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Exploring reaching equilibrium, first on a shorter timescale and then a longer one¶

(but both with identical time steps.)¶

The system starts out with a "concentration pulse" in bin 2 (the 3rd bin from the left) - i.e. that bin is initially the only one with a non-zero concentration of the only chemical species.

Notice the diffusing pulse "bouncing" off the left wall after total time 30.

Then the system is left undisturbed, and followed to equilibrium.

NO log file.

LAST REVISED: May 27, 2023

In [1]:

import set_path      # Importing this module will add the project's home directory to sys.path

Added 'D:\Docs\- MY CODE\BioSimulations\life123-Win7' to sys.path

In [2]:

from src.modules.reactions.reaction_data import ReactionData as chem
from src.life_1D.bio_sim_1d import BioSim1D

In [3]:

chem_data = chem(diffusion_rates=[0.1])
bio = BioSim1D(n_bins=10, chem_data=chem_data)

bio.set_uniform_concentration(species_index=0, conc=0.)
bio.inject_conc_to_bin(species_index=0, bin_address=2, delta_conc=10.)

bio.describe_state()

SYSTEM STATE at Time t = 0:
10 bins and 1 species:
  Species 0 (Chemical 1). Diff rate: 0.1. Conc: [ 0.  0. 10.  0.  0.  0.  0.  0.  0.  0.]

In [4]:

print("\n\nSTARTING on SHORTER time scales.  Dtime=10, with time steps of 0.1 ...")


STARTING on SHORTER time scales.  Dtime=10, with time steps of 0.1 ...

In [5]:

for i in range(10):
    delta_time = 10.
    status = bio.diffuse(total_duration=delta_time, time_step=0.1)
    print(f"\nAfter Delta time {delta_time}.  ({status['steps']} steps taken):")
    bio.describe_state(concise=True)

After Delta time 10.0.  (100 steps taken):
SYSTEM STATE at Time t = 10:
[[1.22598070e+00 2.22414009e+00 3.08221111e+00 2.15823525e+00
  9.37782076e-01 2.88503658e-01 6.79378836e-02 1.28711509e-02
  2.03304706e-03 3.05037621e-04]]

After Delta time 10.0.  (100 steps taken):
SYSTEM STATE at Time t = 20:
[[1.79154498 2.04604996 2.15752876 1.81408657 1.18572897 0.61493163
  0.26031377 0.09234937 0.02835038 0.00911562]]

After Delta time 10.0.  (100 steps taken):
SYSTEM STATE at Time t = 30:
[[1.908894   1.93254508 1.86205856 1.60230147 1.1912129  0.75904212
  0.41665574 0.19951697 0.08641213 0.04136102]]

After Delta time 10.0.  (100 steps taken):
SYSTEM STATE at Time t = 40:
[[1.89162641 1.84625985 1.72030668 1.48693078 1.1664388  0.82118645
  0.51779486 0.29499154 0.15846579 0.09599884]]

After Delta time 10.0.  (100 steps taken):
SYSTEM STATE at Time t = 50:
[[1.83433746 1.76930884 1.63070397 1.41626323 1.14422761 0.85269498
  0.58491221 0.37309998 0.2318666  0.16258513]]

After Delta time 10.0.  (100 steps taken):
SYSTEM STATE at Time t = 60:
[[1.76697624 1.69877596 1.56309588 1.36661912 1.12701103 0.87222369
  0.63367319 0.43785006 0.30151635 0.23225847]]

After Delta time 10.0.  (100 steps taken):
SYSTEM STATE at Time t = 70:
[[1.69980096 1.63420894 1.50697719 1.32775575 1.11331789 0.8864918
  0.67231694 0.49325804 0.36586375 0.30000873]]

After Delta time 10.0.  (100 steps taken):
SYSTEM STATE at Time t = 80:
[[1.63637931 1.57533401 1.45817295 1.29515888 1.10189171 0.89806096
  0.7048592  0.54188555 0.42468407 0.36357336]]

After Delta time 10.0.  (100 steps taken):
SYSTEM STATE at Time t = 90:
[[1.57781285 1.52179206 1.41478512 1.26674457 1.09200065 0.90798758
  0.73325992 0.58522943 0.47821243 0.42217538]]

After Delta time 10.0.  (100 steps taken):
SYSTEM STATE at Time t = 100:
[[1.5242553  1.47317189 1.37581121 1.2414767  1.08324636 0.91675072
  0.75852442 0.6241924  0.52682923 0.47574177]]

Notice the diffusing pulse "bounces" off the left wall after total time 30:
the concentration at cell 0 increases from t=0 to 30, and then it's coming down by t=40

In [6]:

print("\n\nREPEATING to LONGER time scales.  Dtime=100, again with time steps of 0.1 ...")

# Reset the concentrations
bio.set_uniform_concentration(species_index=0, conc=0.)
bio.inject_conc_to_bin(species_index=0, bin_address=2, delta_conc=10.)

#total_time = 0.
for i in range(20):
    delta_time = 100.
    status = bio.diffuse(total_duration=delta_time, time_step=0.1)
    print(f"\nAfter Delta time {delta_time}.  ({status['steps']} steps taken):")
    bio.describe_state(concise=True)


REPEATING to LONGER time scales.  Dtime=100, again with time steps of 0.1 ...

After Delta time 100.0.  (1000 steps taken):
SYSTEM STATE at Time t = 200:
[[1.5242553  1.47317189 1.37581121 1.2414767  1.08324636 0.91675072
  0.75852442 0.6241924  0.52682923 0.47574177]]

After Delta time 100.0.  (1000 steps taken):
SYSTEM STATE at Time t = 300:
[[1.19700758 1.17772317 1.14104198 1.09055457 1.03120299 0.96879701
  0.90944543 0.85895802 0.82227683 0.80299242]]

After Delta time 100.0.  (1000 steps taken):
SYSTEM STATE at Time t = 400:
[[1.07398731 1.06674491 1.05296906 1.03400823 1.01171844 0.98828156
  0.96599177 0.94703094 0.93325509 0.92601269]]

After Delta time 100.0.  (1000 steps taken):
SYSTEM STATE at Time t = 500:
[[1.02778634 1.02506642 1.01989282 1.01277198 1.00440092 0.99559908
  0.98722802 0.98010718 0.97493358 0.97221366]]

After Delta time 100.0.  (1000 steps taken):
SYSTEM STATE at Time t = 600:
[[1.01043531 1.00941383 1.00747086 1.00479659 1.00165279 0.99834721
  0.99520341 0.99252914 0.99058617 0.98956469]]

After Delta time 100.0.  (1000 steps taken):
SYSTEM STATE at Time t = 700:
[[1.00391904 1.00353542 1.00280572 1.00180138 1.00062071 0.99937929
  0.99819862 0.99719428 0.99646458 0.99608096]]

After Delta time 100.0.  (1000 steps taken):
SYSTEM STATE at Time t = 800:
[[1.00147182 1.00132774 1.0010537  1.00067652 1.00023311 0.99976689
  0.99932348 0.9989463  0.99867226 0.99852818]]

After Delta time 100.0.  (1000 steps taken):
SYSTEM STATE at Time t = 900:
[[1.00055275 1.00049864 1.00039572 1.00025407 1.00008755 0.99991245
  0.99974593 0.99960428 0.99950136 0.99944725]]

After Delta time 100.0.  (1000 steps taken):
SYSTEM STATE at Time t = 1,000:
[[1.00020759 1.00018727 1.00014862 1.00009542 1.00003288 0.99996712
  0.99990458 0.99985138 0.99981273 0.99979241]]

After Delta time 100.0.  (1000 steps taken):
SYSTEM STATE at Time t = 1,100:
[[1.00007796 1.00007033 1.00005581 1.00003583 1.00001235 0.99998765
  0.99996417 0.99994419 0.99992967 0.99992204]]

After Delta time 100.0.  (1000 steps taken):
SYSTEM STATE at Time t = 1,200:
[[1.00002928 1.00002641 1.00002096 1.00001346 1.00000464 0.99999536
  0.99998654 0.99997904 0.99997359 0.99997072]]

After Delta time 100.0.  (1000 steps taken):
SYSTEM STATE at Time t = 1,300:
[[1.000011   1.00000992 1.00000787 1.00000505 1.00000174 0.99999826
  0.99999495 0.99999213 0.99999008 0.999989  ]]

After Delta time 100.0.  (1000 steps taken):
SYSTEM STATE at Time t = 1,400:
[[1.00000413 1.00000373 1.00000296 1.0000019  1.00000065 0.99999935
  0.9999981  0.99999704 0.99999627 0.99999587]]

After Delta time 100.0.  (1000 steps taken):
SYSTEM STATE at Time t = 1,500:
[[1.00000155 1.0000014  1.00000111 1.00000071 1.00000025 0.99999975
  0.99999929 0.99999889 0.9999986  0.99999845]]

After Delta time 100.0.  (1000 steps taken):
SYSTEM STATE at Time t = 1,600:
[[1.00000058 1.00000053 1.00000042 1.00000027 1.00000009 0.99999991
  0.99999973 0.99999958 0.99999947 0.99999942]]

After Delta time 100.0.  (1000 steps taken):
SYSTEM STATE at Time t = 1,700:
[[1.00000022 1.0000002  1.00000016 1.0000001  1.00000003 0.99999997
  0.9999999  0.99999984 0.9999998  0.99999978]]

After Delta time 100.0.  (1000 steps taken):
SYSTEM STATE at Time t = 1,800:
[[1.00000008 1.00000007 1.00000006 1.00000004 1.00000001 0.99999999
  0.99999996 0.99999994 0.99999993 0.99999992]]

After Delta time 100.0.  (1000 steps taken):
SYSTEM STATE at Time t = 1,900:
[[1.00000003 1.00000003 1.00000002 1.00000001 1.         1.
  0.99999999 0.99999998 0.99999997 0.99999997]]

After Delta time 100.0.  (1000 steps taken):
SYSTEM STATE at Time t = 2,000:
[[1.00000001 1.00000001 1.00000001 1.00000001 1.         1.
  0.99999999 0.99999999 0.99999999 0.99999999]]

After Delta time 100.0.  (1000 steps taken):
SYSTEM STATE at Time t = 2,100:
[[1. 1. 1. 1. 1. 1. 1. 1. 1. 1.]]

The system has now reached equilibrium¶

In [ ]: