=0.0 after 41 steps
Step: 9 - phi=0.4080000000000001, PE=0.0 after 45 steps
Step: 9 - phi=0.4080000000000001, PE=0.0 after 35 steps
Step: 9 - phi=0.4080000000000001, PE=0.0 after 42 steps
Step: 9 - phi=0.4080000000000001, PE=0.0 after 50 steps
Step: 9 - phi=0.4080000000000001, PE=0.0 after 35 steps
Step: 10 - phi=0.4090000000000001, PE=0.0 after 35 steps
Step: 10 - phi=0.4090000000000001, PE=0.0 after 48 steps
Step: 10 - phi=0.4090000000000001, PE=0.0 after 35 steps
Step: 10 - phi=0.4090000000000001, PE=0.0 after 35 steps
Step: 10 - phi=0.4090000000000001, PE=0.0 after 39 steps
Step: 10 - phi=0.4090000000000001, PE=0.0 after 42 steps
Step: 10 - phi=0.4090000000000001, PE=0.0 after 35 steps
Step: 10 - phi=0.4090000000000001, PE=0.0 after 42 steps
Step: 10 - phi=0.4090000000000001, PE=0.0 after 48 steps
Step: 10 - phi=0.4090000000000001, PE=0.0 after 35 steps
Step: 11 - phi=0.4100000000000001, PE=0.0 after 35 steps
Step: 11 - phi=0.4100000000000001, PE=0.0 after 47 steps
Step: 11 - phi=0.4100000000000001, PE=0.0 after 35 steps
Step: 11 - phi=0.4100000000000001, PE=0.0 after 35 steps
Step: 11 - phi=0.4100000000000001, PE=0.0 after 38 steps
Step: 11 - phi=0.4100000000000001, PE=0.0 after 41 steps
Step: 11 - phi=0.4100000000000001, PE=0.0 after 35 steps
Step: 11 - phi=0.4100000000000001, PE=0.0 after 42 steps
Step: 11 - phi=0.4100000000000001, PE=0.0 after 49 steps
Step: 11 - phi=0.4100000000000001, PE=0.0 after 35 steps
Step: 12 - phi=0.4110000000000001, PE=0.0 after 35 steps
Step: 12 - phi=0.4110000000000001, PE=0.0 after 48 steps
Step: 12 - phi=0.4110000000000001, PE=0.0 after 35 steps
Step: 12 - phi=0.4110000000000001, PE=0.0 after 35 steps
Step: 12 - phi=0.4110000000000001, PE=0.0 after 38 steps
Step: 12 - phi=0.4110000000000001, PE=0.0 after 41 steps
Step: 12 - phi=0.4110000000000001, PE=0.0 after 35 steps
Step: 12 - phi=0.4110000000000001, PE=0.0 after 42 steps
Step: 12 - phi=0.4110000000000001, PE=0.0 after 49 steps
Step: 12 - phi=0.4110000000000001, PE=0.0 after 35 steps
Step: 13 - phi=0.4120000000000001, PE=0.0 after 35 steps
Step: 13 - phi=0.4120000000000001, PE=0.0 after 48 steps
Step: 13 - phi=0.4120000000000001, PE=0.0 after 35 steps
Step: 13 - phi=0.4120000000000001, PE=0.0 after 35 steps
Step: 13 - phi=0.4120000000000001, PE=0.0 after 38 steps
Step: 13 - phi=0.4120000000000001, PE=0.0 after 40 steps
Step: 13 - phi=0.4120000000000001, PE=0.0 after 35 steps
Step: 13 - phi=0.4120000000000001, PE=0.0 after 42 steps
Step: 13 - phi=0.4120000000000001, PE=0.0 after 49 steps
Step: 13 - phi=0.4120000000000001, PE=0.0 after 35 steps
Step: 14 - phi=0.4130000000000001, PE=0.0 after 66 steps
Step: 14 - phi=0.4130000000000001, PE=0.0 after 50 steps
Step: 14 - phi=0.4130000000000001, PE=0.0 after 35 steps
Step: 14 - phi=0.4130000000000001, PE=0.0 after 35 steps
Step: 14 - phi=0.4130000000000001, PE=0.0 after 35 steps
Step: 14 - phi=0.4130000000000001, PE=0.0 after 38 steps
Step: 14 - phi=0.4130000000000001, PE=0.0 after 40 steps
Step: 14 - phi=0.4130000000000001, PE=0.0 after 35 steps
Step: 14 - phi=0.4130000000000001, PE=0.0 after 42 steps
Step: 14 - phi=0.4130000000000001, PE=0.0 after 49 steps
Step: 15 - phi=0.4140000000000001, PE=0.0 after 42 steps
Step: 15 - phi=0.4140000000000001, PE=0.0 after 48 steps
Step: 15 - phi=0.4140000000000001, PE=0.0 after 35 steps
Step: 15 - phi=0.4140000000000001, PE=0.0 after 35 steps
Step: 15 - phi=0.4140000000000001, PE=0.0 after 38 steps
Step: 15 - phi=0.4140000000000001, PE=0.0 after 40 steps
Step: 15 - phi=0.4140000000000001, PE=0.0 after 35 steps
Step: 15 - phi=0.4140000000000001, PE=0.0 after 42 steps
Step: 15 - phi=0.4140000000000001, PE=0.0 after 49 steps
Step: 15 - phi=0.4140000000000001, PE=0.0 after 35 steps
Step: 16 - phi=0.4150000000000001, PE=0.0 after 42 steps
Step: 16 - phi=0.4150000000000001, PE=0.0 after 48 steps
Step: 16 - phi=0.4150000000000001, PE=0.0 after 35 steps
Step: 16 - phi=0.4150000000000001, PE=0.0 after 35 steps
Step: 16 - phi=0.4150000000000001, PE=0.0 after 38 steps
Step: 16 - phi=0.4150000000000001, PE=0.0 after 40 steps
Step: 16 - phi=0.4150000000000001, PE=0.0 after 35 steps
Step: 16 - phi=0.4150000000000001, PE=0.0 after 42 steps
Step: 16 - phi=0.4150000000000001, PE=0.0 after 49 steps
Step: 16 - phi=0.4150000000000001, PE=0.0 after 35 steps
Step: 17 - phi=0.4160000000000001, PE=0.0 after 42 steps
Step: 17 - phi=0.4160000000000001, PE=0.0 after 49 steps
Step: 17 - phi=0.4160000000000001, PE=0.0 after 35 steps
Step: 17 - phi=0.4160000000000001, PE=0.0 after 35 steps
Step: 17 - phi=0.4160000000000001, PE=0.0 after 38 steps
Step: 17 - phi=0.4160000000000001, PE=0.0 after 40 steps
Step: 17 - phi=0.4160000000000001, PE=0.0 after 35 steps
Step: 17 - phi=0.4160000000000001, PE=0.0 after 42 steps
Step: 17 - phi=0.4160000000000001, PE=0.0 after 49 steps
Step: 17 - phi=0.4160000000000001, PE=0.0 after 35 steps
Step: 18 - phi=0.4170000000000001, PE=0.0 after 41 steps
Step: 18 - phi=0.4170000000000001, PE=0.0 after 48 steps
Step: 18 - phi=0.4170000000000001, PE=0.0 after 35 steps
Step: 18 - phi=0.4170000000000001, PE=0.0 after 35 steps
Step: 18 - phi=0.4170000000000001, PE=0.0 after 53 steps
Step: 18 - phi=0.4170000000000001, PE=0.0 after 40 steps
Step: 18 - phi=0.4170000000000001, PE=0.0 after 35 steps
Step: 18 - phi=0.4170000000000001, PE=0.0 after 42 steps
Step: 18 - phi=0.4170000000000001, PE=0.0 after 49 steps
Step: 18 - phi=0.4170000000000001, PE=0.0 after 35 steps
Step: 19 - phi=0.4180000000000001, PE=0.0 after 41 steps
Step: 19 - phi=0.4180000000000001, PE=0.0 after 48 steps
Step: 19 - phi=0.4180000000000001, PE=0.0 after 35 steps
Step: 19 - phi=0.4180000000000001, PE=0.0 after 35 steps
Step: 19 - phi=0.4180000000000001, PE=0.0 after 44 steps
Step: 19 - phi=0.4180000000000001, PE=0.0 after 40 steps
Step: 19 - phi=0.4180000000000001, PE=0.0 after 35 steps
Step: 19 - phi=0.4180000000000001, PE=0.0 after 42 steps
Step: 19 - phi=0.4180000000000001, PE=0.0 after 49 steps
Step: 19 - phi=0.4180000000000001, PE=0.0 after 35 steps
Step: 20 - phi=0.4190000000000001, PE=0.0 after 41 steps
Step: 20 - phi=0.4190000000000001, PE=0.0 after 48 steps
Step: 20 - phi=0.4190000000000001, PE=0.0 after 87 steps
Step: 20 - phi=0.4190000000000001, PE=0.0 after 35 steps
Step: 20 - phi=0.4190000000000001, PE=0.0 after 44 steps
Step: 20 - phi=0.4190000000000001, PE=0.0 after 40 steps
Step: 20 - phi=0.4190000000000001, PE=0.0 after 35 steps
Step: 20 - phi=0.4190000000000001, PE=0.0 after 42 steps
Step: 20 - phi=0.4190000000000001, PE=0.0 after 49 steps
Step: 20 - phi=0.4190000000000001, PE=0.0 after 35 steps
Step: 21 - phi=0.4200000000000001, PE=0.0 after 41 steps
Step: 21 - phi=0.4200000000000001, PE=0.0 after 48 steps
Step: 21 - phi=0.4200000000000001, PE=0.0 after 39 steps
Step: 21 - phi=0.4200000000000001, PE=0.0 after 35 steps
Step: 21 - phi=0.4200000000000001, PE=0.0 after 42 steps
Step: 21 - phi=0.4200000000000001, PE=0.0 after 40 steps
Step: 21 - phi=0.4200000000000001, PE=0.0 after 35 steps
Step: 21 - phi=0.4200000000000001, PE=0.0 after 63 steps
Step: 21 - phi=0.4200000000000001, PE=0.0 after 49 steps
Step: 21 - phi=0.4200000000000001, PE=0.0 after 35 steps
Step: 22 - phi=0.4210000000000001, PE=0.0 after 41 steps
Step: 22 - phi=0.4210000000000001, PE=0.0 after 48 steps
Step: 22 - phi=0.4210000000000001, PE=0.0 after 40 steps
Step: 22 - phi=0.4210000000000001, PE=0.0 after 35 steps
Step: 22 - phi=0.4210000000000001, PE=4.5970932795468835e-17 after 42 steps
Step: 22 - phi=0.4210000000000001, PE=0.0 after 40 steps
Step: 22 - phi=0.4210000000000001, PE=0.0 after 35 steps
Step: 22 - phi=0.4210000000000001, PE=0.0 after 61 steps
Step: 22 - phi=0.4210000000000001, PE=0.0 after 49 steps
Step: 22 - phi=0.4210000000000001, PE=0.0 after 35 steps
Step: 23 - phi=0.4220000000000001, PE=0.0 after 41 steps
Step: 23 - phi=0.4220000000000001, PE=0.0 after 48 steps
Step: 23 - phi=0.4220000000000001, PE=0.0 after 39 steps
Step: 23 - phi=0.4220000000000001, PE=0.0 after 38 steps
Step: 23 - phi=0.4220000000000001, PE=0.0 after 42 steps
Step: 23 - phi=0.4220000000000001, PE=0.0 after 40 steps
Step: 23 - phi=0.4220000000000001, PE=0.0 after 35 steps
Step: 23 - phi=0.4220000000000001, PE=0.0 after 60 steps
Step: 23 - phi=0.4220000000000001, PE=0.0 after 49 steps
Step: 23 - phi=0.4220000000000001, PE=0.0 after 35 steps
Step: 24 - phi=0.4230000000000001, PE=0.0 after 41 steps
Step: 24 - phi=0.4230000000000001, PE=0.0 after 48 steps
Step: 24 - phi=0.4230000000000001, PE=0.0 after 39 steps
Step: 24 - phi=0.4230000000000001, PE=0.0 after 39 steps
Step: 24 - phi=0.4230000000000001, PE=0.0 after 42 steps
Step: 24 - phi=0.4230000000000001, PE=0.0 after 40 steps
Step: 24 - phi=0.4230000000000001, PE=0.0 after 35 steps
Step: 24 - phi=0.4230000000000001, PE=0.0 after 60 steps
Step: 24 - phi=0.4230000000000001, PE=0.0 after 49 steps
Step: 24 - phi=0.4230000000000001, PE=0.0 after 35 steps
Step: 25 - phi=0.4240000000000001, PE=0.0 after 41 steps
Step: 25 - phi=0.4240000000000001, PE=0.0 after 48 steps
Step: 25 - phi=0.4240000000000001, PE=0.0 after 39 steps
Step: 25 - phi=0.4240000000000001, PE=0.0 after 38 steps
Step: 25 - phi=0.4240000000000001, PE=0.0 after 45 steps
Step: 25 - phi=0.4240000000000001, PE=0.0 after 40 steps
Step: 25 - phi=0.4240000000000001, PE=0.0 after 35 steps
Step: 25 - phi=0.4240000000000001, PE=0.0 after 60 steps
Step: 25 - phi=0.4240000000000001, PE=0.0 after 49 steps
Step: 25 - phi=0.4240000000000001, PE=0.0 after 35 steps
Step: 26 - phi=0.4250000000000001, PE=0.0 after 41 steps
Step: 26 - phi=0.4250000000000001, PE=0.0 after 48 steps
Step: 26 - phi=0.4250000000000001, PE=0.0 after 39 steps
Step: 26 - phi=0.4250000000000001, PE=0.0 after 38 steps
Step: 26 - phi=0.4250000000000001, PE=0.0 after 43 steps
Step: 26 - phi=0.4250000000000001, PE=0.0 after 40 steps
Step: 26 - phi=0.4250000000000001, PE=0.0 after 35 steps
Step: 26 - phi=0.4250000000000001, PE=0.0 after 59 steps
Step: 26 - phi=0.4250000000000001, PE=0.0 after 49 steps
Step: 26 - phi=0.4250000000000001, PE=0.0 after 35 steps
Step: 27 - phi=0.4260000000000001, PE=0.0 after 41 steps
Step: 27 - phi=0.4260000000000001, PE=0.0 after 48 steps
Step: 27 - phi=0.4260000000000001, PE=0.0 after 39 steps
Step: 27 - phi=0.4260000000000001, PE=0.0 after 38 steps
Step: 27 - phi=0.4260000000000001, PE=0.0 after 44 steps
Step: 27 - phi=0.4260000000000001, PE=0.0 after 40 steps
Step: 27 - phi=0.4260000000000001, PE=0.0 after 35 steps
Step: 27 - phi=0.4260000000000001, PE=0.0 after 59 steps
Step: 27 - phi=0.4260000000000001, PE=0.0 after 49 steps
Step: 27 - phi=0.4260000000000001, PE=0.0 after 35 steps
Step: 28 - phi=0.4270000000000001, PE=0.0 after 41 steps
Step: 28 - phi=0.4270000000000001, PE=0.0 after 48 steps
Step: 28 - phi=0.4270000000000001, PE=0.0 after 39 steps
Step: 28 - phi=0.4270000000000001, PE=0.0 after 38 steps
Step: 28 - phi=0.4270000000000001, PE=0.0 after 44 steps
Step: 28 - phi=0.4270000000000001, PE=0.0 after 40 steps
Step: 28 - phi=0.4270000000000001, PE=0.0 after 35 steps
Step: 28 - phi=0.4270000000000001, PE=0.0 after 59 steps
Step: 28 - phi=0.4270000000000001, PE=0.0 after 49 steps
Step: 28 - phi=0.4270000000000001, PE=0.0 after 35 steps
Step: 29 - phi=0.4280000000000001, PE=0.0 after 41 steps
Step: 29 - phi=0.4280000000000001, PE=0.0 after 48 steps
Step: 29 - phi=0.4280000000000001, PE=0.0 after 39 steps
Step: 29 - phi=0.4280000000000001, PE=0.0 after 38 steps
Step: 29 - phi=0.4280000000000001, PE=0.0 after 44 steps
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Step: 394 - phi=0.7930000000000004, PE=0.0 after 672 steps
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Step: 394 - phi=0.7930000000000004, PE=0.0 after 110 steps
Step: 395 - phi=0.7940000000000004, PE=7.413241929065243e-17 after 196 steps
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Step: 395 - phi=0.7940000000000004, PE=0.0 after 134 steps
Step: 395 - phi=0.7836650390625004, PE=3.148188084698453e-14 after 1509 steps
Step: 395 - phi=0.7940000000000004, PE=0.0 after 296 steps
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Step: 396 - phi=0.7950000000000004, PE=7.769972093620242e-17 after 168 steps
Step: 396 - phi=0.7836645507812504, PE=8.689598503193162e-17 after 216 steps
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Step: 396 - phi=0.7950000000000004, PE=2.582019391544122e-07 after 1099 steps
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Step: 397 - phi=0.7960000000000004, PE=7.421767398255203e-17 after 439 steps
Step: 397 - phi=0.7836647949218754, PE=7.118345232619367e-16 after 2129 steps
Step: 397 - phi=0.7960000000000004, PE=0.0 after 292 steps
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Step: 397 - phi=0.7960000000000004, PE=0.0 after 240 steps
Step: 397 - phi=0.7945000000000004, PE=3.8497868364762016e-08 after 1108 steps
Step: 397 - phi=0.7960000000000004, PE=0.0 after 136 steps
Step: 397 - phi=0.7960000000000004, PE=0.0 after 124 steps
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Step: 398 - phi=0.7970000000000004, PE=0.0 after 467 steps
Step: 398 - phi=0.7970000000000004, PE=0.0 after 371 steps
Step: 398 - phi=0.7836646728515628, PE=9.066973651077371e-17 after 162 steps
Step: 398 - phi=0.7942500000000003, PE=1.6063392089033056e-09 after 1085 steps
Step: 398 - phi=0.7970000000000004, PE=7.530281800156e-17 after 296 steps
Step: 398 - phi=0.7970000000000004, PE=0.0 after 176 steps
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Step: 398 - phi=0.7970000000000004, PE=0.0 after 106 steps
Step: 399 - phi=0.7980000000000004, PE=0.0 after 197 steps
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Step: 399 - phi=0.7980000000000004, PE=0.0 after 339 steps
Step: 399 - phi=0.7836647338867191, PE=9.975408069427044e-17 after 1651 steps
Step: 399 - phi=0.7980000000000004, PE=8.695693242566504e-17 after 303 steps
Step: 399 - phi=0.7980000000000004, PE=0.0 after 200 steps
Step: 399 - phi=0.7980000000000004, PE=0.0 after 288 steps
Step: 399 - phi=0.7941250000000004, PE=2.7494464994347628e-17 after 495 steps
Step: 399 - phi=0.7980000000000004, PE=0.0 after 154 steps
Step: 399 - phi=0.7980000000000004, PE=0.0 after 127 steps
Step: 400 - phi=0.7990000000000004, PE=9.065724907802432e-17 after 383 steps
Step: 400 - phi=0.7990000000000004, PE=0.0 after 211 steps
Step: 400 - phi=0.7990000000000004, PE=1.703835082013069e-19 after 322 steps
Step: 400 - phi=0.7836647644042972, PE=9.979557260040026e-17 after 1657 steps
Step: 400 - phi=0.7990000000000004, PE=2.2050590250237662e-17 after 590 steps
Step: 400 - phi=0.7990000000000004, PE=0.0 after 171 steps
Step: 400 - phi=0.7990000000000004, PE=0.0 after 267 steps
Step: 400 - phi=0.7941875000000004, PE=1.059860502308518e-12 after 1285 steps
Step: 400 - phi=0.7990000000000004, PE=0.0 after 129 steps
Step: 400 - phi=0.7990000000000004, PE=0.0 after 128 steps
Step: 401 - phi=0.8000000000000004, PE=9.643281208813087e-17 after 374 steps
Step: 401 - phi=0.8000000000000004, PE=4.031870954377483e-17 after 331 steps
Step: 401 - phi=0.8000000000000004, PE=0.0 after 260 steps
Step: 401 - phi=0.8000000000000004, PE=0.0 after 275 steps
Step: 401 - phi=0.7836647796630862, PE=2.978478914512456e-16 after 1169 steps
Step: 401 - phi=0.7941562500000003, PE=9.595138470123945e-17 after 381 steps
Step: 401 - phi=0.8000000000000004, PE=0.0 after 127 steps
Step: 401 - phi=0.8000000000000004, PE=0.0 after 133 steps
Step: 401 - phi=0.8000000000000004, PE=1.504241913332282e-07 after 3387 steps
Step: 401 - phi=0.8000000000000004, PE=0.0 after 169 steps
Step: 402 - phi=0.8010000000000004, PE=8.444805968081359e-17 after 327 steps
Step: 402 - phi=0.8010000000000004, PE=0.0 after 186 steps
Step: 402 - phi=0.8010000000000004, PE=0.0 after 256 steps
Step: 402 - phi=0.7836647720336918, PE=1.5743451960754535e-16 after 1195 steps
Step: 402 - phi=0.7995000000000003, PE=3.959145051010812e-09 after 4759 steps
Step: 402 - phi=0.8010000000000004, PE=0.0 after 170 steps
Step: 402 - phi=0.8010000000000004, PE=1.8893818021306369e-07 after 1295 steps
Step: 402 - phi=0.7941718750000004, PE=7.680316209655904e-17 after 376 steps
Step: 402 - phi=0.8010000000000004, PE=0.0 after 142 steps
Step: 402 - phi=0.8010000000000004, PE=0.0 after 124 steps
Step: 403 - phi=0.8020000000000004, PE=6.457178353818226e-17 after 351 steps
Step: 403 - phi=0.8020000000000004, PE=0.0 after 158 steps
Step: 403 - phi=0.8020000000000004, PE=8.550047534211978e-17 after 300 steps
Step: 403 - phi=0.7836647682189946, PE=1.038728215521313e-16 after 1347 steps
Step: 403 - phi=0.7992500000000003, PE=0.0 after 6450 steps
Step: 403 - phi=0.8020000000000004, PE=0.0 after 194 steps
Step: 403 - phi=0.8005000000000004, PE=3.497032055909739e-08 after 2250 steps
Step: 403 - phi=0.7941796875000005, PE=7.633881242004375e-17 after 376 steps
Step: 403 - phi=0.8020000000000004, PE=0.0 after 119 steps
Step: 403 - phi=0.8020000000000004, PE=0.0 after 123 steps
Step: 404 - phi=0.8030000000000004, PE=8.577918574921738e-17 after 638 steps
Step: 404 - phi=0.8030000000000004, PE=0.0 after 1896 steps
Step: 404 - phi=0.8030000000000004, PE=0.0 after 250 steps
Step: 404 - phi=0.7836647663116458, PE=9.998811169430911e-17 after 640 steps
Step: 404 - phi=0.7993750000000004, PE=0.0 after 1458 steps
Step: 404 - phi=0.8030000000000004, PE=0.0 after 193 steps
Step: 404 - phi=0.8002500000000003, PE=3.9278112767531286e-09 after 2792 steps
Step: 404 - phi=0.7941835937500004, PE=2.5355334446318335e-17 after 373 steps
Step: 404 - phi=0.8030000000000004, PE=0.0 after 117 steps
Step: 404 - phi=0.8030000000000004, PE=0.0 after 96 steps
Step: 405 - phi=0.8040000000000004, PE=0.0 after 330 steps
Step: 405 - phi=0.8040000000000004, PE=0.0 after 600 steps
Step: 405 - phi=0.8040000000000004, PE=4.3414714564935465e-17 after 232 steps
Step: 405 - phi=0.7836647672653202, PE=9.997485404325755e-17 after 439 steps
Step: 405 - phi=0.7994375000000004, PE=4.959582123915381e-10 after 1386 steps
Step: 405 - phi=0.8040000000000004, PE=6.157077588810969e-17 after 176 steps
Step: 405 - phi=0.8001250000000004, PE=1.4634628214763632e-13 after 5128 steps
Step: 405 - phi=0.7941855468750003, PE=6.795646996140907e-17 after 372 steps
Step: 405 - phi=0.8040000000000004, PE=0.0 after 117 steps
Step: 405 - phi=0.8040000000000004, PE=0.0 after 96 steps
Step: 406 - phi=0.8050000000000004, PE=3.0827808058675484e-17 after 360 steps
Step: 406 - phi=0.8050000000000004, PE=0.0 after 406 steps
Step: 406 - phi=0.8000625000000003, PE=0.0 after 322 steps
Step: 406 - phi=0.8050000000000004, PE=0.0 after 201 steps
Step: 406 - phi=0.7941865234375003, PE=1.75803632183595e-13 after 778 steps
Step: 406 - phi=0.7836647677421573, PE=9.996644919071832e-17 after 313 steps
Step: 406 - phi=0.8050000000000004, PE=0.0 after 248 steps
Step: 406 - phi=0.8050000000000004, PE=0.0 after 94 steps
Step: 406 - phi=0.7994062500000003, PE=3.768652231659084e-12 after 1738 steps
Step: 406 - phi=0.8050000000000004, PE=0.0 after 145 steps
Step: 407 - phi=0.8060000000000004, PE=0.0 after 309 steps
Step: 407 - phi=0.8060000000000004, PE=0.0 after 360 steps
Step: 407 - phi=0.8000937500000004, PE=9.972497360767455e-17 after 1475 steps
Step: 407 - phi=0.7941860351562503, PE=1.3038417687838587e-14 after 843 steps
Step: 407 - phi=0.8060000000000004, PE=0.0 after 208 steps
Step: 407 - phi=0.8060000000000004, PE=0.0 after 161 steps
Step: 407 - phi=0.7836647679805759, PE=1.0089365612428733e-16 after 713 steps
Step: 407 - phi=0.7993906250000004, PE=8.868983211611106e-17 after 1224 steps
Step: 407 - phi=0.8060000000000004, PE=0.0 after 213 steps
Step: 407 - phi=0.8060000000000004, PE=8.102646866120476e-17 after 206 steps
Step: 408 - phi=0.8070000000000004, PE=0.0 after 286 steps
Step: 408 - phi=0.8070000000000004, PE=0.0 after 403 steps
Step: 408 - phi=0.8070000000000004, PE=0.0 after 234 steps
Step: 408 - phi=0.7836647678613666, PE=9.998222868049246e-17 after 165 steps
Step: 408 - phi=0.7993984375000003, PE=7.594768580831802e-17 after 1159 steps
Step: 408 - phi=0.8070000000000004, PE=0.0 after 149 steps
Step: 408 - phi=0.8001093750000003, PE=9.984018584272909e-17 after 4180 steps
Step: 408 - phi=0.7941857910156254, PE=9.196348306656508e-17 after 382 steps
Step: 408 - phi=0.8070000000000004, PE=0.0 after 200 steps
Step: 408 - phi=0.8070000000000004, PE=0.0 after 114 steps
Step: 409 - phi=0.8080000000000004, PE=0.0 after 298 steps
Step: 409 - phi=0.8080000000000004, PE=0.0 after 392 steps
Step: 409 - phi=0.8080000000000004, PE=0.0 after 236 steps
Step: 409 - phi=0.7836647679209713, PE=1.001556410684188e-16 after 605 steps
Step: 409 - phi=0.7994023437500003, PE=9.436079740166348e-17 after 1138 steps
Step: 409 - phi=0.8080000000000004, PE=0.0 after 145 steps
Step: 409 - phi=0.8001171875000004, PE=9.335076150774921e-17 after 3294 steps
Step: 409 - phi=0.7941859130859379, PE=1.4371634399368849e-15 after 726 steps
Step: 409 - phi=0.8080000000000004, PE=0.0 after 205 steps
Step: 409 - phi=0.8080000000000004, PE=9.222323774639169e-17 after 285 steps
Step: 410 - phi=0.8090000000000004, PE=0.0 after 257 steps
Step: 410 - phi=0.8090000000000004, PE=2.7857482509997877e-17 after 346 steps
Step: 410 - phi=0.8090000000000004, PE=7.056137007420136e-17 after 251 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 410 - phi=0.7994042968750004, PE=4.4981703160169423e-13 after 1396 steps
Step: 410 - phi=0.8090000000000004, PE=0.0 after 175 steps
Step: 410 - phi=0.8001210937500004, PE=8.039998401397799e-17 after 3057 steps
Step: 410 - phi=0.7941858520507816, PE=9.823248214754447e-17 after 323 steps
Step: 410 - phi=0.8090000000000004, PE=0.0 after 216 steps
Step: 410 - phi=0.8090000000000004, PE=0.0 after 126 steps
Step: 411 - phi=0.8100000000000004, PE=0.0 after 232 steps
Step: 411 - phi=0.8100000000000004, PE=1.3413038230838437e-18 after 382 steps
Step: 411 - phi=0.8100000000000004, PE=0.0 after 117 steps
Step: 411 - phi=0.8100000000000004, PE=0.0 after 242 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 411 - phi=0.7994033203125004, PE=1.2511942626217253e-15 after 1566 steps
Step: 411 - phi=0.8100000000000004, PE=0.0 after 150 steps
Step: 411 - phi=0.8001230468750005, PE=9.889220152992658e-17 after 2946 steps
Step: 411 - phi=0.7941858825683598, PE=3.5498126101697544e-16 after 696 steps
Step: 411 - phi=0.8100000000000004, PE=5.62068400020364e-17 after 216 steps
Step: 412 - phi=0.8110000000000004, PE=0.0 after 240 steps
Step: 412 - phi=0.8110000000000004, PE=9.80602548202907e-17 after 699 steps
Step: 412 - phi=0.8110000000000004, PE=0.0 after 196 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 412 - phi=0.7994028320312503, PE=9.74403024228988e-17 after 1109 steps
Step: 412 - phi=0.8110000000000004, PE=0.0 after 157 steps
Step: 412 - phi=0.8001240234375004, PE=9.516859698798394e-17 after 2883 steps
Step: 412 - phi=0.7941858673095707, PE=9.870878940622291e-17 after 248 steps
Step: 412 - phi=0.8110000000000004, PE=7.5070443719391e-17 after 255 steps
Step: 412 - phi=0.8110000000000004, PE=0.0 after 160 steps
Step: 413 - phi=0.8120000000000004, PE=0.0 after 251 steps
Step: 413 - phi=0.8120000000000004, PE=0.0 after 372 steps
Step: 413 - phi=0.8120000000000004, PE=5.490050013235783e-17 after 991 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 413 - phi=0.7994030761718753, PE=9.983558795519502e-17 after 1070 steps
Step: 413 - phi=0.8120000000000004, PE=0.0 after 166 steps
Step: 413 - phi=0.8001245117187504, PE=1.93408142034399e-14 after 2462 steps
Step: 413 - phi=0.7941858749389652, PE=1.9806897313210142e-16 after 503 steps
Step: 413 - phi=0.8120000000000004, PE=6.484477931427259e-17 after 787 steps
Step: 413 - phi=0.8120000000000004, PE=0.0 after 126 steps
Step: 414 - phi=0.8130000000000004, PE=0.0 after 242 steps
Step: 414 - phi=0.8130000000000004, PE=4.912434199254903e-17 after 474 steps
Step: 414 - phi=0.8130000000000004, PE=0.0 after 428 steps
Step: 414 - phi=0.8001242675781255, PE=3.003375147198116e-16 after 3326 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 414 - phi=0.7994031982421879, PE=9.888174929282237e-17 after 1025 steps
Step: 414 - phi=0.8130000000000004, PE=0.0 after 222 steps
Step: 414 - phi=0.794185871124268, PE=1.3665782623760742e-16 after 722 steps
Step: 414 - phi=0.8130000000000004, PE=3.5879276345332607e-07 after 806 steps
Step: 414 - phi=0.8130000000000004, PE=0.0 after 140 steps
Step: 415 - phi=0.8140000000000004, PE=6.966645835097421e-17 after 1142 steps
Step: 415 - phi=0.8140000000000004, PE=2.6629083030240127e-19 after 371 steps
Step: 415 - phi=0.8140000000000004, PE=5.631779840668704e-17 after 485 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 415 - phi=0.7994032592773441, PE=9.979148676748057e-17 after 963 steps
Step: 415 - phi=0.8140000000000004, PE=5.5172660395013316e-17 after 440 steps
Step: 415 - phi=0.800124145507813, PE=9.991296925843032e-17 after 2641 steps
Step: 415 - phi=0.7941858692169194, PE=1.1021349835801584e-16 after 458 steps
Step: 415 - phi=0.8125000000000004, PE=8.938645661634334e-08 after 872 steps
Step: 415 - phi=0.8140000000000004, PE=0.0 after 131 steps
Step: 416 - phi=0.8150000000000004, PE=8.590013428949277e-17 after 438 steps
Step: 416 - phi=0.8150000000000004, PE=0.0 after 299 steps
Step: 416 - phi=0.8150000000000004, PE=0.0 after 272 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 416 - phi=0.7994032897949223, PE=2.4083004168537697e-16 after 1233 steps
Step: 416 - phi=0.8150000000000004, PE=0.0 after 207 steps
Step: 416 - phi=0.8001242065429692, PE=9.960934569512092e-17 after 2444 steps
Step: 416 - phi=0.794185868263245, PE=9.992985716610599e-17 after 100 steps
Step: 416 - phi=0.8122500000000004, PE=2.214045655094772e-08 after 767 steps
Step: 416 - phi=0.8150000000000004, PE=0.0 after 127 steps
Step: 417 - phi=0.8160000000000004, PE=0.0 after 350 steps
Step: 417 - phi=0.8160000000000004, PE=7.647702520699225e-17 after 332 steps
Step: 417 - phi=0.8160000000000004, PE=0.0 after 268 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 417 - phi=0.7994032745361332, PE=9.981848009014792e-17 after 732 steps
Step: 417 - phi=0.8160000000000004, PE=2.6865896722434845e-17 after 839 steps
Step: 417 - phi=0.8001242370605474, PE=9.984402901091651e-17 after 2162 steps
Step: 417 - phi=0.7941858687400822, PE=1.0404629971900642e-16 after 537 steps
Step: 417 - phi=0.8121250000000004, PE=5.426485247718906e-09 after 434 steps
Step: 417 - phi=0.8160000000000004, PE=0.0 after 567 steps
Step: 418 - phi=0.8170000000000004, PE=0.0 after 296 steps
Step: 418 - phi=0.8170000000000004, PE=0.0 after 273 steps
Step: 418 - phi=0.8170000000000004, PE=0.0 after 469 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 418 - phi=0.7994032821655277, PE=1.1141474598689113e-16 after 919 steps
Step: 418 - phi=0.8170000000000004, PE=4.3825236991779114e-10 after 2799 steps
Step: 418 - phi=0.8001242523193364, PE=9.989451599594521e-17 after 1821 steps
Step: 418 - phi=0.7941858685016636, PE=1.0102927769378416e-16 after 467 steps
Step: 418 - phi=0.8120625000000004, PE=1.3023472602415243e-09 after 725 steps
Step: 418 - phi=0.8170000000000004, PE=5.757100707580774e-17 after 946 steps
Step: 419 - phi=0.8180000000000004, PE=4.888945547495414e-10 after 1721 steps
Step: 419 - phi=0.8180000000000004, PE=0.0 after 266 steps
Step: 419 - phi=0.8180000000000004, PE=0.0 after 369 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 419 - phi=0.7994032783508305, PE=9.984584515800533e-17 after 439 steps
Step: 419 - phi=0.8165000000000004, PE=4.289125599673775e-17 after 647 steps
Step: 419 - phi=0.8001242599487309, PE=1.8294827007847915e-16 after 1091 steps
Step: 419 - phi=0.7941858683824543, PE=9.999868208565307e-17 after 84 steps
Step: 419 - phi=0.8120312500000004, PE=2.9918886704135906e-10 after 792 steps
Step: 419 - phi=0.8180000000000004, PE=0.0 after 468 steps
Step: 420 - phi=0.8175000000000003, PE=0.0 after 894 steps
Step: 420 - phi=0.8190000000000004, PE=0.0 after 207 steps
Step: 420 - phi=0.8190000000000004, PE=5.716741096223139e-17 after 421 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 420 - phi=0.7994032802581791, PE=9.990242210711991e-17 after 316 steps
Step: 420 - phi=0.8167500000000004, PE=0.0 after 562 steps
Step: 420 - phi=0.8001242561340336, PE=1.3510880145371518e-16 after 1068 steps
Step: 420 - phi=0.794185868442059, PE=1.0028196044618577e-16 after 559 steps
Step: 420 - phi=0.8120156250000004, PE=6.242464838132664e-11 after 807 steps
Step: 420 - phi=0.8190000000000004, PE=3.2014935540592773e-18 after 415 steps
Step: 421 - phi=0.8177500000000004, PE=8.65516252238557e-17 after 763 steps
Step: 421 - phi=0.8200000000000004, PE=0.0 after 200 steps
Step: 421 - phi=0.8200000000000004, PE=3.039783878290553e-17 after 361 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 421 - phi=0.7994032812118534, PE=9.988772946509644e-17 after 228 steps
Step: 421 - phi=0.8168750000000005, PE=2.154766387075232e-17 after 608 steps
Step: 421 - phi=0.800124254226685, PE=1.139028573349591e-16 after 934 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 421 - phi=0.8120078125000003, PE=1.0257199032373236e-11 after 831 steps
Step: 421 - phi=0.8200000000000004, PE=7.639514318036601e-20 after 333 steps
Step: 422 - phi=0.8178750000000004, PE=7.046903991039838e-17 after 598 steps
Step: 422 - phi=0.8210000000000004, PE=0.0 after 219 steps
Step: 422 - phi=0.8210000000000004, PE=0.0 after 312 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 422 - phi=0.7994032816886906, PE=1.0496221600967914e-16 after 487 steps
Step: 422 - phi=0.8169375000000004, PE=3.720124103167536e-17 after 572 steps
Step: 422 - phi=0.8001242532730106, PE=1.0397833352787205e-16 after 1028 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 422 - phi=0.8120039062500004, PE=7.285037597320769e-13 after 882 steps
Step: 422 - phi=0.8210000000000004, PE=0.0 after 298 steps
Step: 423 - phi=0.8179375000000004, PE=3.3453761096096085e-17 after 579 steps
Step: 423 - phi=0.8220000000000004, PE=0.0 after 187 steps
Step: 423 - phi=0.8220000000000004, PE=8.066950456890254e-17 after 375 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 423 - phi=0.7994032814502721, PE=1.0180812779264239e-16 after 499 steps
Step: 423 - phi=0.8169687500000005, PE=7.459995876752879e-12 after 1795 steps
Step: 423 - phi=0.8001242527961735, PE=9.9999100253091e-17 after 400 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 423 - phi=0.8120019531250005, PE=8.892965645890904e-17 after 554 steps
Step: 423 - phi=0.8220000000000004, PE=0.0 after 294 steps
Step: 424 - phi=0.8179687500000004, PE=8.133207057187702e-12 after 1397 steps
Step: 424 - phi=0.8230000000000004, PE=0.0 after 249 steps
Step: 424 - phi=0.8230000000000004, PE=0.0 after 267 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 424 - phi=0.7994032813310628, PE=1.0024912650493317e-16 after 437 steps
Step: 424 - phi=0.8169531250000004, PE=6.825462339247298e-17 after 582 steps
Step: 424 - phi=0.800124253034592, PE=1.0156787453046848e-16 after 710 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 424 - phi=0.8120029296875004, PE=7.087815714156348e-14 after 873 steps
Step: 424 - phi=0.8230000000000004, PE=0.0 after 265 steps
Step: 425 - phi=0.8179531250000004, PE=7.85480470613085e-17 after 561 steps
Step: 425 - phi=0.8240000000000004, PE=0.0 after 211 steps
Step: 425 - phi=0.8240000000000004, PE=0.0 after 497 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 425 - phi=0.7994032812714581, PE=9.999896189766012e-17 after 68 steps
Step: 425 - phi=0.8169609375000004, PE=8.423559638126125e-17 after 561 steps
Step: 425 - phi=0.8001242529153827, PE=1.0037324467323648e-16 after 876 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 425 - phi=0.8120024414062504, PE=8.950156020082043e-17 after 512 steps
Step: 425 - phi=0.8240000000000004, PE=0.0 after 302 steps
Step: 426 - phi=0.8179609375000003, PE=6.861143383756887e-17 after 575 steps
Step: 426 - phi=0.8250000000000004, PE=2.138174645501198e-17 after 228 steps
Step: 426 - phi=0.8250000000000004, PE=0.0 after 308 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 426 - phi=0.8169648437500004, PE=2.0671039431052034e-13 after 1839 steps
Step: 426 - phi=0.8001242528557782, PE=9.999958899023633e-17 after 152 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 426 - phi=0.8120026855468754, PE=1.4257685390344394e-14 after 669 steps
Step: 426 - phi=0.8250000000000004, PE=0.0 after 273 steps
Step: 427 - phi=0.8179648437500003, PE=1.9740708732836108e-13 after 1176 steps
Step: 427 - phi=0.8260000000000004, PE=0.0 after 179 steps
Step: 427 - phi=0.8260000000000004, PE=8.586395892743394e-17 after 577 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 427 - phi=0.8169628906250004, PE=8.458807405343166e-17 after 568 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 427 - phi=0.8120025634765629, PE=2.115404309817189e-15 after 717 steps
Step: 427 - phi=0.8260000000000004, PE=2.6740335157203803e-17 after 302 steps
Step: 428 - phi=0.8179628906250003, PE=9.064347258464154e-17 after 536 steps
Step: 428 - phi=0.8270000000000004, PE=9.315881606503223e-17 after 543 steps
Step: 428 - phi=0.8270000000000004, PE=1.3181617400025803e-17 after 355 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 428 - phi=0.8169638671875004, PE=9.986970933598539e-17 after 541 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 428 - phi=0.8120025024414066, PE=9.835347280519074e-17 after 435 steps
Step: 428 - phi=0.8270000000000004, PE=0.0 after 208 steps
Step: 429 - phi=0.8179638671875002, PE=9.8845043773595e-17 after 539 steps
Step: 429 - phi=0.8280000000000004, PE=8.867636215470846e-17 after 992 steps
Step: 429 - phi=0.8280000000000004, PE=9.970143229405145e-17 after 471 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 429 - phi=0.8169643554687505, PE=2.891841639711948e-14 after 1663 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 429 - phi=0.8120025329589847, PE=7.639980278540098e-16 after 484 steps
Step: 429 - phi=0.8280000000000004, PE=0.0 after 644 steps
Step: 430 - phi=0.8179643554687503, PE=2.0550847246033565e-14 after 1092 steps
Step: 430 - phi=0.8290000000000004, PE=1.8671479886477325e-07 after 2030 steps
Step: 430 - phi=0.8290000000000004, PE=1.8671479886470327e-07 after 1875 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 430 - phi=0.8169641113281254, PE=7.702041040963017e-16 after 1699 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 430 - phi=0.8120025177001957, PE=3.409196035563419e-16 after 514 steps
Step: 430 - phi=0.8290000000000004, PE=0.0 after 411 steps
Step: 431 - phi=0.8179641113281253, PE=9.824040179620418e-17 after 504 steps
Step: 431 - phi=0.8285000000000005, PE=1.4057819721189573e-08 after 2563 steps
Step: 431 - phi=0.8285000000000005, PE=1.4057819721180393e-08 after 2431 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 431 - phi=0.8169639892578129, PE=9.532386165853777e-17 after 477 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 431 - phi=0.8120025100708012, PE=1.9253658648862337e-16 after 534 steps
Step: 431 - phi=0.8300000000000004, PE=0.0 after 330 steps
Step: 432 - phi=0.8179642333984378, PE=4.640087630815318e-15 after 824 steps
Step: 432 - phi=0.8282500000000004, PE=0.0 after 970 steps
Step: 432 - phi=0.8282500000000004, PE=0.0 after 939 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 432 - phi=0.8169640502929691, PE=9.826199376100217e-17 after 462 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 432 - phi=0.8120025062561038, PE=1.34134123278551e-16 after 496 steps
Step: 432 - phi=0.8310000000000004, PE=0.0 after 283 steps
Step: 433 - phi=0.8179641723632816, PE=9.302154979786906e-16 after 815 steps
Step: 433 - phi=0.8283750000000004, PE=1.6099285315717866e-09 after 2280 steps
Step: 433 - phi=0.8283750000000004, PE=1.609928531572332e-09 after 2025 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 433 - phi=0.8169640808105473, PE=9.997685169762676e-17 after 678 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 433 - phi=0.8120025043487552, PE=1.0888015268544422e-16 after 557 steps
Step: 433 - phi=0.8320000000000004, PE=0.0 after 245 steps
Step: 434 - phi=0.8179641418457034, PE=1.3665734691395333e-16 after 900 steps
Step: 434 - phi=0.8283125000000005, PE=8.001331032438044e-13 after 8764 steps
Step: 434 - phi=0.8283125000000005, PE=8.001331032423379e-13 after 6995 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 434 - phi=0.8169640960693363, PE=3.5564925379612924e-16 after 1064 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 434 - phi=0.8120025033950808, PE=9.990245497669913e-17 after 97 steps
Step: 434 - phi=0.8330000000000004, PE=0.0 after 224 steps
Step: 435 - phi=0.8179641265869144, PE=9.914837398855138e-17 after 333 steps
Step: 435 - phi=0.8282812500000004, PE=9.550667814066008e-17 after 892 steps
Step: 435 - phi=0.8282812500000004, PE=7.340663171726418e-17 after 812 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 435 - phi=0.8169640884399418, PE=2.076976944168632e-16 after 1038 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 435 - phi=0.8120025038719181, PE=1.0297783475211342e-16 after 416 steps
Step: 435 - phi=0.8340000000000004, PE=9.871929014568763e-08 after 970 steps
Step: 436 - phi=0.8179641342163089, PE=9.985803022550164e-17 after 270 steps
Step: 436 - phi=0.8282968750000004, PE=7.835607316881805e-17 after 773 steps
Step: 436 - phi=0.8282968750000004, PE=9.155047328640924e-17 after 800 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 436 - phi=0.8169640846252446, PE=1.485533905531563e-16 after 1022 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 436 - phi=0.8120025036334995, PE=1.0008835332484519e-16 after 388 steps
Step: 436 - phi=0.8335000000000004, PE=1.6035042032405925e-10 after 921 steps
Step: 437 - phi=0.8179641380310061, PE=9.984248286723937e-17 after 207 steps
Step: 437 - phi=0.8283046875000004, PE=8.138549374907807e-17 after 754 steps
Step: 437 - phi=0.8283046875000004, PE=9.390340857169316e-17 after 780 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 437 - phi=0.8169640827178959, PE=1.2268910887632805e-16 after 933 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 437 - phi=0.8120025035142902, PE=9.996127588493766e-17 after 51 steps
Step: 437 - phi=0.8332500000000004, PE=0.0 after 222 steps
Step: 438 - phi=0.8179641399383548, PE=1.1055401601517663e-16 after 830 steps
Step: 438 - phi=0.8283085937500004, PE=8.807540006831065e-17 after 733 steps
Step: 438 - phi=0.8283085937500004, PE=6.10804430773488e-17 after 728 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 438 - phi=0.8169640817642216, PE=1.1068393535992921e-16 after 902 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 438 - phi=0.8120025035738948, PE=9.997449829311119e-17 after 52 steps
Step: 438 - phi=0.8333750000000004, PE=9.483349270010613e-17 after 229 steps
Step: 439 - phi=0.8179641389846805, PE=9.989107486676599e-17 after 117 steps
Step: 439 - phi=0.8283105468750005, PE=9.529566763068544e-17 after 735 steps
Step: 439 - phi=0.8283105468750005, PE=8.801584852188584e-17 after 759 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 439 - phi=0.8169640812873844, PE=1.0491308971683511e-16 after 955 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 439 - phi=0.8120025036036971, PE=9.999016815677058e-17 after 55 steps
Step: 439 - phi=0.8334375000000004, PE=9.075589359678297e-17 after 233 steps
Step: 440 - phi=0.8179641394615176, PE=1.0446005785602989e-16 after 496 steps
Step: 440 - phi=0.8283115234375005, PE=7.924049874239407e-14 after 13377 steps
Step: 440 - phi=0.8283115234375005, PE=7.924049877847881e-14 after 10510 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 440 - phi=0.8169640810489658, PE=1.0208560424702146e-16 after 980 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 439 - phi=0.8120025036036971, PE=9.999016815677058e-17 after 55 steps
Step: 440 - phi=0.8334687500000004, PE=7.222941029841828e-17 after 251 steps
Step: 441 - phi=0.817964139223099, PE=1.014778615812693e-16 after 544 steps
Step: 441 - phi=0.8283110351562505, PE=9.997588851147562e-17 after 25380 steps
Step: 441 - phi=0.8283110351562505, PE=9.999044482665615e-17 after 20487 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 441 - phi=0.8169640809297565, PE=1.0068634418278865e-16 after 806 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 439 - phi=0.8120025036036971, PE=9.999016815677058e-17 after 55 steps
Step: 441 - phi=0.8334843750000004, PE=1.0446767415287624e-11 after 807 steps
Step: 442 - phi=0.8179641391038897, PE=1.0000295509941813e-16 after 546 steps
Step: 442 - phi=0.8283112792968754, PE=1.6446907263924536e-14 after 11805 steps
Step: 442 - phi=0.8283112792968754, PE=1.6446907261257107e-14 after 11884 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 442 - phi=0.8169640808701519, PE=9.999976261934744e-17 after 334 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 439 - phi=0.8120025036036971, PE=9.999016815677058e-17 after 55 steps
Step: 442 - phi=0.8334765625000005, PE=5.8475709926202e-17 after 202 steps
Step: 443 - phi=0.8179641390442851, PE=9.99995110409369e-17 after 42 steps
Step: 443 - phi=0.8283111572265629, PE=2.6646003322121706e-15 after 16277 steps
Step: 443 - phi=0.8283111572265629, PE=2.6646003349949283e-15 after 16258 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 443 - phi=0.8169640808999542, PE=1.0033803977353837e-16 after 863 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 439 - phi=0.8120025036036971, PE=9.999016815677058e-17 after 55 steps
Step: 443 - phi=0.8334804687500004, PE=7.645214284150883e-13 after 772 steps
Step: 444 - phi=0.8179641390740874, PE=9.999215981045002e-17 after 50 steps
Step: 444 - phi=0.8283110961914066, PE=1.7707342977463596e-16 after 22226 steps
Step: 444 - phi=0.8283110961914066, PE=1.7707343063801986e-16 after 22161 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 443 - phi=0.8169640808999542, PE=1.0033803977353837e-16 after 863 steps
Step: 439 - phi=0.8120025036036971, PE=9.999016815677058e-17 after 55 steps
Step: 444 - phi=0.8334785156250004, PE=9.128541590881474e-17 after 200 steps
Step: 444 - phi=0.8179641390740874, PE=9.999215981045002e-17 after 50 steps
Step: 445 - phi=0.8283110656738286, PE=9.998443165150935e-17 after 20656 steps
Step: 445 - phi=0.8283110656738286, PE=9.999019621846623e-17 after 20656 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 443 - phi=0.8169640808999542, PE=1.0033803977353837e-16 after 863 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 439 - phi=0.8120025036036971, PE=9.999016815677058e-17 after 55 steps
Step: 445 - phi=0.8334794921875004, PE=8.117957782747e-14 after 720 steps
Step: 444 - phi=0.8179641390740874, PE=9.999215981045002e-17 after 50 steps
Step: 446 - phi=0.8283110809326176, PE=9.998199241494212e-17 after 17359 steps
Step: 446 - phi=0.8283110809326176, PE=9.998509447027177e-17 after 17359 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 443 - phi=0.8169640808999542, PE=1.0033803977353837e-16 after 863 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 439 - phi=0.8120025036036971, PE=9.999016815677058e-17 after 55 steps
Step: 446 - phi=0.8334790039062504, PE=8.794307517262946e-17 after 191 steps
Step: 444 - phi=0.8179641390740874, PE=9.999215981045002e-17 after 50 steps
Step: 447 - phi=0.8283110885620122, PE=9.998826039248043e-17 after 13860 steps
Step: 447 - phi=0.8283110885620122, PE=9.998990018735287e-17 after 13860 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 443 - phi=0.8169640808999542, PE=1.0033803977353837e-16 after 863 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 439 - phi=0.8120025036036971, PE=9.999016815677058e-17 after 55 steps
Step: 447 - phi=0.8334792480468753, PE=1.8922146829583813e-14 after 626 steps
Step: 444 - phi=0.8179641390740874, PE=9.999215981045002e-17 after 50 steps
Step: 448 - phi=0.8283110923767094, PE=1.1907915345787394e-16 after 8599 steps
Step: 448 - phi=0.8283110923767094, PE=1.1907915192878546e-16 after 8755 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 443 - phi=0.8169640808999542, PE=1.0033803977353837e-16 after 863 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 439 - phi=0.8120025036036971, PE=9.999016815677058e-17 after 55 steps
Step: 448 - phi=0.8334791259765628, PE=4.0802069501595975e-15 after 629 steps
Step: 444 - phi=0.8179641390740874, PE=9.999215981045002e-17 after 50 steps
Step: 449 - phi=0.8283110904693608, PE=9.999858750594778e-17 after 7764 steps
Step: 449 - phi=0.8283110904693608, PE=9.999396007495935e-17 after 7765 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 443 - phi=0.8169640808999542, PE=1.0033803977353837e-16 after 863 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 439 - phi=0.8120025036036971, PE=9.999016815677058e-17 after 55 steps
Step: 449 - phi=0.8334790649414066, PE=7.309365516195586e-16 after 629 steps
Step: 444 - phi=0.8179641390740874, PE=9.999215981045002e-17 after 50 steps
Step: 450 - phi=0.8283110914230352, PE=1.0637242368514926e-16 after 4271 steps
Step: 450 - phi=0.8283110914230352, PE=1.0637242297550647e-16 after 4202 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 443 - phi=0.8169640808999542, PE=1.0033803977353837e-16 after 863 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 439 - phi=0.8120025036036971, PE=9.999016815677058e-17 after 55 steps
Step: 450 - phi=0.8334790344238285, PE=9.949628268883557e-17 after 148 steps
Step: 444 - phi=0.8179641390740874, PE=9.999215981045002e-17 after 50 steps
Step: 451 - phi=0.8283110909461979, PE=1.0028783524141966e-16 after 4342 steps
Step: 451 - phi=0.8283110909461979, PE=1.002878357472616e-16 after 4303 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 443 - phi=0.8169640808999542, PE=1.0033803977353837e-16 after 863 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 439 - phi=0.8120025036036971, PE=9.999016815677058e-17 after 55 steps
Step: 451 - phi=0.8334790496826175, PE=3.1775459826221456e-16 after 493 steps
Step: 444 - phi=0.8179641390740874, PE=9.999215981045002e-17 after 50 steps
Step: 452 - phi=0.8283110907077793, PE=9.999995400844247e-17 after 2867 steps
Step: 452 - phi=0.8283110907077793, PE=9.99996057504784e-17 after 2865 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 443 - phi=0.8169640808999542, PE=1.0033803977353837e-16 after 863 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 439 - phi=0.8120025036036971, PE=9.999016815677058e-17 after 55 steps
Step: 452 - phi=0.833479042053223, PE=1.7478397974332419e-16 after 453 steps
Step: 444 - phi=0.8179641390740874, PE=9.999215981045002e-17 after 50 steps
Step: 453 - phi=0.8283110908269886, PE=9.999926815470811e-17 after 2039 steps
Step: 453 - phi=0.8283110908269886, PE=9.999934342431164e-17 after 2039 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 443 - phi=0.8169640808999542, PE=1.0033803977353837e-16 after 863 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 439 - phi=0.8120025036036971, PE=9.999016815677058e-17 after 55 steps
Step: 453 - phi=0.8334790382385258, PE=1.1920376417741e-16 after 521 steps
Step: 444 - phi=0.8179641390740874, PE=9.999215981045002e-17 after 50 steps
Step: 454 - phi=0.8283110908865933, PE=9.999904642828461e-17 after 1449 steps
Step: 454 - phi=0.8283110908865933, PE=9.999919805641563e-17 after 1449 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 443 - phi=0.8169640808999542, PE=1.0033803977353837e-16 after 863 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 439 - phi=0.8120025036036971, PE=9.999016815677058e-17 after 55 steps
Step: 454 - phi=0.8334790363311771, PE=9.99526190930269e-17 after 74 steps
Step: 444 - phi=0.8179641390740874, PE=9.999215981045002e-17 after 50 steps
Step: 455 - phi=0.8283110909163955, PE=9.999965523620645e-17 after 1028 steps
Step: 455 - phi=0.8283110909163955, PE=9.999985514392955e-17 after 1028 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 443 - phi=0.8169640808999542, PE=1.0033803977353837e-16 after 863 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 439 - phi=0.8120025036036971, PE=9.999016815677058e-17 after 55 steps
Step: 455 - phi=0.8334790372848515, PE=1.0696549049369028e-16 after 485 steps
Step: 444 - phi=0.8179641390740874, PE=9.999215981045002e-17 after 50 steps
Step: 455 - phi=0.8283110909163955, PE=9.999965523620645e-17 after 1028 steps
Step: 455 - phi=0.8283110909163955, PE=9.999985514392955e-17 after 1028 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 443 - phi=0.8169640808999542, PE=1.0033803977353837e-16 after 863 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 439 - phi=0.8120025036036971, PE=9.999016815677058e-17 after 55 steps
Step: 456 - phi=0.8334790368080143, PE=1.0109487217709492e-16 after 403 steps
Step: 444 - phi=0.8179641390740874, PE=9.999215981045002e-17 after 50 steps
Step: 455 - phi=0.8283110909163955, PE=9.999965523620645e-17 after 1028 steps
Step: 457 - phi=0.8334790365695957, PE=9.995503469993689e-17 after 57 steps
Step: 455 - phi=0.8283110909163955, PE=9.999985514392955e-17 after 1028 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 443 - phi=0.8169640808999542, PE=1.0033803977353837e-16 after 863 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 439 - phi=0.8120025036036971, PE=9.999016815677058e-17 after 55 steps
Step: 444 - phi=0.8179641390740874, PE=9.999215981045002e-17 after 50 steps
Step: 455 - phi=0.8283110909163955, PE=9.999965523620645e-17 after 1028 steps
Step: 455 - phi=0.8283110909163955, PE=9.999985514392955e-17 after 1028 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 443 - phi=0.8169640808999542, PE=1.0033803977353837e-16 after 863 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 439 - phi=0.8120025036036971, PE=9.999016815677058e-17 after 55 steps
Step: 458 - phi=0.833479036688805, PE=9.99762357196307e-17 after 69 steps
Step: 444 - phi=0.8179641390740874, PE=9.999215981045002e-17 after 50 steps
Step: 455 - phi=0.8283110909163955, PE=9.999965523620645e-17 after 1028 steps
Step: 455 - phi=0.8283110909163955, PE=9.999985514392955e-17 after 1028 steps
Step: 410 - phi=0.783664767891169, PE=9.999522016493433e-17 after 91 steps
Step: 426 - phi=0.7994032813012604, PE=9.999962785436833e-17 after 57 steps
Step: 443 - phi=0.8169640808999542, PE=1.0033803977353837e-16 after 863 steps
Step: 427 - phi=0.8001242528855804, PE=1.000756908529721e-16 after 580 steps
Step: 421 - phi=0.7941858684122567, PE=9.999676427078802e-17 after 85 steps
Step: 439 - phi=0.8120025036036971, PE=9.999016815677058e-17 after 55 steps
Step: 459 - phi=0.8334790367484096, PE=1.0037269428303476e-16 after 333 steps
Final potential energy: [1.00372694e-16 1.00088352e-16 1.00281960e-16 1.00373245e-16
1.00686347e-16 1.00249128e-16 1.00155641e-16 1.00287835e-16
1.00287836e-16 1.00002956e-16]
Final packing fraction: [0.83347904 0.8120025 0.79418587 0.80012425 0.81696408 0.79940328
0.78366477 0.82831109 0.82831109 0.81796414]
Run the Jamming Algorithm for a Single System#
We can also run the jamming algorithm on a single system by passing the state and system to the jamming function. This is slightly more convenient.
state, system = build_microstate(0)
result = jdem.utils.jamming.bisection_jam(state, system)
state, system = result.jammed_state, result.jammed_system
print(f"Final potential energy: {result.potential_energy}")
print(f"Final packing fraction: {result.packing_fraction}")
Initial minimization took 47 steps.
Step: 1 - phi=0.4000000000000001, PE=0.0 after 0 steps
Step: 2 - phi=0.4010000000000001, PE=0.0 after 0 steps
Step: 3 - phi=0.4020000000000001, PE=0.0 after 35 steps
Step: 4 - phi=0.4030000000000001, PE=0.0 after 35 steps
Step: 5 - phi=0.4040000000000001, PE=0.0 after 35 steps
Step: 6 - phi=0.4050000000000001, PE=0.0 after 35 steps
Step: 7 - phi=0.4060000000000001, PE=0.0 after 35 steps
Step: 8 - phi=0.4070000000000001, PE=0.0 after 35 steps
Step: 9 - phi=0.4080000000000001, PE=0.0 after 35 steps
Step: 10 - phi=0.4090000000000001, PE=0.0 after 35 steps
Step: 11 - phi=0.4100000000000001, PE=0.0 after 35 steps
Step: 12 - phi=0.4110000000000001, PE=0.0 after 35 steps
Step: 13 - phi=0.4120000000000001, PE=0.0 after 35 steps
Step: 14 - phi=0.4130000000000001, PE=0.0 after 35 steps
Step: 15 - phi=0.4140000000000001, PE=0.0 after 35 steps
Step: 16 - phi=0.4150000000000001, PE=0.0 after 35 steps
Step: 17 - phi=0.4160000000000001, PE=0.0 after 35 steps
Step: 18 - phi=0.4170000000000001, PE=0.0 after 35 steps
Step: 19 - phi=0.4180000000000001, PE=0.0 after 35 steps
Step: 20 - phi=0.4190000000000001, PE=0.0 after 35 steps
Step: 21 - phi=0.4200000000000001, PE=0.0 after 35 steps
Step: 22 - phi=0.4210000000000001, PE=0.0 after 35 steps
Step: 23 - phi=0.4220000000000001, PE=0.0 after 35 steps
Step: 24 - phi=0.4230000000000001, PE=0.0 after 35 steps
Step: 25 - phi=0.4240000000000001, PE=0.0 after 35 steps
Step: 26 - phi=0.4250000000000001, PE=0.0 after 35 steps
Step: 27 - phi=0.4260000000000001, PE=0.0 after 35 steps
Step: 28 - phi=0.4270000000000001, PE=0.0 after 35 steps
Step: 29 - phi=0.4280000000000001, PE=0.0 after 35 steps
Step: 30 - phi=0.4290000000000001, PE=0.0 after 35 steps
Step: 31 - phi=0.4300000000000001, PE=0.0 after 35 steps
Step: 32 - phi=0.4310000000000001, PE=0.0 after 35 steps
Step: 33 - phi=0.4320000000000001, PE=0.0 after 35 steps
Step: 34 - phi=0.4330000000000001, PE=0.0 after 35 steps
Step: 35 - phi=0.4340000000000001, PE=0.0 after 35 steps
Step: 36 - phi=0.4350000000000001, PE=0.0 after 35 steps
Step: 37 - phi=0.4360000000000001, PE=0.0 after 35 steps
Step: 38 - phi=0.4370000000000001, PE=0.0 after 35 steps
Step: 39 - phi=0.4380000000000001, PE=0.0 after 35 steps
Step: 40 - phi=0.4390000000000001, PE=0.0 after 35 steps
Step: 41 - phi=0.4400000000000001, PE=0.0 after 35 steps
Step: 42 - phi=0.4410000000000001, PE=0.0 after 35 steps
Step: 43 - phi=0.4420000000000001, PE=0.0 after 34 steps
Step: 44 - phi=0.4430000000000001, PE=0.0 after 34 steps
Step: 45 - phi=0.4440000000000001, PE=0.0 after 34 steps
Step: 46 - phi=0.4450000000000001, PE=0.0 after 34 steps
Step: 47 - phi=0.4460000000000001, PE=0.0 after 41 steps
Step: 48 - phi=0.4470000000000001, PE=0.0 after 41 steps
Step: 49 - phi=0.4480000000000001, PE=0.0 after 41 steps
Step: 50 - phi=0.4490000000000001, PE=0.0 after 41 steps
Step: 51 - phi=0.4500000000000001, PE=0.0 after 41 steps
Step: 52 - phi=0.4510000000000001, PE=0.0 after 41 steps
Step: 53 - phi=0.4520000000000001, PE=0.0 after 41 steps
Step: 54 - phi=0.4530000000000001, PE=0.0 after 41 steps
Step: 55 - phi=0.4540000000000001, PE=0.0 after 41 steps
Step: 56 - phi=0.4550000000000001, PE=0.0 after 41 steps
Step: 57 - phi=0.4560000000000001, PE=0.0 after 41 steps
Step: 58 - phi=0.45700000000000013, PE=0.0 after 41 steps
Step: 59 - phi=0.45800000000000013, PE=0.0 after 41 steps
Step: 60 - phi=0.45900000000000013, PE=0.0 after 41 steps
Step: 61 - phi=0.46000000000000013, PE=0.0 after 41 steps
Step: 62 - phi=0.46100000000000013, PE=0.0 after 41 steps
Step: 63 - phi=0.46200000000000013, PE=0.0 after 41 steps
Step: 64 - phi=0.46300000000000013, PE=0.0 after 41 steps
Step: 65 - phi=0.46400000000000013, PE=0.0 after 41 steps
Step: 66 - phi=0.46500000000000014, PE=0.0 after 41 steps
Step: 67 - phi=0.46600000000000014, PE=0.0 after 41 steps
Step: 68 - phi=0.46700000000000014, PE=0.0 after 41 steps
Step: 69 - phi=0.46800000000000014, PE=0.0 after 41 steps
Step: 70 - phi=0.46900000000000014, PE=0.0 after 41 steps
Step: 71 - phi=0.47000000000000014, PE=0.0 after 41 steps
Step: 72 - phi=0.47100000000000014, PE=0.0 after 41 steps
Step: 73 - phi=0.47200000000000014, PE=0.0 after 41 steps
Step: 74 - phi=0.47300000000000014, PE=0.0 after 41 steps
Step: 75 - phi=0.47400000000000014, PE=0.0 after 41 steps
Step: 76 - phi=0.47500000000000014, PE=0.0 after 41 steps
Step: 77 - phi=0.47600000000000015, PE=0.0 after 41 steps
Step: 78 - phi=0.47700000000000015, PE=0.0 after 41 steps
Step: 79 - phi=0.47800000000000015, PE=0.0 after 41 steps
Step: 80 - phi=0.47900000000000015, PE=0.0 after 41 steps
Step: 81 - phi=0.48000000000000015, PE=0.0 after 41 steps
Step: 82 - phi=0.48100000000000015, PE=0.0 after 41 steps
Step: 83 - phi=0.48200000000000015, PE=0.0 after 41 steps
Step: 84 - phi=0.48300000000000015, PE=0.0 after 41 steps
Step: 85 - phi=0.48400000000000015, PE=0.0 after 41 steps
Step: 86 - phi=0.48500000000000015, PE=0.0 after 41 steps
Step: 87 - phi=0.48600000000000015, PE=0.0 after 41 steps
Step: 88 - phi=0.48700000000000015, PE=0.0 after 42 steps
Step: 89 - phi=0.48800000000000016, PE=0.0 after 42 steps
Step: 90 - phi=0.48900000000000016, PE=0.0 after 42 steps
Step: 91 - phi=0.49000000000000016, PE=0.0 after 42 steps
Step: 92 - phi=0.49100000000000016, PE=0.0 after 42 steps
Step: 93 - phi=0.49200000000000016, PE=0.0 after 42 steps
Step: 94 - phi=0.49300000000000016, PE=0.0 after 42 steps
Step: 95 - phi=0.49400000000000016, PE=0.0 after 42 steps
Step: 96 - phi=0.49500000000000016, PE=0.0 after 42 steps
Step: 97 - phi=0.49600000000000016, PE=0.0 after 42 steps
Step: 98 - phi=0.49700000000000016, PE=0.0 after 42 steps
Step: 99 - phi=0.49800000000000016, PE=0.0 after 42 steps
Step: 100 - phi=0.49900000000000017, PE=0.0 after 42 steps
Step: 101 - phi=0.5000000000000001, PE=0.0 after 42 steps
Step: 102 - phi=0.5010000000000001, PE=0.0 after 42 steps
Step: 103 - phi=0.5020000000000001, PE=0.0 after 42 steps
Step: 104 - phi=0.5030000000000001, PE=0.0 after 42 steps
Step: 105 - phi=0.5040000000000001, PE=0.0 after 42 steps
Step: 106 - phi=0.5050000000000001, PE=0.0 after 42 steps
Step: 107 - phi=0.5060000000000001, PE=0.0 after 41 steps
Step: 108 - phi=0.5070000000000001, PE=0.0 after 41 steps
Step: 109 - phi=0.5080000000000001, PE=0.0 after 41 steps
Step: 110 - phi=0.5090000000000001, PE=0.0 after 41 steps
Step: 111 - phi=0.5100000000000001, PE=0.0 after 41 steps
Step: 112 - phi=0.5110000000000001, PE=0.0 after 41 steps
Step: 113 - phi=0.5120000000000001, PE=0.0 after 41 steps
Step: 114 - phi=0.5130000000000001, PE=0.0 after 41 steps
Step: 115 - phi=0.5140000000000001, PE=0.0 after 41 steps
Step: 116 - phi=0.5150000000000001, PE=0.0 after 41 steps
Step: 117 - phi=0.5160000000000001, PE=0.0 after 41 steps
Step: 118 - phi=0.5170000000000001, PE=0.0 after 41 steps
Step: 119 - phi=0.5180000000000001, PE=0.0 after 41 steps
Step: 120 - phi=0.5190000000000001, PE=0.0 after 41 steps
Step: 121 - phi=0.5200000000000001, PE=0.0 after 41 steps
Step: 122 - phi=0.5210000000000001, PE=0.0 after 41 steps
Step: 123 - phi=0.5220000000000001, PE=0.0 after 41 steps
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Step: 447 - phi=0.8334792480468753, PE=1.8922146829583813e-14 after 626 steps
Step: 448 - phi=0.8334791259765628, PE=4.0802069501595975e-15 after 629 steps
Step: 449 - phi=0.8334790649414066, PE=7.309365516195586e-16 after 629 steps
Step: 450 - phi=0.8334790344238285, PE=9.949628268883557e-17 after 148 steps
Step: 451 - phi=0.8334790496826175, PE=3.1775459826221456e-16 after 493 steps
Step: 452 - phi=0.833479042053223, PE=1.7478397974332419e-16 after 453 steps
Step: 453 - phi=0.8334790382385258, PE=1.1920376417741e-16 after 521 steps
Step: 454 - phi=0.8334790363311771, PE=9.99526190930269e-17 after 74 steps
Step: 455 - phi=0.8334790372848515, PE=1.0696549049369028e-16 after 485 steps
Step: 456 - phi=0.8334790368080143, PE=1.0109487217709492e-16 after 403 steps
Step: 457 - phi=0.8334790365695957, PE=9.995503469993689e-17 after 57 steps
Step: 458 - phi=0.833479036688805, PE=9.99762357196307e-17 after 69 steps
Step: 459 - phi=0.8334790367484096, PE=1.0037269428303476e-16 after 333 steps
Final potential energy: 1.0037269428303476e-16
Final packing fraction: 0.8334790367186073
Total running time of the script: (0 minutes 23.300 seconds)