1. Simulating Mass Budget

(The contents presented in this section were re-developed principally by Dr. P. K. Yadav. The original tool, Spreadsheet based, was developed by Prof. Rudolf Liedl)

1.1. How to use the tool?

1. Go to the Binder by clicking the rocket button (top-right of the page)

2. Execute the code cell

3. Change the values of different quantities in the box.

This tool can also be downloaded and run locally. For that download the deacy.ipynb file and execute the process in any editor (e.g., JUPYTER notebook, JUPYTER lab) that is able to read and execute this file-type.

The code may also be executed in the book page.

The codes are licensed under CC by 4.0 (use anyways, but acknowledge the original work)

# Used library
import numpy as np # for calculation
import matplotlib.pyplot as plt # for plots
import pandas as pd  # for table
import ipywidgets as widgets  # for widgets

# The main function

def mass_bal(n_simulation, MA, MB, MC, R_A, R_B):
    
    A = np.zeros(n_simulation) # creat an array with zros
    B = np.zeros(n_simulation)
    C = np.zeros(n_simulation) 
    time  = np.arange(n_simulation)
    
    for i in range(0,n_simulation-1):
        A[0] = MA  # starting input value
        
        B[0] = MB
        C[0] = MC
        A[i+1] = A[i]-R_A*A[i]
        B[i+1] = B[i]+R_A*A[i]-R_B*B[i] 
        C[i+1] = C[i]+R_B*B[i]
        summ = A[i]+B[i]+C[i]
        
    d = {"Mass_A": A, "Mass_B": B, "Mass_C": C, "Total Mass": summ}
    df = pd.DataFrame(d) # Generating result table
    label = ["Mass A (g)", "Mass B (g)", "Mass C (g)"]
    fig = plt.figure(figsize=(6,4))
    plt.plot(time, A, time, B, time, C, linewidth=3);  # plotting the results
    plt.xlabel("Time [Time Unit]"); plt.ylabel("Mass [g]") # placing axis labels
    plt.legend(label, loc=0);plt.grid(); plt.xlim([0,n_simulation]); plt.ylim(bottom=0) # legends, grids, x,y limits
    plt.show() # display plot
    
    return print(df.round(2)) 

# Widgets and interactive

N = widgets.BoundedIntText(value=20,min=0,max=100,step=1,description= 'Δ t (day)',disabled=False)

A = widgets.BoundedFloatText(value=100,min=0,max=1000.0,step=1,description='M<sub>A</sub> (kg)',disabled=False)

B = widgets.BoundedFloatText(value=5,min=0,max=1000.0,step=1,description='M<sub>B</sub> (kg)',disabled=False)

C = widgets.BoundedFloatText(value=10,min=0,max=1000,step=0.1,description='M<sub>C</sub> (kg)',disabled=False)

RA = widgets.BoundedFloatText(value=0.2,min=0,max=100,step=0.1,description='R<sub>A</sub> (day<sup>-1 </sup>)',disabled=False)

RB = widgets.BoundedFloatText(value=0.2,min=0,max=100,step=0.1,description='R<sub>B</sub> (day<sup>-1 </sup>)',disabled=False)


interactive_plot = widgets.interactive(mass_bal, n_simulation = N, MA=A, MB=B, MC=C, R_A=RA, R_B=RB,)
output = interactive_plot.children[-1]  
#output.layout.height = '350px'
interactive_plot