#%% #Libraries import numpy as np from scipy.integrate import odeint import matplotlib.pyplot as plt import matplotlib matplotlib.rcParams.update({'font.size': 13}) from matplotlib.widgets import Slider, Button #%% def ODEfun(Yfuncvec, t): # Explicit equations C1= 0.0038746 + 0.2739782*t + 1.574621*t**2 - 0.2550041*t**3 C2= -33.43818 + 37.18972*t - 11.58838*t**2 + 1.695303*t**3 - 0.1298667*t**4 + 0.005028*t**5 - 7.743*10**-5*t**6 C = np.where(t<=4, C1, C2) E=C/51 dFdt=E dtmdt=t*E # Differential equations return np.array([dFdt, dtmdt]) tspan = np.linspace(0, 14, 100) y0 = np.array([0,0]) #%% fig, (ax1, ax2) = plt.subplots(1, 2) fig.suptitle("""LEP-16-2: Mean Residence Time and Variance Calculations (Part a,b)""", x = 0.24, y=0.98, fontweight='bold') plt.subplots_adjust(left = 0.3) C1= 0.0038746 + 0.2739782*tspan + 1.574621*tspan**2 - 0.2550041*tspan**3 C2= -33.43818 + 37.18972*tspan - 11.58838*tspan**2 + 1.695303*tspan**3 - 0.1298667*tspan**4 + 0.005028*tspan**5 - 7.743*10**-5*tspan**6 C = np.where(tspan<=4, C1, C2) E=C/51 sol = odeint(ODEfun, y0, tspan) F = sol[:, 0] tm = sol[:, 1] ax1.plot(tspan, tm) ax1.legend(['$t_m$'], loc='best') ax1.set_xlabel('t (min)', fontsize='medium') ax1.set_ylabel('$t_m (min)$', fontsize='medium') #ax1.set_ylim(0,10) ax1.set_xlim(0,14) ax1.set_ylim(0,8) ax1.grid() ax1.text(-12.5, 3,'Differential Equations' '\n\n' r'$\dfrac{dF}{dt} = E$' '\n\n' r'$\dfrac{dt_m}{dt} = t.E$' '\n\n' 'Explicit Equations' '\n\n' r'$C_1= +0.0038746 + 0.2739782t$''\n\t' r'$+ 1.574621t^2 - 0.2550041t^3$''\n\n' r'$C2= -33.43818 + 37.18972t$''\n\t' r'$- 11.58838t^2 + 1.695303t^3$''\n\t' r'$- 0.1298667t^4 + 0.005028t^5$''\n\t' r'$- 7.743.10{^-5}t^6$' '\n\n' r'$C = If\hspace{0.5} (t<=t1)\hspace{0.5} then\hspace{0.5} (C_1) \hspace{0.5}else\hspace{0.5} (C_2)$' '\n\n' r'$E = \dfrac{C}{51}$' , ha='left', wrap = True, fontsize=13, bbox=dict(facecolor='none', edgecolor='black', pad=10.0), fontweight='bold') ax2.plot(tspan, F) ax2.legend(['F'], loc='best') ax2.set_xlabel('t (min)', fontsize='medium') ax2.set_ylabel('F(t)', fontsize='medium') #ax2.set_ylim(0,10) ax2.set_xlim(0,14) ax2.set_ylim(0,1) ax2.grid()