Ondes électriques amorties dans un coaxial

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SimulationProgramme Python

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# -*- coding: utf-8 -*-
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"""
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Coaxial
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O. Thual, 21/08/2021
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"""
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#  clear all
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for iglob in list(globals().keys()):
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    if(iglob[0] != '_'):
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        exec('del {}'.format(iglob))
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# import libraries
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import numpy as np
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import matplotlib.pyplot as plt
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import os
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def inifig(xaxe=0,yaxe=0,xlab='x',ylab='y'):
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    plt.figure(2)
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    plt.axvline(xaxe)
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    plt.axhline(yaxe)
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    plt.xticks(fontsize=12)
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    plt.yticks(fontsize=12)
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    plt.xlabel(xlab,fontsize=16 )
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    plt.ylabel(ylab,fontsize=16)
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def zfi(x,le=2):
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    miss=le-len(str(x))
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    a='0'*miss+str(x)
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    return a
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def animation(name):
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    acont=np.linspace(0,L,501);
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    t=0; 
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    dt=Time/Nt
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    for i in range(0,Nt):
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        title=name+" i="+zfi(i)
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        titlefig=name
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        print(title)
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        fig=plt.figure(1,figsize=(7,4))
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        plt.xlabel(r'$x$',fontsize=16 )
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        plt.ylabel(r'Courant $I$',fontsize=16)
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        plt.title(titlefig,fontsize=16)
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        # signal
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        t=dt*i;
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        xicont=signal(acont,t)
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        plt.plot(acont,xicont,color='black',linewidth=3)
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        plt.xlim(0,L)
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        plt.ylim(ymin,ymax)
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        namei=name+zfi(i)+'.png';
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        plt.grid(color='black', axis='y', linestyle='-', linewidth=1)        
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        plt.grid(color='black', axis='x', linestyle='-', linewidth=1)        
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        plt.savefig(namei)
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        plt.show()
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        plt.close()
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    gifanim="Anim"+name+".gif"
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    #os.system('/opt/local/bin/convert -set delay '+delay+' '+name+'* '+gifanim);
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    os.system('/usr/local/bin/convert -set delay '+delay+' '+name+'* '+gifanim);
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    if Flagrm: os.system('rm '+name+'*');   
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def anistatio(name):
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    acont=np.linspace(0,L,501);
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    t=0; 
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    dt=Time/Nt
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    fig=plt.figure(1,figsize=(7,4))
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    plt.xlabel(r'$x$',fontsize=16 )
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    plt.ylabel(r'Déplacement $y$',fontsize=16)
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    plt.xlim(0,L)
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    plt.ylim(ymin,ymax)
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    titlefig=name
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    plt.title(titlefig,fontsize=16)
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    title=name
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    print(title)
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    for i in range(0,Nt+1):
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        # signal
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        t=dt*i;
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        xicont=signal(acont,t)
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        plt.plot(acont,xicont,color='black',linewidth=1)
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        namei=name+zfi(i)+'.png';
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        plt.grid(color='black', axis='y', linestyle='-', linewidth=1)        
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        plt.grid(color='black', axis='x', linestyle='-', linewidth=1)        
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    xicont=signal(acont,t)
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    plt.plot(acont,xicont,color='red',linewidth=3)
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    plt.savefig(namei)
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    plt.show()
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def spirale(name):
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    ti=np.linspace(0,Time,501);
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    I=np.exp(-la*ti)*np.sin(-omega*ti)
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    dIdt=-np.exp(-la*ti)*np.cos(-omega*ti)
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    dt=Time/Nt
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    fig=plt.figure(1,figsize=(7,7))
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    plt.xlim(-1,1)
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    plt.ylim(-1,1)
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    titlefig=name
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    plt.title(titlefig,fontsize=16)
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    title=name
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    print(title)
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    plt.grid(color='black', axis='y', linestyle='-', linewidth=1)        
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    plt.grid(color='black', axis='x', linestyle='-', linewidth=1)        
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    plt.plot(I,dIdt,color='blue',linewidth=3)
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    plt.savefig(name)
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    plt.show()
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# Main 
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F=False; T=True
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Flagrm=F; Redpoint=F
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def pulse(a,d):
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    al=0*a[a<-d]; ac=a[np.abs(a)<=d]; ar=0*a[a>d];
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    k=np.pi/d; fc=.5*(1+np.cos(k*ac));
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    f=np.concatenate((al,fc,ar))
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    return f
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def statio(a,d):
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    k=np.pi/d; fc=.5*(1+np.cos(k*ac));
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    f=np.cos
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    return f
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 # Progressive amortissement temporel
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if F: 
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    L=10; c=1; 
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    Nt=30; 
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    k=20*np.pi/L; la=0.3;
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    omega=k*c; Time=7*2*np.pi/omega
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    ymin=-1; ymax=1;
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    delay="20"
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    # signal 
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    def signal(a,t):
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        xi=np.sin(k*a-omega*t)*np.exp(-la*t)
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        return xi
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    nom="POM-amortissement-temporel"
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    print(nom)
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    animation(nom) 
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 # Spirale
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if F: 
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    L=10; c=1; 
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    Nt=30; 
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    k=20*np.pi/L; la=0.3;
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    omega=k*c; Time=7*2*np.pi/omega
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    # signal 
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    nom="POM-amortissement-en-un-point"
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    print(nom)
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    spirale(nom) 
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 # Progressive amortissement spatial gauche
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if F: 
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    L=10; c=1; 
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    Nt=20; 
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    k=20*np.pi/L; la=0.1;
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    omega=k*c; Time=2*np.pi/omega
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    ymin=-1; ymax=1;
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    delay="10"
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    # signal 
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    def signal(a,t):
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        xi=np.sin(k*a+omega*t)*np.exp(-la*(L-a))
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        return xi
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    nom="POM-amortissement-spatial-gauche"
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    print(nom)
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    animation(nom)     
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 # Progressive amortissement spatial droit
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if F: 
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    L=10; c=1; 
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    Nt=20; 
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    k=20*np.pi/L; la=0.1;
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    omega=k*c; Time=2*np.pi/omega
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    ymin=-1; ymax=1;
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    delay="10"
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    # signal 
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    def signal(a,t):
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        xi=np.sin(k*a-omega*t)*np.exp(-la*a)
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        return xi
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    nom="POM-amortissement-spatial-droit"
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    print(nom)
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    animation(nom)  
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# Application numerique
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if T:
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    Ga=1.e-10;
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    La=16.e-8;
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    ro=2.e-8;
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    g=1.e-11;
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    c=1/np.sqrt(La*Ga); print("c/1.e8=",c/1.e8)
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    mu=ro/(2*La); print("mu=",mu)
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    nu=g/(2*Ga); print("nu=",nu)    
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