Exploring reaching equilibrium¶

The system starts out with a pulse in bins near the left and the right endpoints

LAST REVISED: June 23, 2024 (using v. 1.0 beta34.1)

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 experiments.get_notebook_info import get_notebook_basename

from life123 import BioSim1D

import plotly.express as px

from life123 import ChemData as chem
from life123 import HtmlLog as log
from life123 import GraphicLog

In [3]:

# Initialize the HTML logging
log_file = get_notebook_basename() + ".log.htm"    # Use the notebook base filename for the log file
GraphicLog.config(filename=log_file,
                  components=["vue_heatmap_11", "vue_curves_3"])

-> Output will be LOGGED into the file 'reach_equilibrium_2.log.htm'

In [4]:

# Set the heatmap parameters
heatmap_pars = {"range": [0, 2.5],
                "outer_width": 850, "outer_height": 150,
                "margins": {"top": 30, "right": 30, "bottom": 30, "left": 55}
                }

# Set the parameters of the line plots
lineplot_pars = {"range": [0, 10],
                "outer_width": 850, "outer_height": 250,
                "margins": {"top": 30, "right": 30, "bottom": 30, "left": 55}
                }

In [5]:

# Initialize the system
chem_data = chem(names=["A"], diffusion_rates=[0.1])
bio = BioSim1D(n_bins=9, chem_data=chem_data)

bio.set_uniform_concentration(species_index=0, conc=0.)

# Start out with a pulse in bins near the *left* and the *right* endpoints.  
# A total of 20 "units of concentration" is injected
bio.inject_conc_to_bin(species_index=0, bin_address=2, delta_conc=10.)
bio.inject_conc_to_bin(species_index=0, bin_address=6, delta_conc=10.)

bio.describe_state()

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

In [6]:

bio.show_system_snapshot()

SYSTEM SNAPSHOT at time 0:
      A
0   0.0
1   0.0
2  10.0
3   0.0
4   0.0
5   0.0
6  10.0
7   0.0
8   0.0

In [7]:

fig = px.line(data_frame=bio.system_snapshot(), y=["A"], 
              title= f"Diffusion. System snapshot at time t={bio.system_time}",
              color_discrete_sequence = ['red'],
              labels={"value":"concentration", "variable":"Chemical", "index":"Bin number"})
fig.show()

In [8]:

# Output to the log file
log.write("1-D diffusion to equilibrium of a single species, with Diffusion rate 0.1. Time steps of 0.1",
          style=log.h2)

log.write(f"System state at time t={bio.system_time}:", blanks_before=2, style=log.bold)

# Output a heatmap to the log file
bio.single_species_heatmap(species_index=0, heatmap_pars=heatmap_pars, header=f"Time {bio.system_time} :\n", graphic_component="vue_heatmap_11")
# Output a line plot the log file
bio.single_species_line_plot(species_index=0, plot_pars=lineplot_pars, graphic_component="vue_curves_3")

1-D diffusion to equilibrium of a single species, with Diffusion rate 0.1. Time steps of 0.1


System state at time t=0:
[GRAPHIC ELEMENT SENT TO LOG FILE `reach_equilibrium_2.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `reach_equilibrium_2.log.htm`]

Start the simulation steps¶

In [9]:

delta_time = 3.

In [10]:

for i in range(15):
    status = bio.diffuse(total_duration=delta_time, time_step=0.1)

    print(f"\nAfter Delta time {delta_time}.  TOTAL TIME {bio.system_time}  ({status['steps']} steps taken):")
    bio.describe_state(concise=True)

    fig = px.line(data_frame=bio.system_snapshot(), y=["A"], 
              title= f"Diffusion. System snapshot at time t={bio.system_time}",
              color_discrete_sequence = ['red'],
              labels={"value":"concentration", "variable":"Chemical", "index":"Bin number"})
    fig.show()

    #if i<2 or i==6 or i>=14:
    bio.single_species_heatmap(species_index=0, heatmap_pars=heatmap_pars, header=f"Time {bio.system_time}\n", graphic_component="vue_heatmap_11")
    # Output a line plot the log file
    bio.single_species_line_plot(species_index=0, plot_pars=lineplot_pars, graphic_component="vue_curves_3")

After Delta time 3.0.  TOTAL TIME 3.0000000000000013  (30 steps taken):
SYSTEM STATE at Time t = 3:
[[0.27757451 1.74303541 5.96050983 1.76527256 0.5072154  1.76527256
  5.96050983 1.74303541 0.27757451]]

[GRAPHIC ELEMENT SENT TO LOG FILE `reach_equilibrium_2.log.htm`]
[GRAPHIC ELEMENT SENT TO LOG FILE `reach_equilibrium_2.log.htm`]

After Delta time 3.0.  TOTAL TIME 5.999999999999995  (30 steps taken):
SYSTEM STATE at Time t = 6:
[[0.73152765 2.1834153  4.18877184 2.28238941 1.22779161 2.28238941
  4.18877184 2.1834153  0.73152765]]

[GRAPHIC ELEMENT SENT TO LOG FILE `reach_equilibrium_2.log.htm`]
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After Delta time 3.0.  TOTAL TIME 8.999999999999984  (30 steps taken):
SYSTEM STATE at Time t = 9:
[[1.12120196 2.24355388 3.33164561 2.4287678  1.7496615  2.4287678
  3.33164561 2.24355388 1.12120196]]

[GRAPHIC ELEMENT SENT TO LOG FILE `reach_equilibrium_2.log.htm`]
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After Delta time 3.0.  TOTAL TIME 11.999999999999973  (30 steps taken):
SYSTEM STATE at Time t = 12:
[[1.40992642 2.21285813 2.88112821 2.46180799 2.06855851 2.46180799
  2.88112821 2.21285813 1.40992642]]

[GRAPHIC ELEMENT SENT TO LOG FILE `reach_equilibrium_2.log.htm`]
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After Delta time 3.0.  TOTAL TIME 14.999999999999963  (30 steps taken):
SYSTEM STATE at Time t = 15:
[[1.61375804 2.17517282 2.62918072 2.4582931  2.24719065 2.4582931
  2.62918072 2.17517282 1.61375804]]

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After Delta time 3.0.  TOTAL TIME 17.999999999999986  (30 steps taken):
SYSTEM STATE at Time t = 18:
[[1.75622069 2.14971234 2.4820061  2.44230075 2.33952022 2.44230075
  2.4820061  2.14971234 1.75622069]]

[GRAPHIC ELEMENT SENT TO LOG FILE `reach_equilibrium_2.log.htm`]
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After Delta time 3.0.  TOTAL TIME 21.00000000000003  (30 steps taken):
SYSTEM STATE at Time t = 21:
[[1.8567287  2.13705992 2.39331754 2.42217874 2.38143019 2.42217874
  2.39331754 2.13705992 1.8567287 ]]

[GRAPHIC ELEMENT SENT TO LOG FILE `reach_equilibrium_2.log.htm`]
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After Delta time 3.0.  TOTAL TIME 24.00000000000007  (30 steps taken):
SYSTEM STATE at Time t = 24:
[[1.92909045 2.13366871 2.33854991 2.40125523 2.39487141 2.40125523
  2.33854991 2.13366871 1.92909045]]

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After Delta time 3.0.  TOTAL TIME 27.000000000000114  (30 steps taken):
SYSTEM STATE at Time t = 27:
[[1.98256145 2.13602714 2.30397039 2.38102863 2.39282476 2.38102863
  2.30397039 2.13602714 1.98256145]]

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After Delta time 3.0.  TOTAL TIME 30.000000000000156  (30 steps taken):
SYSTEM STATE at Time t = 30:
[[2.0231929  2.14155643 2.28163209 2.3622001  2.38283695 2.3622001
  2.28163209 2.14155643 2.0231929 ]]

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After Delta time 3.0.  TOTAL TIME 33.0000000000002  (30 steps taken):
SYSTEM STATE at Time t = 33:
[[2.05491235 2.14857175 2.26683188 2.34506617 2.36923571 2.34506617
  2.26683188 2.14857175 2.05491235]]

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After Delta time 3.0.  TOTAL TIME 36.00000000000024  (30 steps taken):
SYSTEM STATE at Time t = 36:
[[2.0802789  2.15604676 2.2567439  2.32970151 2.35445786 2.32970151
  2.2567439  2.15604676 2.0802789 ]]

[GRAPHIC ELEMENT SENT TO LOG FILE `reach_equilibrium_2.log.htm`]
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After Delta time 3.0.  TOTAL TIME 39.000000000000284  (30 steps taken):
SYSTEM STATE at Time t = 39:
[[2.1009805  2.16339318 2.24965092 2.31605836 2.33983408 2.31605836
  2.24965092 2.16339318 2.1009805 ]]

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After Delta time 3.0.  TOTAL TIME 42.00000000000033  (30 steps taken):
SYSTEM STATE at Time t = 42:
[[2.11815199 2.1702984  2.24449902 2.30402493 2.32605132 2.30402493
  2.24449902 2.1702984  2.11815199]]

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After Delta time 3.0.  TOTAL TIME 45.00000000000037  (30 steps taken):
SYSTEM STATE at Time t = 45:
[[2.13257541 2.1766169  2.24063469 2.29346029 2.31342543 2.29346029
  2.24063469 2.1766169  2.13257541]]

[GRAPHIC ELEMENT SENT TO LOG FILE `reach_equilibrium_2.log.htm`]
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All cells now have essentially uniform concentration

The "20 units of concentration" are now uniformly spread across the 9 bins, leading to a near-constant concentration of 20/9 = 2.22

In [ ]: